ssisl(3P)

NAME

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.

SYNOPSIS

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

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

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