chifa(l) — SunSoft Performance Library

NAME

chifa - compute the UDU factorization of a Hermitian matrix A. It is typical to follow a call to xHIFA with a call to xHISL to solve Ax = b or to xHIDI to compute the determinant, inverse, and inertia of A.

SYNOPSIS

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

CALL CHIFA (CA, LDA, N, IPIVOT, 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 xHISL or xHIDI will divide by zero if called.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER    LDA, N
      PARAMETER (N = 3)
      PARAMETER (LDA = 3)
C
      COMPLEX    A(LDA,N), B(N)
      INTEGER    ICOL, INFO, IPIVOT(N), IROW
C
      EXTERNAL   CHIFA, CHISL
      INTRINSIC CONJG
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          1    1+2i 1+2i         95-180i
C     A = 1+2i   6   -2+6i    b = 545-118i
C         1+2i -2+6i   11         865+ 62i
C
      DATA A / (1.0,0.0), (8E8,8E8), (8E8,8E8),
     $        (1.0,-2.0), (6.0,0.0), (8E8,8E8),
     $        (1.0,-2.0), (6.0,-2.0), (11.0,0.0) /
      DATA B / (95.0,-180.0), (545.0,-118.0), (865.0,62.0) /
C
      PRINT 1000
      DO 100, IROW = 1, N
        PRINT 1010, (CONJG(A(ICOL,IROW)), ICOL = 1, IROW),
     $              (A(IROW,ICOL), ICOL = IROW + 1, N)
100 CONTINUE
      PRINT 1020
      DO 110, IROW = 1, N
        PRINT 1010, (A(IROW,ICOL), ICOL = 1, N)
110 CONTINUE
      PRINT 1030
      PRINT 1040, B
      CALL CHIFA (A, LDA, N, IPIVOT, INFO)
      IF (INFO .EQ. 0) THEN
        CALL CHISL (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, ’(’, F4.1, ’,’, F4.1, ’)’))
1020 FORMAT (/1X, ’A in Hermitian form: (∗ in unused elements)’)
1030 FORMAT (/1X, ’b:’)
1040 FORMAT (3X, ’(’, F6.1, ’,’, F6.1, ’)’)
1050 FORMAT (/1X, ’A∗∗(-1) ∗ b:’)
1060 FORMAT (1X, ’A is singular to working precision.’)
C
      END

SAMPLE OUTPUT

A in full form:
   ( 1.0, 0.0)   ( 1.0,-2.0)   ( 1.0,-2.0)
   ( 1.0, 2.0)   ( 6.0, 0.0)   ( 6.0,-2.0)
   ( 1.0, 2.0)   ( 6.0, 2.0)   (11.0, 0.0)

A in Hermitian form: (∗ in unused elements)
   ( 1.0, 0.0)   ( 1.0,-2.0)   ( 1.0,-2.0)
   (∗∗∗∗,∗∗∗∗)   ( 6.0, 0.0)   ( 6.0,-2.0)
   (∗∗∗∗,∗∗∗∗)   (∗∗∗∗,∗∗∗∗)   (11.0, 0.0)

b:
   ( 95.0,-180.0)
   ( 545.0,-118.0)
   ( 865.0, 62.0)

A∗∗(-1) ∗ b:
   (   5.0,   0.0)
   ( 26.0,   0.0)
   ( 64.0,   0.0)