zhpsl(3P)

NAME

zhpsl - solve the linear system Ax = b for a Hermitian matrix A in packed storage, which has been UDU-factored by xHPCO or xHPFA, and vectors b and x.

SYNOPSIS

SUBROUTINE ZHPSL (ZA, N, IPIVOT, ZB)

SUBROUTINE CHPSL (CA, N, IPIVOT, CB)

#include <sunperf.h>

void zhpsl(doublecomplex ∗za, int n, int ∗ipivot , doublecomplex ∗b) ;

void chpsl(complex ∗ca, int n, int ∗ipivot , complex ∗b) ;

ARGUMENTS

xA On entry, the UDU factorization of the matrix A, as computed xHPCO or xHPFA.

N Order of the matrix A. N >= 0.

IPIVOT Pivot vector as computed by xHPCO or xHPFA.

xB On entry, the right-hand side vector b. On exit, the solution vector x.

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
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)