chpfa(3P)

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)

void zhpfa(doublecomplex ∗za, long int n, long int ∗ipivot,
long int ∗info)

void chpfa(complex ∗ca, long int n, long int ∗ipivot,
long int ∗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)