zhpco(l) — SunSoft Performance Library

NAME

zhpco - compute the UDU factorization and condition number of a Hermitian matrix A in packed storage. If the condition number is not needed then xHPFA is slightly faster. It is typical to follow a call to xHPCO with a call to xHPSL to solve Ax = b or to xHPDI to compute the determinant, inverse, and inertia of A.

SYNOPSIS

CALL ZHPCO (ZA, N, IPIVOT, DRCOND, ZWORK)

CALL CHPCO (CA, N, IPIVOT, SRCOND, CWORK)

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.

xRCONDOn exit, an estimate of the reciprocal condition number of
A. 0.0 <= RCOND <= 1.0. As the value of RCOND gets smaller, operations with A such as solving Ax = b may become less stable. If RCOND satisfies RCOND + 1.0 = 1.0 then A may be singular to working precision.

xWORKScratch array with a dimension of N.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER    LENGTA, N
      PARAMETER (N = 3)
      PARAMETER (LENGTA = (N ∗ N + N) / 2)
C
      REAL       RCOND
      COMPLEX    A(LENGTA), B(N), WORK(N)
      INTEGER    IPIVOT(N)
C
      EXTERNAL   CHPCO, 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 CHPCO (A, N, IPIVOT, RCOND, WORK)
      PRINT 1040, RCOND
      IF ((RCOND + 1.0) .EQ. 1.0) THEN
        PRINT 1050
      END IF
      CALL CHPSL (A, N, IPIVOT, B)
      PRINT 1060
      PRINT 1030, B
C
1000 FORMAT (1X, ’A in full form:’)
1010 FORMAT (3(3X, ’(’, F4.1, ’,’, F4.1, ’)’))
1020 FORMAT (/1X, ’b:’)
1030 FORMAT (3X, ’(’, F6.1, ’,’, F6.1, ’)’)
1040 FORMAT (/1X, ’Reciprocal condition number of A:’, F6.3)
1050 FORMAT (1X, ’A may be singular to working precision.’)
1060 FORMAT (/1X, ’A∗∗(-1) ∗ b:’)
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)

Reciprocal condition number of A: 0.001

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