sppfa(3P)

NAME

sppfa - compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to xPPFA with a call to xPPSL to solve Ax = b or to xPPDI to compute the determinant and inverse of A.

SYNOPSIS

SUBROUTINE DPPFA (DA, N, INFO)

SUBROUTINE SPPFA (SA, N, INFO)

SUBROUTINE ZPPFA (ZA, N, INFO)

SUBROUTINE CPPFA (CA, N, INFO)

#include <sunperf.h>

void dppfa(double ∗dap, int n, int ∗info) ;

void sppfa(float ∗sap, int n, int ∗info) ;

void zppfa(doublecomplex ∗zap, int n, int ∗info) ;

void cppfa(complex ∗cap, int n, int ∗info) ;

ARGUMENTS

xA On entry, the upper triangle of the matrix A. On exit, a Cholesky factorization of the matrix A.

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

INFO On exit:
INFO = 0Subroutine completed normally.
INFO > 0Returns a value k if U(k,k) = 0 to indicate that xGESL will divide by zero if called.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           LENGTA, N
      PARAMETER        (N = 4)
      PARAMETER        (LENGTA = (N ∗ N + N) / 2)
C
      DOUBLE PRECISION A(LENGTA), B(N)
      INTEGER           INFO
C
      EXTERNAL          DPPFA, DPPSL
C
C     Initialize the array A to store in packed symmetric storage
C     mode the matrix A shown below. Initialize the array B to store
C     the vector B shown below.
C
C         4 3 2 1        30
C     A = 3 4 3 2    b = 20
C         2 3 4 3        20
C         1 2 3 4        40
C
      DATA A / 4.0D0, 3.0D0, 4.0D0, 2.0D0, 3.0D0, 4.0D0,
     $         1.0D0, 2.0D0, 3.0D0, 4.0D0 /
      DATA B / 6.0D1, 2.0D1, 2.0D1, 6.0D1 /
C
      PRINT 1000
      PRINT 1010, A(1), A(2), A(4), A(7)
      PRINT 1010, A(2), A(3), A(5), A(8)
      PRINT 1010, A(4), A(5), A(6), A(9)
      PRINT 1010, A(7), A(8), A(9), A(10)
      PRINT 1020
      PRINT 1030, B
      CALL DPPFA (A, N, INFO)
      IF (INFO .EQ. 0) THEN
        CALL DPPSL (A, N, B)
        PRINT 1040
        PRINT 1030, B
      ELSE
        PRINT 1050
      END IF
C
1000 FORMAT (1X, ’A in full form:’)
1010 FORMAT (5(3X, F5.1))
1020 FORMAT (/1X, ’b:’)
1030 FORMAT (3X, F5.1)
1040 FORMAT (/1X, ’A∗∗(-1) ∗ b:’)
1050 FORMAT (/1X, ’A is too ill-conditioned.’)
C
      END

SAMPLE OUTPUT

A in full form:
     4.0     3.0     2.0     1.0
     3.0     4.0     3.0     2.0
     2.0     3.0     4.0     3.0
     1.0     2.0     3.0     4.0

b:
    60.0
    20.0
    20.0
    60.0

A∗∗(-1) ∗ b:
    32.0
   -20.0
   -20.0
    32.0