csisl(3P)

NAME

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.

SYNOPSIS

SUBROUTINE DSISL (DA, LDA, N, IPIVOT, DB)

SUBROUTINE SSISL (SA, LDA, N, IPIVOT, SB)

SUBROUTINE ZSISL (ZA, LDA, N, IPIVOT, ZB)

SUBROUTINE CSISL (CA, LDA, N, IPIVOT, CB)

#include <sunperf.h>

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

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

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

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

ARGUMENTS

xA UDU factorization of the matrix A, as computed by xSICO or xSIFA.

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.

IPIVOT Pivot vector as computed by xSICO or xSIFA.

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, IPIVOT(N), IROW
C
      EXTERNAL          DSICO, DSISL
C
C     Initialize the array A to store the matrix A shown below.
C     Initialize the array B to store the vector B shown below.
C
C         -.5   -.5   -.5   -.5        12
C     A = -.5 -1.5 -1.5 -1.5    b = 6
C         -.5 -1.5 -2.5 -2.5         6
C         -.5 -1.5 -2.5 -3.5        12
C
      DATA A / 4∗-5.0D-1, -5.0D-1, 3∗-1.5D0, -5.0D-1,
     $         -1.5D0, 2∗-2.5D0, -5.0D-1, -1.5D0, -2.5D0, -3.5D0 /
      DATA B / 1.2D1, 6.0D0, 6.0D0, 1.2D1 /
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 DSICO (A, LDA, N, IPIVOT, RCOND, WORK)
      IF ((RCOND + 1.0D0) .EQ. RCOND) THEN
        PRINT 1050
      END IF
      CALL DSISL (A, LDA, N, IPIVOT, B)
      PRINT 1060
      PRINT 1040, B
C
1000 FORMAT (1X, ’A in full form:’)
1010 FORMAT (4(3X, F5.1))
1020 FORMAT (/1X, ’A in symmetric form: (∗ in unused elements)’)
1030 FORMAT (/1X, ’b:’)
1040 FORMAT (3X, F5.1)
1050 FORMAT (/1X, ’A may be singular to working precision.’)
1060 FORMAT (/1X, ’A∗∗(-1) ∗ b:’)
C
      END

SAMPLE OUTPUT

A in full form:
    -0.5    -0.5    -0.5    -0.5
    -0.5    -1.5    -1.5    -1.5
    -0.5    -1.5    -2.5    -2.5
    -0.5    -1.5    -2.5    -3.5

A in symmetric form: (∗ in unused elements)
    -0.5    -0.5    -0.5    -0.5
    -0.5    -1.5    -1.5    -1.5
    -0.5    -1.5    -2.5    -2.5
    -0.5    -1.5    -2.5    -3.5

b:
    12.0
     6.0
     6.0
    12.0

A∗∗(-1) ∗ b:
   -30.0
     6.0
     6.0
    -6.0