cppco(3P)

NAME

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.

SYNOPSIS

CALL DPPCO (DA, N, DRCOND, DWORK, INFO)

CALL SPPCO (SA, N, SRCOND, SWORK, INFO)

CALL ZPPCO (ZA, N, DRCOND, ZWORK, INFO)

CALL CPPCO (CA, N, SRCOND, CWORK, INFO)

void dppco(double ∗dap, long int n, double ∗drcond, long int ∗info)

void sppco(float ∗sap, long int n, float ∗srcond, long int ∗info)

void zppco(doublecomplex ∗zap, long int n, double ∗drcond, long int
∗info)

void cppco(complex ∗cap, long int n, float ∗srcond, long int ∗info)

ARGUMENTS

xAOn entry, the upper triangle of the matrix A.
On exit, a Cholesky factorization of the matrix A.

NOrder of the matrix A. N ∗ 0.

xRCONDOn exit, an estimate of the reciprocal condition number of A.
0.0 <= RCOND <= 1.0. As the value of RCOND gets smaller, operations with A such as solving Ax = b may become less stable. If RCOND satisfies RCOND + 1.0 = 1.0 then A may be singular to working precision.

xWORKScratch array with a dimension of N.

INFOOn exit:
INFO = 0Subroutine completed normally.
INFO ∗ 0Returns a value k if the leading minor of order k is not positive definite.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           LENGTA, N
      PARAMETER        (N = 4)
      PARAMETER        (LENGTA = (N ∗ N + N) / 2)
C
      DOUBLE PRECISION A(LENGTA), B(N), RCOND, WORK(N)
      INTEGER           INFO
C
      EXTERNAL          DPPCO, DPPSL
C
C     Initialize the array A to store in packed symmetric storage
C     mode the matrix A shown below. Initialize the array B to store
C     the matrix B shown below.
C
C         4 3 2 1        60
C     A = 3 4 3 2    b = 20
C         2 3 4 3        20
C         1 2 3 4        60
C
      DATA A / 4.0D0, 3.0D0, 4.0D0, 2.0D0, 3.0D0, 4.0D0,
     $         1.0D0, 2.0D0, 3.0D0, 4.0D0 /
      DATA B / 6.0D1, 2.0D1, 2.0D1, 6.0D1 /
C
      PRINT 1000
      PRINT 1010, A(1), A(2), A(4), A(7)
      PRINT 1010, A(2), A(3), A(5), A(8)
      PRINT 1010, A(4), A(5), A(6), A(9)
      PRINT 1010, A(7), A(8), A(9), A(10)
      PRINT 1020
      PRINT 1030, B
      CALL DPPCO (A, N, RCOND, WORK, INFO)
      IF ((RCOND + 1.0D0) .EQ. RCOND) THEN
        PRINT 1040
      END IF
      CALL DPPSL (A, N, B)
      PRINT 1050, RCOND
      PRINT 1060
      PRINT 1030, B
C
1000 FORMAT (1X, ’A in full form:’)
1010 FORMAT (5(3X, F7.3))
1020 FORMAT (/1X, ’b:’)
1030 FORMAT (3X, F7.3)
1040 FORMAT (1X, ’A may be singular to working precision.’)
1050 FORMAT (/1X, ’Reciprocal condition of A:’, F5.2)
1060 FORMAT (/1X, ’A∗∗(-1) ∗ b:’)
C
      END

SAMPLE OUTPUT

A in full form:
     4.000     3.000     2.000     1.000
     3.000     4.000     3.000     2.000
     2.000     3.000     4.000     3.000
     1.000     2.000     3.000     4.000

b:
    60.000
    20.000
    20.000
    60.000

Reciprocal condition of A: 0.04

A∗∗(-1) ∗ b:
    32.000
   -20.000
   -20.000
    32.000