cposl(3P)

NAME

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.

SYNOPSIS

SUBROUTINE DPOSL (DA, LDA, N, DB)

SUBROUTINE SPOSL (SA, LDA, N, SB)

SUBROUTINE ZPOSL (ZA, LDA, N, ZB)

SUBROUTINE CPOSL (CA, LDA, N, CB)

#include <sunperf.h>

void dposl(double ∗da, int lda, int n, double ∗b) ;

void sposl(float ∗sa, int lda, int n, float ∗b) ;

void cposl(complex ∗ca, int lda, int n, complex ∗b) ;

void zposl(doublecomplex ∗za, int lda, int n, doublecomplex ∗b) ;

ARGUMENTS

xA Cholesky factorization of the matrix A, as computed by xPOCO or xPOFA.

LDA Leading dimension of the array A as specified in a dimension or type statement. LDA >= max(1,N).

N Order of the matrix A. N >= 0.

xB On entry, the right-hand side vector b. On exit, the solution vector x.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           LDA, N
      PARAMETER        (N = 4)
      PARAMETER        (LDA = N)
C
      DOUBLE PRECISION A(LDA,N), B(N), RCOND, WORK(N)
      INTEGER           ICOL, INFO, IROW
C
      EXTERNAL          DPOCO, DPOSL
C
C     Initialize the array A to store in symmetric storage mode
C     the matrix A shown below. Initialize the array B to store
C     the vector B shown below.
C
C         4 3 2 1        20
C     A = 3 4 3 2    b = 20
C         2 3 4 3        20
C         1 2 3 4        20
C
      DATA A / 4.0D0, 3∗8D8, 3.0D0, 4.0D0, 2∗8D8, 2.0D0, 3.0D0, 4.0D0,
     $         8D8, 1.0D0, 2.0D0, 3.0D0, 4.0D0 /
      DATA B / 4∗2.0D1 /
C
      PRINT 1000
      DO 100, IROW = 1, N
        PRINT 1010, (A(ICOL,IROW), ICOL = 1, IROW),
     $              (A(IROW,ICOL), ICOL = IROW + 1, N)
100 CONTINUE
      PRINT 1020
      PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, N)
      PRINT 1030
      PRINT 1040, B
      CALL DPOCO (A, LDA, N, RCOND, WORK, INFO)
      IF ((RCOND + 1.0D0) .EQ. 1.0D0) THEN
        PRINT 1050
      END IF
      CALL DPOSL (A, LDA, N, B)
      PRINT 1060
      PRINT 1040, B
C
1000 FORMAT (1X, ’A in full form:’)
1010 FORMAT (4(3X, F7.3))
1020 FORMAT (/1X, ’A in symmetric form: (∗ in unused entries)’)
1030 FORMAT (/1X, ’b:’)
1040 FORMAT (3X, F7.3)
1050 FORMAT (/1X, ’A may be singular to working precision.’)
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

A in symmetric form: (∗ in unused entries)
     4.000     3.000     2.000     1.000
   ∗∗∗∗∗∗∗     4.000     3.000     2.000
   ∗∗∗∗∗∗∗   ∗∗∗∗∗∗∗     4.000     3.000
   ∗∗∗∗∗∗∗   ∗∗∗∗∗∗∗   ∗∗∗∗∗∗∗     4.000

b:
    20.000
    20.000
    20.000
    20.000

A∗∗(-1) ∗ b:
     4.000
     0.000
     0.000
     4.000