zsisl(3P)

NAME

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.

SYNOPSIS

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

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

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

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

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

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

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

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

ARGUMENTS

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

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

NOrder of the matrix A. N >= 0.

IPIVOTPivot vector as computed by xSICO or xSIFA.

xBOn 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