| caxpy | Compute y := alpha ∗ x + y | |
| cbdsqr | compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B | |
| cchdc | compute the Cholesky decomposition of a symmetric positive definite matrix A. | |
| cchdd | downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. | |
| cchex | compute the Cholesky decomposition of a symmetric positive definite matrix A. | |
| cchud | update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. | |
| ccopy | Copy x to y | |
| cdotc | Compute the dot product of two vectors x and conjg(y). | |
| cdotu | Compute the dot product of two vectors x and y. | |
| cfftb | compute a perodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. | |
| cfftf | compute the Fourier coefficients of a perodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. | |
| cffti | initialize the array xWSAVE, which is used in both xFFTF and xFFTB. | |
| cgbbrd | reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation | |
| cgbco | compute the LU factorization and condition number of a general matrix A in banded storage. If the condition number is not needed then xGBFA is slightly faster. It is typical to follow a call to xGBCO with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A. | |
| cgbcon | estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm, | |
| cgbdi | compute the determinant of a general matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA. | |
| cgbequ | compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number | |
| cgbfa | compute the LU factorization of a matrix A in banded storage. It is typical to follow a call to xGBFA with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A. | |
| cgbmv | perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y, or y := alpha∗A’∗x + beta∗y, or y := alpha∗conjg( A’ )∗x + beta∗y | |
| cgbrfs | improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution | |
| cgbsl | solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA, and vectors b and x. | |
| cgbsv | compute the solution to a complex system of linear equations A ∗ X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices | |
| cgbsvx | use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, | |
| cgbtf2 | compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges | |
| cgbtrf | compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges | |
| cgbtrs | solve a system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B with a general band matrix A using the LU factorization computed by CGBTRF | |
| cgebak | form the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by CGEBAL | |
| cgebal | balance a general complex matrix A | |
| cgebd2 | reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation | |
| cgebrd | reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation | |
| cgeco | compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then xGEFA is slightly faster. It is typical to follow a call to xGECO with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant and inverse of A. | |
| cgecon | estimate the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by CGETRF | |
| cgedi | compute the determinant and inverse of a general matrix A, which has been LU-factored by xGECO or xGEFA. | |
| cgeequ | compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number | |
| cgees | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z | |
| cgeesx | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z | |
| cgeev | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors | |
| cgeevx | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors | |
| cgefa | compute the LU factorization of a general matrix A. It is typical to follow a call to xGEFA with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant of A. | |
| cgegs | compute for a pair of N-by-N complex nonsymmetric matrices A, | |
| cgegv | compute for a pair of N-by-N complex nonsymmetric matrices A and B, the generalized eigenvalues (alpha, beta), and optionally, | |
| cgehd2 | reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation | |
| cgehrd | reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation | |
| cgelq2 | compute an LQ factorization of a complex m by n matrix A | |
| cgelqf | compute an LQ factorization of a complex M-by-N matrix A | |
| cgels | solve overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A | |
| cgelss | compute the minimum norm solution to a complex linear least squares problem | |
| cgelsx | compute the minimum-norm solution to a complex linear least squares problem | |
| cgemm | perform one of the matrix-matrix operations C := alpha∗op( A )∗op( B ) + beta∗C | |
| cgemv | perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y, or y := alpha∗A’∗x + beta∗y, or y := alpha∗conjg( A’ )∗x + beta∗y | |
| cgeql2 | compute a QL factorization of a complex m by n matrix A | |
| cgeqlf | compute a QL factorization of a complex M-by-N matrix A | |
| cgeqpf | compute a QR factorization with column pivoting of a complex M-by-N matrix A | |
| cgeqr2 | compute a QR factorization of a complex m by n matrix A | |
| cgeqrf | compute a QR factorization of a complex M-by-N matrix A | |
| cgerc | perform the rank 1 operation A := alpha∗x∗conjg( y’ ) + A | |
| cgerfs | improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution | |
| cgerq2 | compute an RQ factorization of a complex m by n matrix A | |
| cgerqf | compute an RQ factorization of a complex M-by-N matrix A | |
| cgeru | perform the rank 1 operation A := alpha∗x∗y’ + A | |
| cgesl | solve the linear system Ax = b for a general matrix A, which has been LU- factored by xGECO or xGEFA, and vectors b and x. | |
| cgesv | compute the solution to a complex system of linear equations A ∗ X = B, | |
| cgesvd | compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors | |
| cgesvx | use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B, | |
| cgetf2 | compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges | |
| cgetrf | compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges | |
| cgetri | compute the inverse of a matrix using the LU factorization computed by CGETRF | |
| cgetrs | solve a system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B with a general N-by-N matrix A using the LU factorization computed by CGETRF | |
| cggbak | form the right or left eigenvectors of a complex generalized eigenvalue problem A∗x = lambda∗B∗x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by CGGBAL | |
| cggbal | balance a pair of general complex matrices (A,B) | |
| cggglm | solve a general Gauss-Markov linear model (GLM) problem | |
| cgghrd | reduce a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular | |
| cgglse | solve the linear equality-constrained least squares (LSE) problem | |
| cggqrf | compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B | |
| cggrqf | compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B | |
| cggsvd | compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B | |
| cggsvp | compute unitary matrices U, V and Q such that N-K-L K L U’∗A∗Q = K ( 0 A12 A13 ) if M-K-L >= 0 | |
| cgtcon | estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF | |
| cgtrfs | improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution | |
| cgtsl | solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x. | |
| cgtsv | solve the equation A∗X = B, | |
| cgtsvx | use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, | |
| cgttrf | compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges | |
| cgttrs | solve one of the systems of equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, | |
| chbev | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A | |
| chbevd | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A | |
| chbevx | compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A | |
| chbgst | reduce a complex Hermitian-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y, | |
| chbgv | compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A∗x=(lambda)∗B∗x | |
| chbmv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y | |
| chbtrd | reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation | |
| checon | estimate the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by CHETRF | |
| cheev | compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A | |
| cheevd | compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A | |
| cheevx | compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A | |
| chegs2 | reduce a complex Hermitian-definite generalized eigenproblem to standard form | |
| chegst | reduce a complex Hermitian-definite generalized eigenproblem to standard form | |
| chegv | compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x | |
| chemm | perform one of the matrix-matrix operations C := alpha∗A∗B + beta∗C or C := alpha∗B∗A + beta∗C | |
| chemv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y | |
| cher | perform the hermitian rank 1 operation A := alpha∗x∗conjg( x’ ) + A | |
| cher2 | perform the hermitian rank 2 operation A := alpha∗x∗conjg( y’ ) + conjg( alpha )∗y∗conjg( x’ ) + A | |
| cher2k | perform one of the Hermitian rank 2k operations C := alpha∗A∗conjg( B’ ) + conjg( alpha )∗B∗conjg( A’ ) + beta∗C or C := alpha∗conjg( A’ )∗B + conjg( alpha )∗conjg( B’ )∗A + beta∗C | |
| cherfs | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution | |
| cherk | perform one of the Hermitian rank k operations C := alpha∗A∗conjg( A’ ) + beta∗C or C := alpha∗conjg( A’ )∗A + beta∗C | |
| chesv | compute the solution to a complex system of linear equations A ∗ X = B, | |
| chesvx | use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B, | |
| chetd2 | reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation | |
| chetf2 | compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method | |
| chetrd | reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation | |
| chetrf | compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method | |
| chetri | compute the inverse of a complex Hermitian indefinite matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by CHETRF | |
| chetrs | solve a system of linear equations A∗X = B with a complex Hermitian matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by CHETRF | |
| chgeqz | implement a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation det( A - w(i) B ) = 0 If JOB=’S’, then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both upper triangular) by applying one unitary tranformation (usually called Q) on the left and another (usually called Z) on the right | |
| chico | compute the UDU factorization and condition number of a Hermitian matrix A. If the condition number is not needed then xHIFA is slightly faster. It is typical to follow a call to xHICO with a call to xHISL to solve Ax = b or to xHIDI to compute the determinant, inverse, and inertia of A. | |
| chidi | compute the determinant, inertia, and inverse of a Hermitian matrix A, which has been UDU-factored by xHICO or xHIFA. | |
| chifa | compute the UDU factorization of a Hermitian matrix A. It is typical to follow a call to xHIFA with a call to xHISL to solve Ax = b or to xHIDI to compute the determinant, inverse, and inertia of A. | |
| chisl | solve the linear system Ax = b for a Hermitian matrix A, which has been UDU-factored by xHICO or xHIFA, and vectors b and x. | |
| chpco | compute the UDU factorization and condition number of a Hermitian matrix A in packed storage. If the condition number is not needed then xHPFA is slightly faster. It is typical to follow a call to xHPCO with a call to xHPSL to solve Ax = b or to xHPDI to compute the determinant, inverse, and inertia of A. | |
| chpcon | estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by CHPTRF | |
| chpdi | compute the determinant, inertia, and inverse of a Hermitian matrix A in packed storage, which has been UDU-factored by xHPCO or xHPFA. | |
| chpev | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage | |
| chpevd | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage | |
| chpevx | compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage | |
| chpfa | compute the UDU factorization of a Hermitian matrix A in packed storage. It is typical to follow a call to xHPFA with a call to xHPSL to solve Ax = b or to xHPDI to compute the determinant, inverse, and inertia of A. | |
| chpgst | reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage | |
| chpgv | compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x | |
| chpmv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y | |
| chpr | perform the hermitian rank 1 operation A := alpha∗x∗conjg( x’ ) + A | |
| chpr2 | perform the Hermitian rank 2 operation A := alpha∗x∗conjg( y’ ) + conjg( alpha )∗y∗conjg( x’ ) + A | |
| chprfs | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution | |
| chpsl | solve the linear system Ax = b for a Hermitian matrix A in packed storage, which has been UDU-factored by xHPCO or xHPFA, and vectors b and x. | |
| chpsv | compute the solution to a complex system of linear equations A ∗ X = B, | |
| chpsvx | use the diagonal pivoting factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices | |
| chptrd | reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation | |
| chptrf | compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method | |
| chptri | compute the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by CHPTRF | |
| chptrs | solve a system of linear equations A∗X = B with a complex Hermitian matrix A stored in packed format using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by CHPTRF | |
| chsein | use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H | |
| chseqr | compute the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z∗∗H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors | |
| clabrd | reduce the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal form by a unitary transformation Q’ ∗ A ∗ P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A | |
| clacgv | conjugate a complex vector of length N | |
| clacon | estimate the 1-norm of a square, complex matrix A | |
| clacpy | copie all or part of a two-dimensional matrix A to another matrix B | |
| clacrm | perform a very simple matrix-matrix multiplication | |
| clacrt | applie a plane rotation, where the cos and sin (C and S) are complex and the vectors CX and CY are complex | |
| cladiv | := X / Y, where X and Y are complex | |
| claed0 | the divide and conquer method, CLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix | |
| claed7 | compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix | |
| claed8 | merge the two sets of eigenvalues together into a single sorted set | |
| claein | use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H | |
| claesy | compute the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value | |
| claev2 | compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ] | |
| clags2 | compute 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U’∗A∗Q = U’∗( A1 A2 )∗Q = ( x 0 ) ( 0 A3 ) ( x x ) and V’∗B∗Q = V’∗( B1 B2 )∗Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U’∗A∗Q = U’∗( A1 0 )∗Q = ( x x ) ( A2 A3 ) ( 0 x ) and V’∗B∗Q = V’∗( B1 0 )∗Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ), | |
| clagtm | perform a matrix-vector product of the form B := alpha ∗ A ∗ X + beta ∗ B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1 | |
| clahef | compute a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method | |
| clahqr | i an auxiliary routine called by CHSEQR to update the eigenvalues and Schur decomposition already computed by CHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI | |
| clahrd | reduce the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero | |
| claic1 | applie one step of incremental condition estimation in its simplest version | |
| clangb | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals | |
| clange | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex matrix A | |
| clangt | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex tridiagonal matrix A | |
| clanhb | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n hermitian band matrix A, with k super-diagonals | |
| clanhe | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A | |
| clanhp | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A, supplied in packed form | |
| clanhs | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A | |
| clanht | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix A | |
| clansb | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals | |
| clansp | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form | |
| clansy | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A | |
| clantb | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals | |
| clantp | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form | |
| clantr | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A | |
| clapll | two column vectors X and Y, let A = ( X Y ) | |
| clapmt | rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N | |
| claqgb | equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C | |
| claqge | equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C | |
| claqhb | equilibrate a symmetric band matrix A using the scaling factors in the vector S | |
| claqhe | equilibrate a Hermitian matrix A using the scaling factors in the vector S | |
| claqhp | equilibrate a Hermitian matrix A using the scaling factors in the vector S | |
| claqsb | equilibrate a symmetric band matrix A using the scaling factors in the vector S | |
| claqsp | equilibrate a symmetric matrix A using the scaling factors in the vector S | |
| claqsy | equilibrate a symmetric matrix A using the scaling factors in the vector S | |
| clar2v | applie a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices, | |
| clarf | applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right | |
| clarfb | applie a complex block reflector H or its transpose H’ to a complex M-by-N matrix C, from either the left or the right | |
| clarfg | generate a complex elementary reflector H of order n, such that H’ ∗ ( alpha ) = ( beta ), H’ ∗ H = I | |
| clarft | form the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors | |
| clarfx | applie a complex elementary reflector H to a complex m by n matrix C, from either the left or the right | |
| clargv | generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y | |
| clarnv | return a vector of n random complex numbers from a uniform or normal distribution | |
| clartg | generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ] | |
| clartv | applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y | |
| clascl | multiply the M by N complex matrix A by the real scalar CTO/CFROM | |
| claset | initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals | |
| clasr | perform the transformation A := P∗A, when SIDE = ’L’ or ’l’ ( Left-hand side ) A := A∗P’, when SIDE = ’R’ or ’r’ ( Right-hand side ) where A is an m by n complex matrix and P is an orthogonal matrix, | |
| classq | return the values scl and ssq such that ( scl∗∗2 )∗ssq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq, | |
| claswp | perform a series of row interchanges on the matrix A | |
| clasyf | compute a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method | |
| clatbs | solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b, | |
| clatps | solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b, | |
| clatrd | reduce NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by a unitary similarity transformation Q’ ∗ A ∗ Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A | |
| clatrs | solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b, | |
| clatzm | applie a Householder matrix generated by CTZRQF to a matrix | |
| clauu2 | compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A | |
| clauum | compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A | |
| cosqb | synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. | |
| cosqf | compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. | |
| cosqi | initialize the array xWSAVE, which is used in both xCOSQF and xCOSQB. | |
| cost | compute the discrete Fourier cosine transform of an even sequence. The xCOST transforms are unnormalized inverses of themselves, so a call of xCOST followed by another call of xCOST will multiply the input sequence by 2 ∗ (N - 1). The VxCOST transforms are normalized, so a call of VxCOST followed by a call of VxCOST will return the original sequence. | |
| costi | initialize the array xWSAVE, which is used in xCOST. | |
| cpbco | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in banded storage. If the condition number is not needed then xPBFA is slightly faster. It is typical to follow a call to xPBCO with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A. | |
| cpbcon | estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPBTRF | |
| cpbdi | compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA. | |
| cpbequ | compute row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm) | |
| cpbfa | compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to xPBFA with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A. | |
| cpbrfs | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution | |
| cpbsl | section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA, and vectors b and x. | |
| cpbstf | compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A | |
| cpbsv | compute the solution to a complex system of linear equations A ∗ X = B, | |
| cpbsvx | use the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B, | |
| cpbtf2 | compute the Cholesky factorization of a complex Hermitian positive definite band matrix A | |
| cpbtrf | compute the Cholesky factorization of a complex Hermitian positive definite band matrix A | |
| cpbtrs | solve a system of linear equations A∗X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPBTRF | |
| cpoco | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A. If the condition number is not needed then xPOFA is slightly faster. It is typical to follow a call to xPOCO with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A. | |
| cpocon | estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPOTRF | |
| cpodi | compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO, xPOFA, or xQRDC. | |
| cpoequ | compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm) | |
| cpofa | compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to xPOFA with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A. | |
| cporfs | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, | |
| cposl | solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO or xPOFA, and vectors b and x. | |
| cposv | compute the solution to a complex system of linear equations A ∗ X = B, | |
| cposvx | use the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B, | |
| cpotf2 | compute the Cholesky factorization of a complex Hermitian positive definite matrix A | |
| cpotrf | compute the Cholesky factorization of a complex Hermitian positive definite matrix A | |
| cpotri | compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPOTRF | |
| cpotrs | solve a system of linear equations A∗X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPOTRF | |
| cppco | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in packed storage. If the condition number is not needed then xPPFA is slightly faster. It is typical to follow a call to xPPCO with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A. | |
| cppcon | estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPPTRF | |
| cppdi | compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA. | |
| cppequ | compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm) | |
| cppfa | compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to xPPFA with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A. | |
| cpprfs | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution | |
| cppsl | solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA, and vectors b and x. | |
| cppsv | compute the solution to a complex system of linear equations A ∗ X = B, | |
| cppsvx | use the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B, | |
| cpptrf | compute the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format | |
| cpptri | compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPPTRF | |
| cpptrs | solve a system of linear equations A∗X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by CPPTRF | |
| cptcon | compute the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L∗D∗L∗∗H or A = U∗∗H∗D∗U computed by CPTTRF | |
| cpteqr | compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF and then calling CBDSQR to compute the singular values of the bidiagonal factor | |
| cptrfs | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution | |
| cptsl | solve the linear system Ax = b for a symmetric positive definite tridiagonal matrix A and vectors b and x. | |
| cptsv | compute the solution to a complex system of linear equations A∗X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices | |
| cptsvx | use the factorization A = L∗D∗L∗∗H to compute the solution to a complex system of linear equations A∗X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices | |
| cpttrf | compute the factorization of a complex Hermitian positive definite tridiagonal matrix A | |
| cpttrs | solve a system of linear equations A ∗ X = B with a Hermitian positive definite tridiagonal matrix A using the factorization A = U∗∗H∗D∗U or A = L∗D∗L∗∗H computed by CPTTRF | |
| cqrdc | compute the QR factorization of a general matrix A. It is typical to follow a call to xQRDC with a call to xQRSL to solve Ax = b or to xPODI to compute the determinant of A. | |
| cqrsl | solve the linear system Ax = b for a general matrix A, which has been QR- factored by xQRDC, and vectors b and x. | |
| crot | apply a plane rotation, where the cos (C) is real and the sin (S) is complex, and the vectors CX and CY are complex | |
| crotg | Construct a Given’s plane rotation | |
| cscal | Compute y := alpha ∗ y | |
| csico | compute the UDU factorization and condition number of a symmetric matrix A. If the condition number is not needed then xSIFA is slightly faster. It is typical to follow a call to xSICO with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A. | |
| csidi | compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA. | |
| csifa | compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to xSIFA with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A. | |
| csisl | solve the linear system Ax = b for a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA, and vectors b and x. | |
| cspco | compute the UDU factorization and condition number of a symmetric matrix A in packed storage. If the condition number is not needed then xSPFA is slightly faster. It is typical to follow a call to xSPCO with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A. | |
| cspcon | estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by CSPTRF | |
| cspdi | compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA. | |
| cspfa | compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to xSPFA with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A. | |
| cspmv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y, | |
| cspr | perform the symmetric rank 1 operation A := alpha∗x∗conjg( x’ ) + A, | |
| csprfs | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution | |
| cspsl | solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA, and vectors b and x. | |
| cspsv | compute the solution to a complex system of linear equations A ∗ X = B, | |
| cspsvx | use the diagonal pivoting factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T to compute the solution to a complex system of linear equations A ∗ X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices | |
| csptrf | compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method | |
| csptri | compute the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by CSPTRF | |
| csptrs | solve a system of linear equations A∗X = B with a complex symmetric matrix A stored in packed format using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by CSPTRF | |
| csrot | Apply a Given’s rotation constructed by SROTG. | |
| csrscl | multiply an n-element complex vector x by the real scalar 1/a | |
| csscal | Compute y := alpha ∗ y | |
| cstedc | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method | |
| cstein | compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration | |
| csteqr | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method | |
| csvdc | compute the singular value decomposition of a general matrix A. | |
| cswap | Exchange vectors x and y. | |
| csycon | estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by CSYTRF | |
| csymm | perform one of the matrix-matrix operations C := alpha∗A∗B + beta∗C or C := alpha∗B∗A + beta∗C | |
| csymv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y, | |
| csyr | perform the symmetric rank 1 operation A := alpha∗x∗( x’ ) + A, | |
| csyr2k | perform one of the symmetric rank 2k operations C := alpha∗A∗B’ + alpha∗B∗A’ + beta∗C or C := alpha∗A’∗B + alpha∗B’∗A + beta∗C | |
| csyrfs | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution | |
| csyrk | perform one of the symmetric rank k operations C := alpha∗A∗A’ + beta∗C or C := alpha∗A’∗A + beta∗C | |
| csysv | compute the solution to a complex system of linear equations A ∗ X = B, | |
| csysvx | use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B, | |
| csytf2 | compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method | |
| csytrf | compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method | |
| csytri | compute the inverse of a complex symmetric indefinite matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by CSYTRF | |
| csytrs | solve a system of linear equations A∗X = B with a complex symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by CSYTRF | |
| ctbcon | estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm | |
| ctbmv | perform one of the matrix-vector operations x := A∗x, or x := A’∗x, or x := conjg( A’ )∗x | |
| ctbrfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix | |
| ctbsv | solve one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b | |
| ctbtrs | solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, | |
| ctgevc | compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B) | |
| ctgsja | compute the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B | |
| ctpcon | estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm | |
| ctpmv | perform one of the matrix-vector operations x := A∗x, or x := A’∗x, or x := conjg( A’ )∗x | |
| ctprfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix | |
| ctpsv | solve one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b | |
| ctptri | compute the inverse of a complex upper or lower triangular matrix A stored in packed format | |
| ctptrs | solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, | |
| ctrco | estimate the condition number of a triangular matrix A. It is typical to follow a call to xTRCO with a call to xTRSL to solve Ax = b or to xTRDI to compute the determinant and inverse of A. | |
| ctrcon | estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm | |
| ctrdi | compute the determinant and inverse of a triangular matrix A. | |
| ctrevc | compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T | |
| ctrexc | reorder the Schur factorization of a complex matrix A = Q∗T∗Q∗∗H, so that the diagonal element of T with row index IFST is moved to row ILST | |
| ctrmm | perform one of the matrix-matrix operations B := alpha∗op( A )∗B, or B := alpha∗B∗op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A’ or op( A ) = conjg( A’ ) | |
| ctrmv | perform one of the matrix-vector operations x := A∗x, or x := A’∗x, or x := conjg( A’ )∗x | |
| ctrrfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix | |
| ctrsen | reorder the Schur factorization of a complex matrix A = Q∗T∗Q∗∗H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace | |
| ctrsl | solve the linear system Ax = b for a triangular matrix A and vectors b and x. | |
| ctrsm | solve one of the matrix equations op( A )∗X = alpha∗B, or X∗op( A ) = alpha∗B | |
| ctrsna | estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q∗T∗Q∗∗H with Q unitary) | |
| ctrsv | solve one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b | |
| ctrsyl | solve the complex Sylvester matrix equation | |
| ctrti2 | compute the inverse of a complex upper or lower triangular matrix | |
| ctrtri | compute the inverse of a complex upper or lower triangular matrix A | |
| ctrtrs | solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, | |
| ctzrqf | reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations | |
| cung2l | generate an m by n complex matrix Q with orthonormal columns, | |
| cung2r | generate an m by n complex matrix Q with orthonormal columns, | |
| cungbr | generate one of the complex unitary matrices Q or P∗∗H determined by CGEBRD when reducing a complex matrix A to bidiagonal form | |
| cunghr | generate a complex unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by CGEHRD | |
| cungl2 | generate an m-by-n complex matrix Q with orthonormal rows, | |
| cunglq | generate an M-by-N complex matrix Q with orthonormal rows, | |
| cungql | generate an M-by-N complex matrix Q with orthonormal columns, | |
| cungqr | generate an M-by-N complex matrix Q with orthonormal columns, | |
| cungr2 | generate an m by n complex matrix Q with orthonormal rows, | |
| cungrq | generate an M-by-N complex matrix Q with orthonormal rows, | |
| cungtr | generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by CHETRD | |
| cunm2l | overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’, | |
| cunm2r | overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’, | |
| cunmbr | VECT = ’Q’, CUNMBR overwrites the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| cunmhr | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| cunml2 | overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’, | |
| cunmlq | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| cunmql | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| cunmqr | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| cunmr2 | overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’, | |
| cunmrq | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| cunmtr | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| cupgtr | generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by CHPTRD using packed storage | |
| cupmtr | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| dasum | Return the sum of the absolute values of a vector x. | |
| daxpy | Compute y := alpha ∗ x + y | |
| dbdsqr | compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B | |
| dchdc | compute the Cholesky decomposition of a symmetric positive definite matrix A. | |
| dchdd | downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. | |
| dchex | compute the Cholesky decomposition of a symmetric positive definite matrix A. | |
| dchud | update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. | |
| dcopy | Copy x to y | |
| dcosqb | synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. | |
| dcosqf | compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. | |
| dcosqi | initialize the array xWSAVE, which is used in both xCOSQF and xCOSQB. | |
| dcost | compute the discrete Fourier cosine transform of an even sequence. The xCOST transforms are unnormalized inverses of themselves, so a call of xCOST followed by another call of xCOST will multiply the input sequence by 2 ∗ (N - 1). The VxCOST transforms are normalized, so a call of VxCOST followed by a call of VxCOST will return the original sequence. | |
| dcosti | initialize the array xWSAVE, which is used in xCOST. | |
| ddisna | compute the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general m-by-n matrix | |
| ddot | Compute the dot product of two vectors x and y. | |
| dfftb | compute a perodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. | |
| dfftf | compute the Fourier coefficients of a perodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. | |
| dffti | initialize the array xWSAVE, which is used in both xFFTF and xFFTB. | |
| dgbbrd | reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation | |
| dgbco | compute the LU factorization and condition number of a general matrix A in banded storage. If the condition number is not needed then xGBFA is slightly faster. It is typical to follow a call to xGBCO with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A. | |
| dgbcon | estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm, | |
| dgbdi | compute the determinant of a general matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA. | |
| dgbequ | compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number | |
| dgbfa | compute the LU factorization of a matrix A in banded storage. It is typical to follow a call to xGBFA with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A. | |
| dgbmv | perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y or y := alpha∗A’∗x + beta∗y | |
| dgbrfs | improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution | |
| dgbsl | solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA, and vectors b and x. | |
| dgbsv | compute the solution to a real system of linear equations A ∗ X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices | |
| dgbsvx | use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, | |
| dgbtf2 | compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges | |
| dgbtrf | compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges | |
| dgbtrs | solve a system of linear equations A ∗ X = B or A’ ∗ X = B with a general band matrix A using the LU factorization computed by DGBTRF | |
| dgebak | form the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by DGEBAL | |
| dgebal | balance a general real matrix A | |
| dgebd2 | reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation | |
| dgebrd | reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation | |
| dgeco | compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then xGEFA is slightly faster. It is typical to follow a call to xGECO with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant and inverse of A. | |
| dgecon | estimate the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGETRF | |
| dgedi | compute the determinant and inverse of a general matrix A, which has been LU-factored by xGECO or xGEFA. | |
| dgeequ | compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number | |
| dgees | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z | |
| dgeesx | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z | |
| dgeev | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors | |
| dgeevx | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors | |
| dgefa | compute the LU factorization of a general matrix A. It is typical to follow a call to xGEFA with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant of A. | |
| dgegs | compute for a pair of N-by-N real nonsymmetric matrices A, B | |
| dgegv | compute for a pair of n-by-n real nonsymmetric matrices A and B, the generalized eigenvalues (alphar +/- alphai∗i, beta), and optionally, the left and/or right generalized eigenvectors (VL and VR) | |
| dgehd2 | reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation | |
| dgehrd | reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation | |
| dgelq2 | compute an LQ factorization of a real m by n matrix A | |
| dgelqf | compute an LQ factorization of a real M-by-N matrix A | |
| dgels | solve overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A | |
| dgelss | compute the minimum norm solution to a real linear least squares problem | |
| dgelsx | compute the minimum-norm solution to a real linear least squares problem | |
| dgemm | perform one of the matrix-matrix operations C := alpha∗op( A )∗op( B ) + beta∗C | |
| dgemv | perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y or y := alpha∗A’∗x + beta∗y | |
| dgeql2 | compute a QL factorization of a real m by n matrix A | |
| dgeqlf | compute a QL factorization of a real M-by-N matrix A | |
| dgeqpf | compute a QR factorization with column pivoting of a real M-by-N matrix A | |
| dgeqr2 | compute a QR factorization of a real m by n matrix A | |
| dgeqrf | compute a QR factorization of a real M-by-N matrix A | |
| dger | perform the rank 1 operation A := alpha∗x∗y’ + A | |
| dgerfs | improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution | |
| dgerq2 | compute an RQ factorization of a real m by n matrix A | |
| dgerqf | compute an RQ factorization of a real M-by-N matrix A | |
| dgesl | solve the linear system Ax = b for a general matrix A, which has been LU- factored by xGECO or xGEFA, and vectors b and x. | |
| dgesv | compute the solution to a real system of linear equations A ∗ X = B, | |
| dgesvd | compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors | |
| dgesvx | use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B, | |
| dgetf2 | compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges | |
| dgetrf | compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges | |
| dgetri | compute the inverse of a matrix using the LU factorization computed by DGETRF | |
| dgetrs | solve a system of linear equations A ∗ X = B or A’ ∗ X = B with a general N-by-N matrix A using the LU factorization computed by DGETRF | |
| dggbak | form the right or left eigenvectors of a real generalized eigenvalue problem A∗x = lambda∗B∗x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by DGGBAL | |
| dggbal | balance a pair of general real matrices (A,B) | |
| dggglm | solve a general Gauss-Markov linear model (GLM) problem | |
| dgghrd | reduce a pair of real matrices (A,B) to generalized upper Hessenberg form using orthogonal transformations, where A is a general matrix and B is upper triangular | |
| dgglse | solve the linear equality-constrained least squares (LSE) problem | |
| dggqrf | compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B | |
| dggrqf | compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B | |
| dggsvd | compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B | |
| dggsvp | compute orthogonal matrices U, V and Q such that N-K-L K L U’∗A∗Q = K ( 0 A12 A13 ) if M-K-L >= 0 | |
| dgtcon | estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by DGTTRF | |
| dgtrfs | improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution | |
| dgtsl | solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x. | |
| dgtsv | solve the equation A∗X = B, | |
| dgtsvx | use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B or A∗∗T ∗ X = B, | |
| dgttrf | compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges | |
| dgttrs | solve one of the systems of equations A∗X = B or A’∗X = B, | |
| dhgeqz | implement a single-/double-shift version of the QZ method for finding the generalized eigenvalues w(j)=(ALPHAR(j) + i∗ALPHAI(j))/BETAR(j) of the equation det( A - w(i) B ) = 0 In addition, the pair A,B may be reduced to generalized Schur form | |
| dhsein | use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H | |
| dhseqr | compute the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z∗∗T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors | |
| dlabad | take as input the values computed by SLAMCH for underflow and overflow, and returns the square root of each of these values if the log of LARGE is sufficiently large | |
| dlabrd | reduce the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q’ ∗ A ∗ P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A | |
| dlacon | estimate the 1-norm of a square, real matrix A | |
| dlacpy | copie all or part of a two-dimensional matrix A to another matrix B | |
| dladiv | perform complex division in real arithmetic a + i∗b p + i∗q = --------- c + i∗d The algorithm is due to Robert L | |
| dlae2 | compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ] | |
| dlaebz | contain the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w | |
| dlaed0 | compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method | |
| dlaed1 | compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix | |
| dlaed2 | merge the two sets of eigenvalues together into a single sorted set | |
| dlaed3 | find the roots of the secular equation, as defined by the values in D, W, and RHO, between KSTART and KSTOP | |
| dlaed4 | subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0 | |
| dlaed5 | subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j | |
| dlaed6 | compute the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true | |
| dlaed7 | compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix | |
| dlaed8 | merge the two sets of eigenvalues together into a single sorted set | |
| dlaed9 | find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP | |
| dlaeda | compute the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem | |
| dlaein | use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H | |
| dlaev2 | compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ] | |
| dlaexc | swap adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation | |
| dlag2 | compute the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow | |
| dlags2 | compute 2-by-2 orthogonal matrices U, V and Q, such that if ( UPPER ) then U’∗A∗Q = U’∗( A1 A2 )∗Q = ( x 0 ) ( 0 A3 ) ( x x ) and V’∗B∗Q = V’∗( B1 B2 )∗Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U’∗A∗Q = U’∗( A1 0 )∗Q = ( x x ) ( A2 A3 ) ( 0 x ) and V’∗B∗Q = V’∗( B1 0 )∗Q = ( x x ) ( B2 B3 ) ( 0 x ) The rows of the transformed A and B are parallel, where U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) ( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ ) Z’ denotes the transpose of Z | |
| dlagtf | factorize the matrix (T - lambda∗I), where T is an n by n tridiagonal matrix and lambda is a scalar, as T - lambda∗I = PLU, | |
| dlagtm | perform a matrix-vector product of the form B := alpha ∗ A ∗ X + beta ∗ B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1 | |
| dlagts | may be used to solve one of the systems of equations (T - lambda∗I)∗x = y or (T - lambda∗I)’∗x = y, | |
| dlahqr | i an auxiliary routine called by DHSEQR to update the eigenvalues and Schur decomposition already computed by DHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI | |
| dlahrd | reduce the first NB columns of a real general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero | |
| dlaic1 | applie one step of incremental condition estimation in its simplest version | |
| dlaln2 | solve a system of the form (ca A - w D ) X = s B or (ca A’ - w D) X = s B with possible scaling ("s") and perturbation of A | |
| dlamch | determine double precision machine parameters | |
| dlamrg | will create a permutation list which will merge the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascending order | |
| dlangb | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals | |
| dlange | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A | |
| dlangt | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A | |
| dlanhs | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A | |
| dlansb | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals | |
| dlansp | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form | |
| dlanst | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A | |
| dlansy | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A | |
| dlantb | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals | |
| dlantp | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form | |
| dlantr | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A | |
| dlanv2 | compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form | |
| dlapll | two column vectors X and Y, let A = ( X Y ) | |
| dlapmt | rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N | |
| dlapy2 | return sqrt(x∗∗2+y∗∗2), taking care not to cause unnecessary overflow | |
| dlapy3 | return sqrt(x∗∗2+y∗∗2+z∗∗2), taking care not to cause unnecessary overflow | |
| dlaqgb | equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C | |
| dlaqge | equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C | |
| dlaqsb | equilibrate a symmetric band matrix A using the scaling factors in the vector S | |
| dlaqsp | equilibrate a symmetric matrix A using the scaling factors in the vector S | |
| dlaqsy | equilibrate a symmetric matrix A using the scaling factors in the vector S | |
| dlaqtr | solve the real quasi-triangular system op(T)∗p = scale∗c, if LREAL = .TRUE | |
| dlar2v | applie a vector of real plane rotations from both sides to a sequence of 2-by-2 real symmetric matrices, defined by the elements of the vectors x, y and z | |
| dlarf | applie a real elementary reflector H to a real m by n matrix C, from either the left or the right | |
| dlarfb | applie a real block reflector H or its transpose H’ to a real m by n matrix C, from either the left or the right | |
| dlarfg | generate a real elementary reflector H of order n, such that H ∗ ( alpha ) = ( beta ), H’ ∗ H = I | |
| dlarft | form the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors | |
| dlarfx | applie a real elementary reflector H to a real m by n matrix C, from either the left or the right | |
| dlargv | generate a vector of real plane rotations, determined by elements of the real vectors x and y | |
| dlarnv | return a vector of n random real numbers from a uniform or normal distribution | |
| dlartg | generate a plane rotation so that [ CS SN ] | |
| dlartv | applie a vector of real plane rotations to elements of the real vectors x and y | |
| dlaruv | return a vector of n random real numbers from a uniform (0,1) | |
| dlas2 | compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ] | |
| dlascl | multiply the M by N real matrix A by the real scalar CTO/CFROM | |
| dlaset | initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals | |
| dlasq1 | DLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E | |
| dlasq2 | DLASQ2 computes the singular values of a real N-by-N unreduced bidiagonal matrix with squared diagonal elements in Q and squared off-diagonal elements in E | |
| dlasq3 | DLASQ3 is the workhorse of the whole bidiagonal SVD algorithm | |
| dlasq4 | DLASQ4 estimates TAU, the smallest eigenvalue of a matrix | |
| dlasr | perform the transformation A := P∗A, when SIDE = ’L’ or ’l’ ( Left-hand side ) A := A∗P’, when SIDE = ’R’ or ’r’ ( Right-hand side ) where A is an m by n real matrix and P is an orthogonal matrix, | |
| dlasrt | the numbers in D in increasing order (if ID = ’I’) or in decreasing order (if ID = ’D’ ) | |
| dlassq | return the values scl and smsq such that ( scl∗∗2 )∗smsq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq, | |
| dlasv2 | compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ] | |
| dlaswp | perform a series of row interchanges on the matrix A | |
| dlasy2 | solve for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in op(TL)∗X + ISGN∗X∗op(TR) = SCALE∗B, | |
| dlasyf | compute a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method | |
| dlatbs | solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow, where A is an upper or lower triangular band matrix | |
| dlatps | solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form | |
| dlatrd | reduce NB rows and columns of a real symmetric matrix A to symmetric tridiagonal form by an orthogonal similarity transformation Q’ ∗ A ∗ Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A | |
| dlatrs | solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow | |
| dlatzm | applie a Householder matrix generated by DTZRQF to a matrix | |
| dlauu2 | compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A | |
| dlauum | compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A | |
| dnrm2 | Return the Euclidian norm of a vector. | |
| dopgtr | generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by DSPTRD using packed storage | |
| dopmtr | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| dorg2l | generate an m by n real matrix Q with orthonormal columns, | |
| dorg2r | generate an m by n real matrix Q with orthonormal columns, | |
| dorgbr | generate one of the real orthogonal matrices Q or P∗∗T determined by DGEBRD when reducing a real matrix A to bidiagonal form | |
| dorghr | generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD | |
| dorgl2 | generate an m by n real matrix Q with orthonormal rows, | |
| dorglq | generate an M-by-N real matrix Q with orthonormal rows, | |
| dorgql | generate an M-by-N real matrix Q with orthonormal columns, | |
| dorgqr | generate an M-by-N real matrix Q with orthonormal columns, | |
| dorgr2 | generate an m by n real matrix Q with orthonormal rows, | |
| dorgrq | generate an M-by-N real matrix Q with orthonormal rows, | |
| dorgtr | generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by DSYTRD | |
| dorm2l | overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’, | |
| dorm2r | overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’, | |
| dormbr | VECT = ’Q’, DORMBR overwrites the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| dormhr | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| dorml2 | overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’, | |
| dormlq | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| dormql | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| dormqr | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| dormr2 | overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’, | |
| dormrq | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| dormtr | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| dpbco | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in banded storage. If the condition number is not needed then xPBFA is slightly faster. It is typical to follow a call to xPBCO with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A. | |
| dpbcon | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPBTRF | |
| dpbdi | compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA. | |
| dpbequ | compute row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number (with respect to the two-norm) | |
| dpbfa | compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to xPBFA with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A. | |
| dpbrfs | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution | |
| dpbsl | section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA, and vectors b and x. | |
| dpbstf | compute a split Cholesky factorization of a real symmetric positive definite band matrix A | |
| dpbsv | compute the solution to a real system of linear equations A ∗ X = B, | |
| dpbsvx | use the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B, | |
| dpbtf2 | compute the Cholesky factorization of a real symmetric positive definite band matrix A | |
| dpbtrf | compute the Cholesky factorization of a real symmetric positive definite band matrix A | |
| dpbtrs | solve a system of linear equations A∗X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPBTRF | |
| dpoco | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A. If the condition number is not needed then xPOFA is slightly faster. It is typical to follow a call to xPOCO with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A. | |
| dpocon | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPOTRF | |
| dpodi | compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO, xPOFA, or xQRDC. | |
| dpoequ | compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm) | |
| dpofa | compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to xPOFA with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A. | |
| dporfs | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, | |
| dposl | solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO or xPOFA, and vectors b and x. | |
| dposv | compute the solution to a real system of linear equations A ∗ X = B, | |
| dposvx | use the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B, | |
| dpotf2 | compute the Cholesky factorization of a real symmetric positive definite matrix A | |
| dpotrf | compute the Cholesky factorization of a real symmetric positive definite matrix A | |
| dpotri | compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPOTRF | |
| dpotrs | solve a system of linear equations A∗X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPOTRF | |
| dppco | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in packed storage. If the condition number is not needed then xPPFA is slightly faster. It is typical to follow a call to xPPCO with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A. | |
| dppcon | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPPTRF | |
| dppdi | compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA. | |
| dppequ | compute row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm) | |
| dppfa | compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to xPPFA with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A. | |
| dpprfs | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution | |
| dppsl | solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA, and vectors b and x. | |
| dppsv | compute the solution to a real system of linear equations A ∗ X = B, | |
| dppsvx | use the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B, | |
| dpptrf | compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format | |
| dpptri | compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPPTRF | |
| dpptrs | solve a system of linear equations A∗X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPPTRF | |
| dptcon | compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L∗D∗L∗∗T or A = U∗∗T∗D∗U computed by DPTTRF | |
| dpteqr | compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using DPTTRF, and then calling DBDSQR to compute the singular values of the bidiagonal factor | |
| dptrfs | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution | |
| dptsl | solve the linear system Ax = b for a symmetric positive definite tridiagonal matrix A and vectors b and x. | |
| dptsv | compute the solution to a real system of linear equations A∗X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices | |
| dptsvx | use the factorization A = L∗D∗L∗∗T to compute the solution to a real system of linear equations A∗X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix and X and B are N-by-NRHS matrices | |
| dpttrf | compute the factorization of a real symmetric positive definite tridiagonal matrix A | |
| dpttrs | solve a system of linear equations A ∗ X = B with a symmetric positive definite tridiagonal matrix A using the factorization A = L∗D∗L∗∗T or A = U∗∗T∗D∗U computed by DPTTRF | |
| dqdota | Compute a double precision constant plus an extended precision constant plus the extended precision dot product of two double precision vectors x and y. | |
| dqdoti | Compute a constant plus the extended precision dot product of two double precision vectors x and y. | |
| dqrdc | compute the QR factorization of a general matrix A. It is typical to follow a call to xQRDC with a call to xQRSL to solve Ax = b or to xPODI to compute the determinant of A. | |
| dqrsl | solve the linear system Ax = b for a general matrix A, which has been QR- factored by xQRDC, and vectors b and x. | |
| drot | Apply a Given’s rotation constructed by DROTG. | |
| drotg | Construct a Given’s plane rotation | |
| drotm | Apply a Gentleman’s modified Given’s rotation constructed by DROTMG. | |
| drotmg | Construct a Gentleman’s modified Given’s plane rotation | |
| drscl | multiply an n-element real vector x by the real scalar 1/a | |
| dsbev | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A | |
| dsbevd | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A | |
| dsbevx | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A | |
| dsbgst | reduce a real symmetric-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y, | |
| dsbgv | compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A∗x=(lambda)∗B∗x | |
| dsbmv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y | |
| dsbtrd | reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation | |
| dscal | Compute y := alpha ∗ y | |
| dsdot | Compute the double precision dot product of two single precision vectors x and y. | |
| dsecnd | return the user time for a process in seconds. | |
| dsico | compute the UDU factorization and condition number of a symmetric matrix A. If the condition number is not needed then xSIFA is slightly faster. It is typical to follow a call to xSICO with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A. | |
| dsidi | compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA. | |
| dsifa | compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to xSIFA with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A. | |
| dsinqb | synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. | |
| dsinqf | compute the Fourier coefficients in a sine series representation with only odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. | |
| dsinqi | initialize the array xWSAVE, which is used in both xSINQF and xSINQB. | |
| dsint | compute the discrete Fourier sine transform of an odd sequence. The xSINT transforms are unnormalized inverses of themselves, so a call of xSINT followed by another call of xSINT will multiply the input sequence by 2 ∗ (N+1). The VxSINT transforms are normalized, so a call of VxSINT followed by a call of VxSINT will return the original sequence. | |
| dsinti | initialize the array xWSAVE, which is used in subroutine xSINT. | |
| dsisl | solve the linear system Ax = b for a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA, and vectors b and x. | |
| dspco | compute the UDU factorization and condition number of a symmetric matrix A in packed storage. If the condition number is not needed then xSPFA is slightly faster. It is typical to follow a call to xSPCO with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A. | |
| dspcon | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSPTRF | |
| dspdi | compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA. | |
| dspev | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage | |
| dspevd | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage | |
| dspevx | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage | |
| dspfa | compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to xSPFA with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A. | |
| dspgst | reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage | |
| dspgv | compute all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x | |
| dspmv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y | |
| dspr | perform the symmetric rank 1 operation A := alpha∗x∗x’ + A | |
| dspr2 | perform the symmetric rank 2 operation A := alpha∗x∗y’ + alpha∗y∗x’ + A | |
| dsprfs | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution | |
| dspsl | solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA, and vectors b and x. | |
| dspsv | compute the solution to a real system of linear equations A ∗ X = B, | |
| dspsvx | use the diagonal pivoting factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices | |
| dsptrd | reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation | |
| dsptrf | compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method | |
| dsptri | compute the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSPTRF | |
| dsptrs | solve a system of linear equations A∗X = B with a real symmetric matrix A stored in packed format using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSPTRF | |
| dstebz | compute the eigenvalues of a symmetric tridiagonal matrix T | |
| dstedc | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method | |
| dstein | compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration | |
| dsteqr | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method | |
| dsterf | compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm | |
| dstev | compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A | |
| dstevd | compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix | |
| dstevx | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A | |
| dsvdc | compute the singular value decomposition of a general matrix A. | |
| dswap | Exchange vectors x and y. | |
| dsycon | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSYTRF | |
| dsyev | compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A | |
| dsyevd | compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A | |
| dsyevx | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A | |
| dsygs2 | reduce a real symmetric-definite generalized eigenproblem to standard form | |
| dsygst | reduce a real symmetric-definite generalized eigenproblem to standard form | |
| dsygv | compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x | |
| dsymm | perform one of the matrix-matrix operations C := alpha∗A∗B + beta∗C or C := alpha∗B∗A + beta∗C | |
| dsymv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y | |
| dsyr | perform the symmetric rank 1 operation A := alpha∗x∗x’ + A | |
| dsyr2 | perform the symmetric rank 2 operation A := alpha∗x∗y’ + alpha∗y∗x’ + A | |
| dsyr2k | perform one of the symmetric rank 2k operations C := alpha∗A∗B’ + alpha∗B∗A’ + beta∗C or C := alpha∗A’∗B + alpha∗B’∗A + beta∗C | |
| dsyrfs | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution | |
| dsyrk | perform one of the symmetric rank k operations C := alpha∗A∗A’ + beta∗C or C := alpha∗A’∗A + beta∗C | |
| dsysv | compute the solution to a real system of linear equations A ∗ X = B, | |
| dsysvx | use the diagonal pivoting factorization to compute the solution to a real system of linear equations A ∗ X = B, | |
| dsytd2 | reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation | |
| dsytf2 | compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method | |
| dsytrd | reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation | |
| dsytrf | compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method | |
| dsytri | compute the inverse of a real symmetric indefinite matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSYTRF | |
| dsytrs | solve a system of linear equations A∗X = B with a real symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSYTRF | |
| dtbcon | estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm | |
| dtbmv | perform one of the matrix-vector operations x := A∗x or x := A’∗x | |
| dtbrfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix | |
| dtbsv | solve one of the systems of equations A∗x = b or A’∗x = b | |
| dtbtrs | solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B, | |
| dtgevc | compute some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B) | |
| dtgsja | compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B | |
| dtpcon | estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm | |
| dtpmv | perform one of the matrix-vector operations x := A∗x or x := A’∗x | |
| dtprfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix | |
| dtpsv | solve one of the systems of equations A∗x = b or A’∗x = b | |
| dtptri | compute the inverse of a real upper or lower triangular matrix A stored in packed format | |
| dtptrs | solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B, | |
| dtrco | estimate the condition number of a triangular matrix A. It is typical to follow a call to xTRCO with a call to xTRSL to solve Ax = b or to xTRDI to compute the determinant and inverse of A. | |
| dtrcon | estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm | |
| dtrdi | compute the determinant and inverse of a triangular matrix A. | |
| dtrevc | compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T | |
| dtrexc | reorder the real Schur factorization of a real matrix A = Q∗T∗Q∗∗T, so that the diagonal block of T with row index IFST is moved to row ILST | |
| dtrmm | perform one of the matrix-matrix operations B := alpha∗op( A )∗B, or B := alpha∗B∗op( A ) | |
| dtrmv | perform one of the matrix-vector operations x := A∗x or x := A’∗x | |
| dtrrfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix | |
| dtrsen | reorder the real Schur factorization of a real matrix A = Q∗T∗Q∗∗T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T, | |
| dtrsl | solve the linear system Ax = b for a triangular matrix A and vectors b and x. | |
| dtrsm | solve one of the matrix equations op( A )∗X = alpha∗B, or X∗op( A ) = alpha∗B | |
| dtrsna | estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q∗T∗Q∗∗T with Q orthogonal) | |
| dtrsv | solve one of the systems of equations A∗x = b or A’∗x = b | |
| dtrsyl | solve the real Sylvester matrix equation | |
| dtrti2 | compute the inverse of a real upper or lower triangular matrix | |
| dtrtri | compute the inverse of a real upper or lower triangular matrix A | |
| dtrtrs | solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B, | |
| dtzrqf | reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations | |
| dzasum | Return the sum of the absolute values of a vector x. | |
| dznrm2 | Return the Euclidian norm of a vector. | |
| dzsum1 | take the sum of the absolute values of a complex vector and returns a double precision result | |
| ezfftb | computes a perodic sequence from its Fourier coefficients. EZFFTB is a simplified but slower version of RFFTB. | |
| ezfftf | computes the Fourier coefficients of a perodic sequence. EZFFTF is a simplified but slower version of RFFTF. | |
| ezffti | initializes the array WSAVE, which is used in both EZFFTF and EZFFTB. | |
| icamax | Return the index of the element with largest absolute value. | |
| icmax1 | find the index of the element whose real part has maximum absolute value | |
| idamax | Return the index of the element with largest absolute value. | |
| ilaenv | choose problem-dependent parameters | |
| isamax | Return the index of the element with largest absolute value. | |
| izamax | Return the index of the element with largest absolute value. | |
| izmax1 | find the index of the element whose real part has maximum absolute value | |
| lapack | introduction to LAPACK | |
| lsame | case-insensitive comparison of two characters | |
| lsamen | test if the first N letters of CA are the same as the first N letters of CB, regardless of case | |
| rfftb | compute a perodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. | |
| rfftf | compute the Fourier coefficients of a perodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. | |
| rffti | initialize the array xWSAVE, which is used in both xFFTF and xFFTB. | |
| sasum | Return the sum of the absolute values of a vector x. | |
| saxpy | Compute y := alpha ∗ x + y | |
| sbdsqr | compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B | |
| scasum | Return the sum of the absolute values of a vector x. | |
| schdc | compute the Cholesky decomposition of a symmetric positive definite matrix A. | |
| schdd | downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. | |
| schex | compute the Cholesky decomposition of a symmetric positive definite matrix A. | |
| schud | update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. | |
| scnrm2 | Return the Euclidian norm of a vector. | |
| scopy | Copy x to y | |
| scsum1 | take the sum of the absolute values of a complex vector and returns a single precision result | |
| sdisna | compute the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general m-by-n matrix | |
| sdot | Compute the dot product of two vectors x and y. | |
| sdsdot | Compute a constant plus the double precision dot product of two single precision vectors x and y. | |
| second | return the user time for a process in seconds. | |
| sgbbrd | reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation | |
| sgbco | compute the LU factorization and condition number of a general matrix A in banded storage. If the condition number is not needed then xGBFA is slightly faster. It is typical to follow a call to xGBCO with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A. | |
| sgbcon | estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm, | |
| sgbdi | compute the determinant of a general matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA. | |
| sgbequ | compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number | |
| sgbfa | compute the LU factorization of a matrix A in banded storage. It is typical to follow a call to xGBFA with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A. | |
| sgbmv | perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y or y := alpha∗A’∗x + beta∗y | |
| sgbrfs | improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution | |
| sgbsl | solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA, and vectors b and x. | |
| sgbsv | compute the solution to a real system of linear equations A ∗ X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices | |
| sgbsvx | use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, | |
| sgbtf2 | compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges | |
| sgbtrf | compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges | |
| sgbtrs | solve a system of linear equations A ∗ X = B or A’ ∗ X = B with a general band matrix A using the LU factorization computed by SGBTRF | |
| sgebak | form the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by SGEBAL | |
| sgebal | balance a general real matrix A | |
| sgebd2 | reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation | |
| sgebrd | reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation | |
| sgeco | compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then xGEFA is slightly faster. It is typical to follow a call to xGECO with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant and inverse of A. | |
| sgecon | estimate the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGETRF | |
| sgedi | compute the determinant and inverse of a general matrix A, which has been LU-factored by xGECO or xGEFA. | |
| sgeequ | compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number | |
| sgees | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z | |
| sgeesx | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z | |
| sgeev | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors | |
| sgeevx | compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors | |
| sgefa | compute the LU factorization of a general matrix A. It is typical to follow a call to xGEFA with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant of A. | |
| sgegs | compute for a pair of N-by-N real nonsymmetric matrices A, B | |
| sgegv | compute for a pair of n-by-n real nonsymmetric matrices A and B, the generalized eigenvalues (alphar +/- alphai∗i, beta), and optionally, the left and/or right generalized eigenvectors (VL and VR) | |
| sgehd2 | reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation | |
| sgehrd | reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation | |
| sgelq2 | compute an LQ factorization of a real m by n matrix A | |
| sgelqf | compute an LQ factorization of a real M-by-N matrix A | |
| sgels | solve overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A | |
| sgelss | compute the minimum norm solution to a real linear least squares problem | |
| sgelsx | compute the minimum-norm solution to a real linear least squares problem | |
| sgemm | perform one of the matrix-matrix operations C := alpha∗op( A )∗op( B ) + beta∗C | |
| sgemv | perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y or y := alpha∗A’∗x + beta∗y | |
| sgeql2 | compute a QL factorization of a real m by n matrix A | |
| sgeqlf | compute a QL factorization of a real M-by-N matrix A | |
| sgeqpf | compute a QR factorization with column pivoting of a real M-by-N matrix A | |
| sgeqr2 | compute a QR factorization of a real m by n matrix A | |
| sgeqrf | compute a QR factorization of a real M-by-N matrix A | |
| sger | perform the rank 1 operation A := alpha∗x∗y’ + A | |
| sgerfs | improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution | |
| sgerq2 | compute an RQ factorization of a real m by n matrix A | |
| sgerqf | compute an RQ factorization of a real M-by-N matrix A | |
| sgesl | solve the linear system Ax = b for a general matrix A, which has been LU- factored by xGECO or xGEFA, and vectors b and x. | |
| sgesv | compute the solution to a real system of linear equations A ∗ X = B, | |
| sgesvd | compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors | |
| sgesvx | use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B, | |
| sgetf2 | compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges | |
| sgetrf | compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges | |
| sgetri | compute the inverse of a matrix using the LU factorization computed by SGETRF | |
| sgetrs | solve a system of linear equations A ∗ X = B or A’ ∗ X = B with a general N-by-N matrix A using the LU factorization computed by SGETRF | |
| sggbak | form the right or left eigenvectors of a real generalized eigenvalue problem A∗x = lambda∗B∗x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by SGGBAL | |
| sggbal | balance a pair of general real matrices (A,B) | |
| sggglm | solve a general Gauss-Markov linear model (GLM) problem | |
| sgghrd | reduce a pair of real matrices (A,B) to generalized upper Hessenberg form using orthogonal transformations, where A is a general matrix and B is upper triangular | |
| sgglse | solve the linear equality-constrained least squares (LSE) problem | |
| sggqrf | compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B | |
| sggrqf | compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B | |
| sggsvd | compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B | |
| sggsvp | compute orthogonal matrices U, V and Q such that N-K-L K L U’∗A∗Q = K ( 0 A12 A13 ) if M-K-L >= 0 | |
| sgtcon | estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF | |
| sgtrfs | improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution | |
| sgtsl | solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x. | |
| sgtsv | solve the equation A∗X = B, | |
| sgtsvx | use the LU factorization to compute the solution to a real system of linear equations A ∗ X = B or A∗∗T ∗ X = B, | |
| sgttrf | compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges | |
| sgttrs | solve one of the systems of equations A∗X = B or A’∗X = B, | |
| shgeqz | implement a single-/double-shift version of the QZ method for finding the generalized eigenvalues w(j)=(ALPHAR(j) + i∗ALPHAI(j))/BETAR(j) of the equation det( A - w(i) B ) = 0 In addition, the pair A,B may be reduced to generalized Schur form | |
| shsein | use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H | |
| shseqr | compute the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z∗∗T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors | |
| sinqb | synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. | |
| sinqf | compute the Fourier coefficients in a sine series representation with only odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. | |
| sinqi | initialize the array xWSAVE, which is used in both xSINQF and xSINQB. | |
| sint | compute the discrete Fourier sine transform of an odd sequence. The xSINT transforms are unnormalized inverses of themselves, so a call of xSINT followed by another call of xSINT will multiply the input sequence by 2 ∗ (N+1). The VxSINT transforms are normalized, so a call of VxSINT followed by a call of VxSINT will return the original sequence. | |
| sinti | initialize the array xWSAVE, which is used in subroutine xSINT. | |
| slabad | take as input the values computed by SLAMCH for underflow and overflow, and returns the square root of each of these values if the log of LARGE is sufficiently large | |
| slabrd | reduce the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q’ ∗ A ∗ P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A | |
| slacon | estimate the 1-norm of a square, real matrix A | |
| slacpy | copie all or part of a two-dimensional matrix A to another matrix B | |
| sladiv | perform complex division in real arithmetic a + i∗b p + i∗q = --------- c + i∗d The algorithm is due to Robert L | |
| slae2 | compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ] | |
| slaebz | contain the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w | |
| slaed0 | compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method | |
| slaed1 | compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix | |
| slaed2 | merge the two sets of eigenvalues together into a single sorted set | |
| slaed3 | find the roots of the secular equation, as defined by the values in D, W, and RHO, between KSTART and KSTOP | |
| slaed4 | subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0 | |
| slaed5 | subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j | |
| slaed6 | compute the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true | |
| slaed7 | compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix | |
| slaed8 | merge the two sets of eigenvalues together into a single sorted set | |
| slaed9 | find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP | |
| slaeda | compute the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem | |
| slaein | use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H | |
| slaev2 | compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ] | |
| slaexc | swap adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation | |
| slag2 | compute the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow | |
| slags2 | compute 2-by-2 orthogonal matrices U, V and Q, such that if ( UPPER ) then U’∗A∗Q = U’∗( A1 A2 )∗Q = ( x 0 ) ( 0 A3 ) ( x x ) and V’∗B∗Q = V’∗( B1 B2 )∗Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U’∗A∗Q = U’∗( A1 0 )∗Q = ( x x ) ( A2 A3 ) ( 0 x ) and V’∗B∗Q = V’∗( B1 0 )∗Q = ( x x ) ( B2 B3 ) ( 0 x ) The rows of the transformed A and B are parallel, where U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) ( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ ) Z’ denotes the transpose of Z | |
| slagtf | factorize the matrix (T - lambda∗I), where T is an n by n tridiagonal matrix and lambda is a scalar, as T - lambda∗I = PLU, | |
| slagtm | perform a matrix-vector product of the form B := alpha ∗ A ∗ X + beta ∗ B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1 | |
| slagts | may be used to solve one of the systems of equations (T - lambda∗I)∗x = y or (T - lambda∗I)’∗x = y, | |
| slahqr | i an auxiliary routine called by SHSEQR to update the eigenvalues and Schur decomposition already computed by SHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI | |
| slahrd | reduce the first NB columns of a real general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero | |
| slaic1 | applie one step of incremental condition estimation in its simplest version | |
| slaln2 | solve a system of the form (ca A - w D ) X = s B or (ca A’ - w D) X = s B with possible scaling ("s") and perturbation of A | |
| slamch | determine single precision machine parameters | |
| slamrg | will create a permutation list which will merge the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascending order | |
| slangb | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals | |
| slange | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A | |
| slangt | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A | |
| slanhs | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A | |
| slansb | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals | |
| slansp | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form | |
| slanst | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A | |
| slansy | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A | |
| slantb | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals | |
| slantp | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form | |
| slantr | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A | |
| slanv2 | compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form | |
| slapll | two column vectors X and Y, let A = ( X Y ) | |
| slapmt | rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N | |
| slapy2 | return sqrt(x∗∗2+y∗∗2), taking care not to cause unnecessary overflow | |
| slapy3 | return sqrt(x∗∗2+y∗∗2+z∗∗2), taking care not to cause unnecessary overflow | |
| slaqgb | equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C | |
| slaqge | equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C | |
| slaqsb | equilibrate a symmetric band matrix A using the scaling factors in the vector S | |
| slaqsp | equilibrate a symmetric matrix A using the scaling factors in the vector S | |
| slaqsy | equilibrate a symmetric matrix A using the scaling factors in the vector S | |
| slaqtr | solve the real quasi-triangular system op(T)∗p = scale∗c, if LREAL = .TRUE | |
| slar2v | applie a vector of real plane rotations from both sides to a sequence of 2-by-2 real symmetric matrices, defined by the elements of the vectors x, y and z | |
| slarf | applie a real elementary reflector H to a real m by n matrix C, from either the left or the right | |
| slarfb | applie a real block reflector H or its transpose H’ to a real m by n matrix C, from either the left or the right | |
| slarfg | generate a real elementary reflector H of order n, such that H ∗ ( alpha ) = ( beta ), H’ ∗ H = I | |
| slarft | form the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors | |
| slarfx | applie a real elementary reflector H to a real m by n matrix C, from either the left or the right | |
| slargv | generate a vector of real plane rotations, determined by elements of the real vectors x and y | |
| slarnv | return a vector of n random real numbers from a uniform or normal distribution | |
| slartg | generate a plane rotation so that [ CS SN ] | |
| slartv | applie a vector of real plane rotations to elements of the real vectors x and y | |
| slaruv | return a vector of n random real numbers from a uniform (0,1) | |
| slas2 | compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ] | |
| slascl | multiply the M by N real matrix A by the real scalar CTO/CFROM | |
| slaset | initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals | |
| slasq1 | SLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E | |
| slasq2 | SLASQ2 computes the singular values of a real N-by-N unreduced bidiagonal matrix with squared diagonal elements in Q and squared off-diagonal elements in E | |
| slasq3 | SLASQ3 is the workhorse of the whole bidiagonal SVD algorithm | |
| slasq4 | SLASQ4 estimates TAU, the smallest eigenvalue of a matrix | |
| slasr | perform the transformation A := P∗A, when SIDE = ’L’ or ’l’ ( Left-hand side ) A := A∗P’, when SIDE = ’R’ or ’r’ ( Right-hand side ) where A is an m by n real matrix and P is an orthogonal matrix, | |
| slasrt | the numbers in D in increasing order (if ID = ’I’) or in decreasing order (if ID = ’D’ ) | |
| slassq | return the values scl and smsq such that ( scl∗∗2 )∗smsq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq, | |
| slasv2 | compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ] | |
| slaswp | perform a series of row interchanges on the matrix A | |
| slasy2 | solve for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in op(TL)∗X + ISGN∗X∗op(TR) = SCALE∗B, | |
| slasyf | compute a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method | |
| slatbs | solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow, where A is an upper or lower triangular band matrix | |
| slatps | solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form | |
| slatrd | reduce NB rows and columns of a real symmetric matrix A to symmetric tridiagonal form by an orthogonal similarity transformation Q’ ∗ A ∗ Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A | |
| slatrs | solve one of the triangular systems A ∗x = s∗b or A’∗x = s∗b with scaling to prevent overflow | |
| slatzm | applie a Householder matrix generated by STZRQF to a matrix | |
| slauu2 | compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A | |
| slauum | compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A | |
| snrm2 | Return the Euclidian norm of a vector. | |
| sopgtr | generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by SSPTRD using packed storage | |
| sopmtr | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| sorg2l | generate an m by n real matrix Q with orthonormal columns, | |
| sorg2r | generate an m by n real matrix Q with orthonormal columns, | |
| sorgbr | generate one of the real orthogonal matrices Q or P∗∗T determined by SGEBRD when reducing a real matrix A to bidiagonal form | |
| sorghr | generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by SGEHRD | |
| sorgl2 | generate an m by n real matrix Q with orthonormal rows, | |
| sorglq | generate an M-by-N real matrix Q with orthonormal rows, | |
| sorgql | generate an M-by-N real matrix Q with orthonormal columns, | |
| sorgqr | generate an M-by-N real matrix Q with orthonormal columns, | |
| sorgr2 | generate an m by n real matrix Q with orthonormal rows, | |
| sorgrq | generate an M-by-N real matrix Q with orthonormal rows, | |
| sorgtr | generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by SSYTRD | |
| sorm2l | overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’, | |
| sorm2r | overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’, | |
| sormbr | VECT = ’Q’, SORMBR overwrites the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| sormhr | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| sorml2 | overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’, | |
| sormlq | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| sormql | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| sormqr | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| sormr2 | overwrite the general real m by n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’T’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’T’, | |
| sormrq | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| sormtr | overwrite the general real M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| spbco | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in banded storage. If the condition number is not needed then xPBFA is slightly faster. It is typical to follow a call to xPBCO with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A. | |
| spbcon | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPBTRF | |
| spbdi | compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA. | |
| spbequ | compute row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number (with respect to the two-norm) | |
| spbfa | compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to xPBFA with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A. | |
| spbrfs | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution | |
| spbsl | section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA, and vectors b and x. | |
| spbstf | compute a split Cholesky factorization of a real symmetric positive definite band matrix A | |
| spbsv | compute the solution to a real system of linear equations A ∗ X = B, | |
| spbsvx | use the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B, | |
| spbtf2 | compute the Cholesky factorization of a real symmetric positive definite band matrix A | |
| spbtrf | compute the Cholesky factorization of a real symmetric positive definite band matrix A | |
| spbtrs | solve a system of linear equations A∗X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPBTRF | |
| spoco | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A. If the condition number is not needed then xPOFA is slightly faster. It is typical to follow a call to xPOCO with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A. | |
| spocon | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPOTRF | |
| spodi | compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO, xPOFA, or xQRDC. | |
| spoequ | compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm) | |
| spofa | compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to xPOFA with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A. | |
| sporfs | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, | |
| sposl | solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO or xPOFA, and vectors b and x. | |
| sposv | compute the solution to a real system of linear equations A ∗ X = B, | |
| sposvx | use the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B, | |
| spotf2 | compute the Cholesky factorization of a real symmetric positive definite matrix A | |
| spotrf | compute the Cholesky factorization of a real symmetric positive definite matrix A | |
| spotri | compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPOTRF | |
| spotrs | solve a system of linear equations A∗X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPOTRF | |
| sppco | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in packed storage. If the condition number is not needed then xPPFA is slightly faster. It is typical to follow a call to xPPCO with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A. | |
| sppcon | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPPTRF | |
| sppdi | compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA. | |
| sppequ | compute row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm) | |
| sppfa | compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to xPPFA with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A. | |
| spprfs | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution | |
| sppsl | solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA, and vectors b and x. | |
| sppsv | compute the solution to a real system of linear equations A ∗ X = B, | |
| sppsvx | use the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B, | |
| spptrf | compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format | |
| spptri | compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPPTRF | |
| spptrs | solve a system of linear equations A∗X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by SPPTRF | |
| sptcon | compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L∗D∗L∗∗T or A = U∗∗T∗D∗U computed by SPTTRF | |
| spteqr | compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF, and then calling SBDSQR to compute the singular values of the bidiagonal factor | |
| sptrfs | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution | |
| sptsl | solve the linear system Ax = b for a symmetric positive definite tridiagonal matrix A and vectors b and x. | |
| sptsv | compute the solution to a real system of linear equations A∗X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices | |
| sptsvx | use the factorization A = L∗D∗L∗∗T to compute the solution to a real system of linear equations A∗X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix and X and B are N-by-NRHS matrices | |
| spttrf | compute the factorization of a real symmetric positive definite tridiagonal matrix A | |
| spttrs | solve a system of linear equations A ∗ X = B with a symmetric positive definite tridiagonal matrix A using the factorization A = L∗D∗L∗∗T or A = U∗∗T∗D∗U computed by SPTTRF | |
| sqrdc | compute the QR factorization of a general matrix A. It is typical to follow a call to xQRDC with a call to xQRSL to solve Ax = b or to xPODI to compute the determinant of A. | |
| sqrsl | solve the linear system Ax = b for a general matrix A, which has been QR- factored by xQRDC, and vectors b and x. | |
| srot | Apply a Given’s rotation constructed by SROTG. | |
| srotg | Construct a Given’s plane rotation | |
| srotm | Apply a Gentleman’s modified Given’s rotation constructed by SROTMG. | |
| srotmg | Construct a Gentleman’s modified Given’s plane rotation | |
| srscl | multiply an n-element real vector x by the real scalar 1/a | |
| ssbev | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A | |
| ssbevd | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A | |
| ssbevx | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A | |
| ssbgst | reduce a real symmetric-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y, | |
| ssbgv | compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A∗x=(lambda)∗B∗x | |
| ssbmv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y | |
| ssbtrd | reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation | |
| sscal | Compute y := alpha ∗ y | |
| ssico | compute the UDU factorization and condition number of a symmetric matrix A. If the condition number is not needed then xSIFA is slightly faster. It is typical to follow a call to xSICO with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A. | |
| ssidi | compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA. | |
| ssifa | compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to xSIFA with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A. | |
| ssisl | solve the linear system Ax = b for a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA, and vectors b and x. | |
| sspco | compute the UDU factorization and condition number of a symmetric matrix A in packed storage. If the condition number is not needed then xSPFA is slightly faster. It is typical to follow a call to xSPCO with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A. | |
| sspcon | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by SSPTRF | |
| sspdi | compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA. | |
| sspev | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage | |
| sspevd | compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage | |
| sspevx | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage | |
| sspfa | compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to xSPFA with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A. | |
| sspgst | reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage | |
| sspgv | compute all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x | |
| sspmv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y | |
| sspr | perform the symmetric rank 1 operation A := alpha∗x∗x’ + A | |
| sspr2 | perform the symmetric rank 2 operation A := alpha∗x∗y’ + alpha∗y∗x’ + A | |
| ssprfs | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution | |
| sspsl | solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA, and vectors b and x. | |
| sspsv | compute the solution to a real system of linear equations A ∗ X = B, | |
| sspsvx | use the diagonal pivoting factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T to compute the solution to a real system of linear equations A ∗ X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices | |
| ssptrd | reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation | |
| ssptrf | compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method | |
| ssptri | compute the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by SSPTRF | |
| ssptrs | solve a system of linear equations A∗X = B with a real symmetric matrix A stored in packed format using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by SSPTRF | |
| sstebz | compute the eigenvalues of a symmetric tridiagonal matrix T | |
| sstedc | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method | |
| sstein | compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration | |
| ssteqr | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method | |
| ssterf | compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm | |
| sstev | compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A | |
| sstevd | compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix | |
| sstevx | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A | |
| ssvdc | compute the singular value decomposition of a general matrix A. | |
| sswap | Exchange vectors x and y. | |
| ssycon | estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by SSYTRF | |
| ssyev | compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A | |
| ssyevd | compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A | |
| ssyevx | compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A | |
| ssygs2 | reduce a real symmetric-definite generalized eigenproblem to standard form | |
| ssygst | reduce a real symmetric-definite generalized eigenproblem to standard form | |
| ssygv | compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x | |
| ssymm | perform one of the matrix-matrix operations C := alpha∗A∗B + beta∗C or C := alpha∗B∗A + beta∗C | |
| ssymv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y | |
| ssyr | perform the symmetric rank 1 operation A := alpha∗x∗x’ + A | |
| ssyr2 | perform the symmetric rank 2 operation A := alpha∗x∗y’ + alpha∗y∗x’ + A | |
| ssyr2k | perform one of the symmetric rank 2k operations C := alpha∗A∗B’ + alpha∗B∗A’ + beta∗C or C := alpha∗A’∗B + alpha∗B’∗A + beta∗C | |
| ssyrfs | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution | |
| ssyrk | perform one of the symmetric rank k operations C := alpha∗A∗A’ + beta∗C or C := alpha∗A’∗A + beta∗C | |
| ssysv | compute the solution to a real system of linear equations A ∗ X = B, | |
| ssysvx | use the diagonal pivoting factorization to compute the solution to a real system of linear equations A ∗ X = B, | |
| ssytd2 | reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation | |
| ssytf2 | compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method | |
| ssytrd | reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation | |
| ssytrf | compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method | |
| ssytri | compute the inverse of a real symmetric indefinite matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by SSYTRF | |
| ssytrs | solve a system of linear equations A∗X = B with a real symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by SSYTRF | |
| stbcon | estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm | |
| stbmv | perform one of the matrix-vector operations x := A∗x, or x := A’∗x | |
| stbrfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix | |
| stbsv | solve one of the systems of equations A∗x = b, or A’∗x = b | |
| stbtrs | solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B, | |
| stgevc | compute some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B) | |
| stgsja | compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B | |
| stpcon | estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm | |
| stpmv | perform one of the matrix-vector operations x := A∗x, or x := A’∗x | |
| stprfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix | |
| stpsv | solve one of the systems of equations A∗x = b, or A’∗x = b | |
| stptri | compute the inverse of a real upper or lower triangular matrix A stored in packed format | |
| stptrs | solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B, | |
| strco | estimate the condition number of a triangular matrix A. It is typical to follow a call to xTRCO with a call to xTRSL to solve Ax = b or to xTRDI to compute the determinant and inverse of A. | |
| strcon | estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm | |
| strdi | compute the determinant and inverse of a triangular matrix A. | |
| strevc | compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T | |
| strexc | reorder the real Schur factorization of a real matrix A = Q∗T∗Q∗∗T, so that the diagonal block of T with row index IFST is moved to row ILST | |
| strmm | perform one of the matrix-matrix operations B := alpha∗op( A )∗B, or B := alpha∗B∗op( A ) | |
| strmv | perform one of the matrix-vector operations x := A∗x, or x := A’∗x | |
| strrfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix | |
| strsen | reorder the real Schur factorization of a real matrix A = Q∗T∗Q∗∗T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T, | |
| strsl | solve the linear system Ax = b for a triangular matrix A and vectors b and x. | |
| strsm | solve one of the matrix equations op( A )∗X = alpha∗B, or X∗op( A ) = alpha∗B | |
| strsna | estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q∗T∗Q∗∗T with Q orthogonal) | |
| strsv | solve one of the systems of equations A∗x = b, or A’∗x = b | |
| strsyl | solve the real Sylvester matrix equation | |
| strti2 | compute the inverse of a real upper or lower triangular matrix | |
| strtri | compute the inverse of a real upper or lower triangular matrix A | |
| strtrs | solve a triangular system of the form A ∗ X = B or A∗∗T ∗ X = B, | |
| stzrqf | reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations | |
| vcosqb | synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. | |
| vcosqf | compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. | |
| vcosqi | initialize the array xWSAVE, which is used in both xCOSQF and xCOSQB. | |
| vcost | compute the discrete Fourier cosine transform of an even sequence. The xCOST transforms are unnormalized inverses of themselves, so a call of xCOST followed by another call of xCOST will multiply the input sequence by 2 ∗ (N - 1). The VxCOST transforms are normalized, so a call of VxCOST followed by a call of VxCOST will return the original sequence. | |
| vcosti | initialize the array xWSAVE, which is used in xCOST. | |
| vdcosqb | synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. | |
| vdcosqf | compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The xCOSQ operations are unnormalized inverses of themselves, so a call to xCOSQF followed by a call to xCOSQB will multiply the input sequence by 4 ∗ N. The VxCOSQ operations are normalized, so a call of VxCOSQF followed by a call of VxCOSQB will return the original sequence. | |
| vdcosqi | initialize the array xWSAVE, which is used in both xCOSQF and xCOSQB. | |
| vdcost | compute the discrete Fourier cosine transform of an even sequence. The xCOST transforms are unnormalized inverses of themselves, so a call of xCOST followed by another call of xCOST will multiply the input sequence by 2 ∗ (N - 1). The VxCOST transforms are normalized, so a call of VxCOST followed by a call of VxCOST will return the original sequence. | |
| vdcosti | initialize the array xWSAVE, which is used in xCOST. | |
| vdfftb | compute a perodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. | |
| vdfftf | compute the Fourier coefficients of a perodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. | |
| vdffti | initialize the array xWSAVE, which is used in both xFFTF and xFFTB. | |
| vdsinqb | synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. | |
| vdsinqf | compute the Fourier coefficients in a sine series representation with only odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. | |
| vdsinqi | initialize the array xWSAVE, which is used in both xSINQF and xSINQB. | |
| vdsint | initialize the array xWSAVE, which is used in subroutine xSINT. | [ vdsinti ] |
| vdsinti | initialize the array xWSAVE, which is used in subroutine xSINT. | |
| vrfftb | compute a perodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. | |
| vrfftf | compute the Fourier coefficients of a perodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. | |
| vrffti | initialize the array xWSAVE, which is used in both xFFTF and xFFTB. | |
| vsinqb | synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. | |
| vsinqf | compute the Fourier coefficients in a sine series representation with only odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. | |
| vsinqi | initialize the array xWSAVE, which is used in both xSINQF and xSINQB. | |
| vsint | compute the discrete Fourier sine transform of an odd sequence. The xSINT transforms are unnormalized inverses of themselves, so a call of xSINT followed by another call of xSINT will multiply the input sequence by 2 ∗ (N+1). The VxSINT transforms are normalized, so a call of VxSINT followed by a call of VxSINT will return the original sequence. | |
| vsinti | initialize the array xWSAVE, which is used in subroutine xSINT. | |
| xerbla | error handler for the LAPACK routines | |
| zaxpy | Compute y := alpha ∗ x + y | |
| zbdsqr | compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B | |
| zchdc | compute the Cholesky decomposition of a symmetric positive definite matrix A. | |
| zchdd | downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. | |
| zchex | compute the Cholesky decomposition of a symmetric positive definite matrix A. | |
| zchud | update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition. | |
| zcopy | Copy x to y | |
| zdotc | Compute the dot product of two vectors x and conjg(y). | |
| zdotu | Compute the dot product of two vectors x and y. | |
| zdrscl | multiply an n-element complex vector x by the real scalar 1/a | |
| zdscal | Compute y := alpha ∗ y | |
| zfftb | compute a perodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. | |
| zfftf | compute the Fourier coefficients of a perodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N. The VxFFT operations are normalized, so a call of VxFFTF followed by a call of VxFFTB will return the original sequence. | |
| zffti | initialize the array xWSAVE, which is used in both xFFTF and xFFTB. | |
| zgbbrd | reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation | |
| zgbcon | estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm, | |
| zgbdi | compute the determinant of a general matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA. | |
| zgbequ | compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number | |
| zgbfa | compute the LU factorization of a matrix A in banded storage. It is typical to follow a call to xGBFA with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A. | |
| zgbmv | perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y, or y := alpha∗A’∗x + beta∗y, or y := alpha∗conjg( A’ )∗x + beta∗y | |
| zgbrfs | improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution | |
| zgbsl | solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA, and vectors b and x. | |
| zgbsv | compute the solution to a complex system of linear equations A ∗ X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices | |
| zgbsvx | use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, | |
| zgbtf2 | compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges | |
| zgbtrf | compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges | |
| zgbtrs | solve a system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B with a general band matrix A using the LU factorization computed by ZGBTRF | |
| zgebak | form the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by ZGEBAL | |
| zgebal | balance a general complex matrix A | |
| zgebd2 | reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation | |
| zgebrd | reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation | |
| zgeco | compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then xGEFA is slightly faster. It is typical to follow a call to xGECO with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant and inverse of A. | |
| zgecon | estimate the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF | |
| zgedi | compute the determinant and inverse of a general matrix A, which has been LU-factored by xGECO or xGEFA. | |
| zgeequ | compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number | |
| zgees | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z | |
| zgeesx | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z | |
| zgeev | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors | |
| zgeevx | compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors | |
| zgefa | compute the LU factorization of a general matrix A. It is typical to follow a call to xGEFA with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant of A. | |
| zgegs | compute for a pair of N-by-N complex nonsymmetric matrices A, | |
| zgegv | compute for a pair of N-by-N complex nonsymmetric matrices A and B, the generalized eigenvalues (alpha, beta), and optionally, | |
| zgehd2 | reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation | |
| zgehrd | reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation | |
| zgelq2 | compute an LQ factorization of a complex m by n matrix A | |
| zgelqf | compute an LQ factorization of a complex M-by-N matrix A | |
| zgels | solve overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A | |
| zgelss | compute the minimum norm solution to a complex linear least squares problem | |
| zgelsx | compute the minimum-norm solution to a complex linear least squares problem | |
| zgemm | perform one of the matrix-matrix operations C := alpha∗op( A )∗op( B ) + beta∗C | |
| zgemv | perform one of the matrix-vector operations y := alpha∗A∗x + beta∗y, or y := alpha∗A’∗x + beta∗y, or y := alpha∗conjg( A’ )∗x + beta∗y | |
| zgeql2 | compute a QL factorization of a complex m by n matrix A | |
| zgeqlf | compute a QL factorization of a complex M-by-N matrix A | |
| zgeqpf | compute a QR factorization with column pivoting of a complex M-by-N matrix A | |
| zgeqr2 | compute a QR factorization of a complex m by n matrix A | |
| zgeqrf | compute a QR factorization of a complex M-by-N matrix A | |
| zgerc | perform the rank 1 operation A := alpha∗x∗conjg( y’ ) + A | |
| zgerfs | improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution | |
| zgerq2 | compute an RQ factorization of a complex m by n matrix A | |
| zgerqf | compute an RQ factorization of a complex M-by-N matrix A | |
| zgeru | perform the rank 1 operation A := alpha∗x∗y’ + A | |
| zgesl | solve the linear system Ax = b for a general matrix A, which has been LU- factored by xGECO or xGEFA, and vectors b and x. | |
| zgesv | compute the solution to a complex system of linear equations A ∗ X = B, | |
| zgesvd | compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors | |
| zgesvx | use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B, | |
| zgetf2 | compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges | |
| zgetrf | compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges | |
| zgetri | compute the inverse of a matrix using the LU factorization computed by ZGETRF | |
| zgetrs | solve a system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B with a general N-by-N matrix A using the LU factorization computed by ZGETRF | |
| zggbak | form the right or left eigenvectors of a complex generalized eigenvalue problem A∗x = lambda∗B∗x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by ZGGBAL | |
| zggbal | balance a pair of general complex matrices (A,B) | |
| zggglm | solve a general Gauss-Markov linear model (GLM) problem | |
| zgghrd | reduce a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular | |
| zgglse | solve the linear equality-constrained least squares (LSE) problem | |
| zggqrf | compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B | |
| zggrqf | compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B | |
| zggsvd | compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B | |
| zggsvp | compute unitary matrices U, V and Q such that N-K-L K L U’∗A∗Q = K ( 0 A12 A13 ) if M-K-L >= 0 | |
| zgtcon | estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF | |
| zgtrfs | improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution | |
| zgtsl | solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x. | |
| zgtsv | solve the equation A∗X = B, | |
| zgtsvx | use the LU factorization to compute the solution to a complex system of linear equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, | |
| zgttrf | compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges | |
| zgttrs | solve one of the systems of equations A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, | |
| zhbev | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A | |
| zhbevd | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A | |
| zhbevx | compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A | |
| zhbgst | reduce a complex Hermitian-definite banded generalized eigenproblem A∗x = lambda∗B∗x to standard form C∗y = lambda∗y, | |
| zhbgv | compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A∗x=(lambda)∗B∗x | |
| zhbmv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y | |
| zhbtrd | reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation | |
| zhecon | estimate the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHETRF | |
| zheev | compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A | |
| zheevd | compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A | |
| zheevx | compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A | |
| zhegs2 | reduce a complex Hermitian-definite generalized eigenproblem to standard form | |
| zhegst | reduce a complex Hermitian-definite generalized eigenproblem to standard form | |
| zhegv | compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x | |
| zhemm | perform one of the matrix-matrix operations C := alpha∗A∗B + beta∗C or C := alpha∗B∗A + beta∗C | |
| zhemv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y | |
| zher | perform the hermitian rank 1 operation A := alpha∗x∗conjg( x’ ) + A | |
| zher2 | perform the hermitian rank 2 operation A := alpha∗x∗conjg( y’ ) + conjg( alpha )∗y∗conjg( x’ ) + A | |
| zher2k | perform one of the hermitian rank 2k operations C := alpha∗A∗conjg( B’ ) + conjg( alpha )∗B∗conjg( A’ ) + beta∗C or C := alpha∗conjg( A’ )∗B + conjg( alpha )∗conjg( B’ )∗A + beta∗C | |
| zherfs | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution | |
| zherk | perform one of the hermitian rank k operations C := alpha∗A∗conjg( A’ ) + beta∗C or C := alpha∗conjg( A’ )∗A + beta∗C | |
| zhesv | compute the solution to a complex system of linear equations A ∗ X = B, | |
| zhesvx | use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B, | |
| zhetd2 | reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation | |
| zhetf2 | compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method | |
| zhetrd | reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation | |
| zhetrf | compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method | |
| zhetri | compute the inverse of a complex Hermitian indefinite matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHETRF | |
| zhetrs | solve a system of linear equations A∗X = B with a complex Hermitian matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHETRF | |
| zhgeqz | implement a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation det( A - w(i) B ) = 0 If JOB=’S’, then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both upper triangular) by applying one unitary tranformation (usually called Q) on the left and another (usually called Z) on the right | |
| zhico | compute the UDU factorization and condition number of a Hermitian matrix A. If the condition number is not needed then xHIFA is slightly faster. It is typical to follow a call to xHICO with a call to xHISL to solve Ax = b or to xHIDI to compute the determinant, inverse, and inertia of A. | |
| zhidi | compute the determinant, inertia, and inverse of a Hermitian matrix A, which has been UDU-factored by xHICO or xHIFA. | |
| zhifa | compute the UDU factorization of a Hermitian matrix A. It is typical to follow a call to xHIFA with a call to xHISL to solve Ax = b or to xHIDI to compute the determinant, inverse, and inertia of A. | |
| zhisl | solve the linear system Ax = b for a Hermitian matrix A, which has been UDU-factored by xHICO or xHIFA, and vectors b and x. | |
| zhpco | compute the UDU factorization and condition number of a Hermitian matrix A in packed storage. If the condition number is not needed then xHPFA is slightly faster. It is typical to follow a call to xHPCO with a call to xHPSL to solve Ax = b or to xHPDI to compute the determinant, inverse, and inertia of A. | |
| zhpcon | estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHPTRF | |
| zhpdi | compute the determinant, inertia, and inverse of a Hermitian matrix A in packed storage, which has been UDU-factored by xHPCO or xHPFA. | |
| zhpev | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage | |
| zhpevd | compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage | |
| zhpevx | compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage | |
| zhpfa | compute the UDU factorization of a Hermitian matrix A in packed storage. It is typical to follow a call to xHPFA with a call to xHPSL to solve Ax = b or to xHPDI to compute the determinant, inverse, and inertia of A. | |
| zhpgst | reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage | |
| zhpgv | compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A∗x=(lambda)∗B∗x, A∗Bx=(lambda)∗x, or B∗A∗x=(lambda)∗x | |
| zhpmv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y | |
| zhpr | perform the hermitian rank 1 operation A := alpha∗x∗conjg( x’ ) + A | |
| zhpr2 | perform the hermitian rank 2 operation A := alpha∗x∗conjg( y’ ) + conjg( alpha )∗y∗conjg( x’ ) + A | |
| zhprfs | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution | |
| zhpsl | solve the linear system Ax = b for a Hermitian matrix A in packed storage, which has been UDU-factored by xHPCO or xHPFA, and vectors b and x. | |
| zhpsv | compute the solution to a complex system of linear equations A ∗ X = B, | |
| zhpsvx | use the diagonal pivoting factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices | |
| zhptrd | reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation | |
| zhptrf | compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method | |
| zhptri | compute the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHPTRF | |
| zhptrs | solve a system of linear equations A∗X = B with a complex Hermitian matrix A stored in packed format using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHPTRF | |
| zhsein | use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H | |
| zhseqr | compute the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z∗∗H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors | |
| zlabrd | reduce the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal form by a unitary transformation Q’ ∗ A ∗ P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A | |
| zlacgv | conjugate a complex vector of length N | |
| zlacon | estimate the 1-norm of a square, complex matrix A | |
| zlacpy | copie all or part of a two-dimensional matrix A to another matrix B | |
| zlacrm | perform a very simple matrix-matrix multiplication | |
| zlacrt | applie a plane rotation, where the cos and sin (C and S) are complex and the vectors CX and CY are complex | |
| zladiv | := X / Y, where X and Y are complex | |
| zlaed0 | the divide and conquer method, ZLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix | |
| zlaed7 | compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix | |
| zlaed8 | merge the two sets of eigenvalues together into a single sorted set | |
| zlaein | use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H | |
| zlaesy | compute the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value | |
| zlaev2 | compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ] | |
| zlags2 | compute 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U’∗A∗Q = U’∗( A1 A2 )∗Q = ( x 0 ) ( 0 A3 ) ( x x ) and V’∗B∗Q = V’∗( B1 B2 )∗Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U’∗A∗Q = U’∗( A1 0 )∗Q = ( x x ) ( A2 A3 ) ( 0 x ) and V’∗B∗Q = V’∗( B1 0 )∗Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ), | |
| zlagtm | perform a matrix-vector product of the form B := alpha ∗ A ∗ X + beta ∗ B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1 | |
| zlahef | compute a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method | |
| zlahqr | i an auxiliary routine called by ZHSEQR to update the eigenvalues and Schur decomposition already computed by ZHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI | |
| zlahrd | reduce the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero | |
| zlaic1 | applie one step of incremental condition estimation in its simplest version | |
| zlangb | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals | |
| zlange | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex matrix A | |
| zlangt | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex tridiagonal matrix A | |
| zlanhb | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n hermitian band matrix A, with k super-diagonals | |
| zlanhe | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A | |
| zlanhp | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A, supplied in packed form | |
| zlanhs | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A | |
| zlanht | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix A | |
| zlansb | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals | |
| zlansp | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form | |
| zlansy | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A | |
| zlantb | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals | |
| zlantp | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form | |
| zlantr | return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A | |
| zlapll | two column vectors X and Y, let A = ( X Y ) | |
| zlapmt | rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N | |
| zlaqgb | equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C | |
| zlaqge | equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C | |
| zlaqhb | equilibrate a symmetric band matrix A using the scaling factors in the vector S | |
| zlaqhe | equilibrate a Hermitian matrix A using the scaling factors in the vector S | |
| zlaqhp | equilibrate a Hermitian matrix A using the scaling factors in the vector S | |
| zlaqsb | equilibrate a symmetric band matrix A using the scaling factors in the vector S | |
| zlaqsp | equilibrate a symmetric matrix A using the scaling factors in the vector S | |
| zlaqsy | equilibrate a symmetric matrix A using the scaling factors in the vector S | |
| zlar2v | applie a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices, | |
| zlarf | applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right | |
| zlarfb | applie a complex block reflector H or its transpose H’ to a complex M-by-N matrix C, from either the left or the right | |
| zlarfg | generate a complex elementary reflector H of order n, such that H’ ∗ ( alpha ) = ( beta ), H’ ∗ H = I | |
| zlarft | form the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors | |
| zlarfx | applie a complex elementary reflector H to a complex m by n matrix C, from either the left or the right | |
| zlargv | generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y | |
| zlarnv | return a vector of n random complex numbers from a uniform or normal distribution | |
| zlartg | generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ] | |
| zlartv | applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y | |
| zlascl | multiply the M by N complex matrix A by the real scalar CTO/CFROM | |
| zlaset | initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals | |
| zlasr | perform the transformation A := P∗A, when SIDE = ’L’ or ’l’ ( Left-hand side ) A := A∗P’, when SIDE = ’R’ or ’r’ ( Right-hand side ) where A is an m by n complex matrix and P is an orthogonal matrix, | |
| zlassq | return the values scl and ssq such that ( scl∗∗2 )∗ssq = x( 1 )∗∗2 +...+ x( n )∗∗2 + ( scale∗∗2 )∗sumsq, | |
| zlaswp | perform a series of row interchanges on the matrix A | |
| zlasyf | compute a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method | |
| zlatbs | solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b, | |
| zlatps | solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b, | |
| zlatrd | reduce NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by a unitary similarity transformation Q’ ∗ A ∗ Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A | |
| zlatrs | solve one of the triangular systems A ∗ x = s∗b, A∗∗T ∗ x = s∗b, or A∗∗H ∗ x = s∗b, | |
| zlatzm | applie a Householder matrix generated by ZTZRQF to a matrix | |
| zlauu2 | compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A | |
| zlauum | compute the product U ∗ U’ or L’ ∗ L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A | |
| zpbco | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in banded storage. If the condition number is not needed then xPBFA is slightly faster. It is typical to follow a call to xPBCO with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A. | |
| zpbcon | estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPBTRF | |
| zpbdi | compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA. | |
| zpbequ | compute row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm) | |
| zpbfa | compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to xPBFA with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A. | |
| zpbrfs | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution | |
| zpbsl | section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA, and vectors b and x. | |
| zpbstf | compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A | |
| zpbsv | compute the solution to a complex system of linear equations A ∗ X = B, | |
| zpbsvx | use the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B, | |
| zpbtf2 | compute the Cholesky factorization of a complex Hermitian positive definite band matrix A | |
| zpbtrf | compute the Cholesky factorization of a complex Hermitian positive definite band matrix A | |
| zpbtrs | solve a system of linear equations A∗X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPBTRF | |
| zpoco | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A. If the condition number is not needed then xPOFA is slightly faster. It is typical to follow a call to xPOCO with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A. | |
| zpocon | estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPOTRF | |
| zpodi | compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO, xPOFA, or xQRDC. | |
| zpoequ | compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm) | |
| zpofa | compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to xPOFA with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A. | |
| zporfs | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, | |
| zposl | solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO or xPOFA, and vectors b and x. | |
| zposv | compute the solution to a complex system of linear equations A ∗ X = B, | |
| zposvx | use the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B, | |
| zpotf2 | compute the Cholesky factorization of a complex Hermitian positive definite matrix A | |
| zpotrf | compute the Cholesky factorization of a complex Hermitian positive definite matrix A | |
| zpotri | compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPOTRF | |
| zpotrs | solve a system of linear equations A∗X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPOTRF | |
| zppco | compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in packed storage. If the condition number is not needed then xPPFA is slightly faster. It is typical to follow a call to xPPCO with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A. | |
| zppcon | estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPPTRF | |
| zppdi | compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA. | |
| zppequ | compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm) | |
| zppfa | compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to xPPFA with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A. | |
| zpprfs | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution | |
| zppsl | solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA, and vectors b and x. | |
| zppsv | compute the solution to a complex system of linear equations A ∗ X = B, | |
| zppsvx | use the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H to compute the solution to a complex system of linear equations A ∗ X = B, | |
| zpptrf | compute the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format | |
| zpptri | compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPPTRF | |
| zpptrs | solve a system of linear equations A∗X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U∗∗H∗U or A = L∗L∗∗H computed by ZPPTRF | |
| zptcon | compute the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L∗D∗L∗∗H or A = U∗∗H∗D∗U computed by ZPTTRF | |
| zpteqr | compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using DPTTRF and then calling ZBDSQR to compute the singular values of the bidiagonal factor | |
| zptrfs | improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution | |
| zptsl | solve the linear system Ax = b for a symmetric positive definite tridiagonal matrix A and vectors b and x. | |
| zptsv | compute the solution to a complex system of linear equations A∗X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices | |
| zptsvx | use the factorization A = L∗D∗L∗∗H to compute the solution to a complex system of linear equations A∗X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices | |
| zpttrf | compute the factorization of a complex Hermitian positive definite tridiagonal matrix A | |
| zpttrs | solve a system of linear equations A ∗ X = B with a Hermitian positive definite tridiagonal matrix A using the factorization A = U∗∗H∗D∗U or A = L∗D∗L∗∗H computed by ZPTTRF | |
| zqrdc | compute the QR factorization of a general matrix A. It is typical to follow a call to xQRDC with a call to xQRSL to solve Ax = b or to xPODI to compute the determinant of A. | |
| zqrsl | solve the linear system Ax = b for a general matrix A, which has been QR- factored by xQRDC, and vectors b and x. | |
| zrot | apply a plane rotation, where the cos (C) is real and the sin (S) is complex, and the vectors CX and CY are complex | |
| zrotg | Construct a Given’s plane rotation | |
| zscal | Compute y := alpha ∗ y | |
| zsico | compute the UDU factorization and condition number of a symmetric matrix A. If the condition number is not needed then xSIFA is slightly faster. It is typical to follow a call to xSICO with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A. | |
| zsidi | compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA. | |
| zsifa | compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to xSIFA with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A. | |
| zsisl | solve the linear system Ax = b for a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA, and vectors b and x. | |
| zspco | compute the UDU factorization and condition number of a symmetric matrix A in packed storage. If the condition number is not needed then xSPFA is slightly faster. It is typical to follow a call to xSPCO with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A. | |
| zspcon | estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by ZSPTRF | |
| zspdi | compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA. | |
| zspfa | compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to xSPFA with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A. | |
| zspmv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y, | |
| zspr | perform the symmetric rank 1 operation A := alpha∗x∗conjg( x’ ) + A, | |
| zsprfs | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution | |
| zspsl | solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA, and vectors b and x. | |
| zspsv | compute the solution to a complex system of linear equations A ∗ X = B, | |
| zspsvx | use the diagonal pivoting factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T to compute the solution to a complex system of linear equations A ∗ X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices | |
| zsptrf | compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method | |
| zsptri | compute the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by ZSPTRF | |
| zsptrs | solve a system of linear equations A∗X = B with a complex symmetric matrix A stored in packed format using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by ZSPTRF | |
| zstedc | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method | |
| zstein | compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration | |
| zsteqr | compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method | |
| zsvdc | compute the singular value decomposition of a general matrix A. | |
| zswap | Exchange vectors x and y. | |
| zsycon | estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by ZSYTRF | |
| zsymm | perform one of the matrix-matrix operations C := alpha∗A∗B + beta∗C or C := alpha∗B∗A + beta∗C | |
| zsymv | perform the matrix-vector operation y := alpha∗A∗x + beta∗y, | |
| zsyr | perform the symmetric rank 1 operation A := alpha∗x∗( x’ ) + A, | |
| zsyr2k | perform one of the symmetric rank 2k operations C := alpha∗A∗B’ + alpha∗B∗A’ + beta∗C or C := alpha∗A’∗B + alpha∗B’∗A + beta∗C | |
| zsyrfs | improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution | |
| zsyrk | perform one of the symmetric rank k operations C := alpha∗A∗A’ + beta∗C or C := alpha∗A’∗A + beta∗C | |
| zsysv | compute the solution to a complex system of linear equations A ∗ X = B, | |
| zsysvx | use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A ∗ X = B, | |
| zsytf2 | compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method | |
| zsytrf | compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method | |
| zsytri | compute the inverse of a complex symmetric indefinite matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by ZSYTRF | |
| zsytrs | solve a system of linear equations A∗X = B with a complex symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by ZSYTRF | |
| ztbcon | estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm | |
| ztbmv | perform one of the matrix-vector operations x := A∗x, or x := A’∗x, or x := conjg( A’ )∗x | |
| ztbrfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix | |
| ztbsv | solve one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b | |
| ztbtrs | solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, | |
| ztgevc | compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B) | |
| ztgsja | compute the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B | |
| ztpcon | estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm | |
| ztpmv | perform one of the matrix-vector operations x := A∗x, or x := A’∗x, or x := conjg( A’ )∗x | |
| ztprfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix | |
| ztpsv | solve one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b | |
| ztptri | compute the inverse of a complex upper or lower triangular matrix A stored in packed format | |
| ztptrs | solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, | |
| ztrco | estimate the condition number of a triangular matrix A. It is typical to follow a call to xTRCO with a call to xTRSL to solve Ax = b or to xTRDI to compute the determinant and inverse of A. | |
| ztrcon | estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm | |
| ztrdi | compute the determinant and inverse of a triangular matrix A. | |
| ztrevc | compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T | |
| ztrexc | reorder the Schur factorization of a complex matrix A = Q∗T∗Q∗∗H, so that the diagonal element of T with row index IFST is moved to row ILST | |
| ztrmm | perform one of the matrix-matrix operations B := alpha∗op( A )∗B or B := alpha∗B∗op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A’ or op( A ) = conjg( A’ ) | |
| ztrmv | perform one of the matrix-vector operations x := A∗x, or x := A’∗x, or x := conjg( A’ )∗x | |
| ztrrfs | provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix | |
| ztrsen | reorder the Schur factorization of a complex matrix A = Q∗T∗Q∗∗H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace | |
| ztrsl | solve the linear system Ax = b for a triangular matrix A and vectors b and x. | |
| ztrsm | solve one of the matrix equations op( A )∗X = alpha∗B, or X∗op( A ) = alpha∗B | |
| ztrsna | estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q∗T∗Q∗∗H with Q unitary) | |
| ztrsv | solve one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b | |
| ztrsyl | solve the complex Sylvester matrix equation | |
| ztrti2 | compute the inverse of a complex upper or lower triangular matrix | |
| ztrtri | compute the inverse of a complex upper or lower triangular matrix A | |
| ztrtrs | solve a triangular system of the form A ∗ X = B, A∗∗T ∗ X = B, or A∗∗H ∗ X = B, | |
| ztzrqf | reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations | |
| zung2l | generate an m by n complex matrix Q with orthonormal columns, | |
| zung2r | generate an m by n complex matrix Q with orthonormal columns, | |
| zungbr | generate one of the complex unitary matrices Q or P∗∗H determined by ZGEBRD when reducing a complex matrix A to bidiagonal form | |
| zunghr | generate a complex unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by ZGEHRD | |
| zungl2 | generate an m-by-n complex matrix Q with orthonormal rows, | |
| zunglq | generate an M-by-N complex matrix Q with orthonormal rows, | |
| zungql | generate an M-by-N complex matrix Q with orthonormal columns, | |
| zungqr | generate an M-by-N complex matrix Q with orthonormal columns, | |
| zungr2 | generate an m by n complex matrix Q with orthonormal rows, | |
| zungrq | generate an M-by-N complex matrix Q with orthonormal rows, | |
| zungtr | generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by ZHETRD | |
| zunm2l | overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’, | |
| zunm2r | overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’, | |
| zunmbr | VECT = ’Q’, ZUNMBR overwrites the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| zunmhr | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| zunml2 | overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’, | |
| zunmlq | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| zunmql | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| zunmqr | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| zunmr2 | overwrite the general complex m-by-n matrix C with Q ∗ C if SIDE = ’L’ and TRANS = ’N’, or Q’∗ C if SIDE = ’L’ and TRANS = ’C’, or C ∗ Q if SIDE = ’R’ and TRANS = ’N’, or C ∗ Q’ if SIDE = ’R’ and TRANS = ’C’, | |
| zunmrq | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| zunmtr | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |
| zupgtr | generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by ZHPTRD using packed storage | |
| zupmtr | overwrite the general complex M-by-N matrix C with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’ | |