csifa(3P)

NAME

csifa - compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to xSIFA with a call to xSISL to solve Ax = b or to xSIDI to compute the determinant, inverse, and inertia of A.

SYNOPSIS

CALL DSIFA (DA, LDA, N, IPIVOT, INFO)

CALL SSIFA (SA, LDA, N, IPIVOT, INFO)

CALL ZSIFA (ZA, LDA, N, IPIVOT, INFO)

CALL CSIFA (CA, LDA, N, IPIVOT, INFO)

void dsifa(double ∗da, long int lda, long int n, long int ∗kpvt,
long int ∗info)

void ssifa(float ∗sa, long int lda, long int n, long int ∗kpvt,
long int ∗info)

void zsifa(doublecomplex ∗za, long int lda, long int n,
long int ∗kpvt, long int ∗info)

void csifa(complex ∗ca, long int lda, long int n,
long int ∗kpvt, long int ∗info)

ARGUMENTS

xAOn entry, the upper triangle of the matrix A.
On exit, a UDU factorization of the matrix A. The strict lower triangle of A is not referenced.

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.

IPIVOTOn exit, a vector of pivot indices.

INFOOn exit:
INFO = 0Subroutine completed normally.
INFO > 0Returns a value k if the kth pivot block is singular to indicate that xSISL or xSIDI will divide by zero if called.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           LDA, N
      PARAMETER        (N = 4)
      PARAMETER        (LDA = N)
C
      DOUBLE PRECISION A(LDA,N), B(N)
      INTEGER           ICOL, INFO, IPIVOT(N), IROW
C
      EXTERNAL          DSIFA, 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         6
C     A = -.5 -1.5 -1.5 -1.5    b = 12
C         -.5 -1.5 -2.5 -2.5         6
C         -.5 -1.5 -2.5 -3.5        12
C
      DATA A / -5.0D-1, 3∗8D8, -5.0D-1, -1.5D0, 2∗8D8, -5.0D-1,
     $         -1.5D0, -2.5D0, 8D8, -5.0D-1, -1.5D0, -2.5D0, -3.5D0 /
      DATA B / 6.0D0, 1.2D1, 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 DSIFA (A, LDA, N, IPIVOT, INFO)
      IF (INFO .EQ. 0) THEN
        CALL DSISL (A, LDA, N, IPIVOT, B)
        PRINT 1050
        PRINT 1040, B
      ELSE
        PRINT 1060
      END IF
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∗∗(-1) ∗ b:’)
1060 FORMAT (/1X, ’A is too poorly conditioned.’)
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
   ∗∗∗∗∗    -1.5    -1.5    -1.5
   ∗∗∗∗∗   ∗∗∗∗∗    -2.5    -2.5
   ∗∗∗∗∗   ∗∗∗∗∗   ∗∗∗∗∗    -3.5

b:
     6.0
    12.0
     6.0
    12.0

A∗∗(-1) ∗ b:
    -6.0
   -12.0
    12.0
    -6.0