chpfa(l) — SunSoft Performance Library

NAME

chpfa - compute the UDU factorization of a Hermitian matrix A in packed storage. It is typical to follow a call to xHPFA with a call to xHPSL to solve Ax = b or to xHPDI to compute the determinant, inverse, and inertia of A.

SYNOPSIS

CALL ZHPFA (ZA, N, IPIVOT, INFO)

CALL CHPFA (CA, N, IPIVOT, INFO)

ARGUMENTS

xAOn entry, the upper triangle of the matrix A.
On exit, a UDU factorization of the matrix A.

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 xHPSL or xHPDI will divide by zero if called.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER    LENGTA, N
      PARAMETER (N = 3)
      PARAMETER (LENGTA = (N ∗ N + N) / 2)
C
      COMPLEX    A(LENGTA), B(N)
      INTEGER    INFO, IPIVOT(N)
C
      EXTERNAL   CHPFA, CHPSL
      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), (1.0,-2.0), (6.0,0.0),
     $         (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
      PRINT 1010, A(1), A(2), A(4)
      PRINT 1010, CONJG(A(2)), A(3), A(5)
      PRINT 1010, CONJG(A(4)), CONJG(A(5)), A(6)
      PRINT 1020
      PRINT 1030, B
      CALL CHPFA (A, N, IPIVOT, INFO)
      IF (INFO .EQ. 0) THEN
        CALL CHPSL (A, N, IPIVOT, B)
        PRINT 1040
        PRINT 1030, B
      ELSE
        PRINT 1050
      END IF
C
1000 FORMAT (1X, ’A in full form:’)
1010 FORMAT (4(: 3X, ’(’, F4.1, ’,’, F4.1, ’)’))
1020 FORMAT (/1X, ’b:’)
1030 FORMAT (3X, ’(’, F6.1, ’,’, F6.1, ’)’)
1040 FORMAT (/1X, ’A∗∗(-1) ∗ b:’)
1050 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)

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)