spofa(3P)

NAME

spofa - compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to xPOFA with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A.

SYNOPSIS

CALL DPOFA (DA, LDA, N, INFO)

CALL SPOFA (SA, LDA, N, INFO)

CALL ZPOFA (ZA, LDA, N, INFO)

CALL CPOFA (CA, LDA, N, INFO)

void dpofa(double ∗da, long int lda, long int n, long int ∗info)

void spofa(float ∗sa, long int lda, long int n, long int ∗info)

void cpofa(complex ∗ca, long int lda, long int n, long int ∗info)

void zpofa(doublecomplex ∗za, long int lda, long int n,
long int ∗info)

ARGUMENTS

xAOn entry, the upper triangle of the matrix A.
On exit, a Cholesky factorization of the matrix A. The strict lower triangle of A is not referenced.

LDALeading dimension of the array A as specified in a dimension
or type statement. LDA >= max(1,N).

NOrder of the matrix A. N >= 0.

INFOOn exit:
INFO = 0Subroutine completed normally.
INFO > 0Returns a value k if the leading minor of order k is not positive definite.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           LDA, N
      PARAMETER        (N = 5)
      PARAMETER        (LDA = N)
C
      DOUBLE PRECISION A(LDA,N), B(N)
      INTEGER           ICOL, INFO, IROW
C
      EXTERNAL          DPOFA, DPOSL
C
C     Initialize the array A to store in symmetric storage mode the
C     matrix A shown below. Initialize the array B to store the vector
C     B shown below.
C
C          5 4 3 2 1        120
C          4 5 4 3 2         60
C     A = 3 4 5 4 3    b = 40
C          2 3 4 5 4         60
C          1 2 3 4 5        120
C
      DATA A / 5.0D0, 4∗8D8, 4.0D0, 5.0D0, 3∗8D8, 3.0D0, 4.0D0, 5.0D0,
     $         2∗8D8, 2.0D0, 3.0D0, 4.0D0, 5.0D0, 1∗8D8, 1.0D0, 2.0D0,
     $         3.0D0, 4.0D0, 5.0D0 /
      DATA B / 1.2D2, 6.0D1, 4.0D1, 6.0D1, 1.2D2 /
C
      PRINT 1000
      DO 100, IROW = 1, N
        PRINT 1010, (A(ICOL,IROW), ICOL = 1, IROW),
     $              (A(IROW,ICOL), ICOL = IROW + 1, N)
100 CONTINUE
      PRINT 1020
      PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, N)
      PRINT 1030
      PRINT 1040, B
      CALL DPOFA (A, LDA, N, INFO)
      IF (INFO .EQ. 0) THEN
        CALL DPOSL (A, LDA, N, B)
        PRINT 1050
        PRINT 1040, B
      ELSE
        PRINT 1060
      END IF
C
1000 FORMAT (1X, ’A in full form:’)
1010 FORMAT (5(3X, F7.3))
1020 FORMAT (/1X, ’A in symmetric form: (∗ in unused entries)’)
1030 FORMAT (/1X, ’b:’)
1040 FORMAT (3X, F7.3)
1050 FORMAT (/1X, ’A∗∗(-1) ∗ b:’)
1060 FORMAT (/1X, ’A is not positive definite.’)
C
      END

SAMPLE OUTPUT

A in full form:
     5.000     4.000     3.000     2.000     1.000
     4.000     5.000     4.000     3.000     2.000
     3.000     4.000     5.000     4.000     3.000
     2.000     3.000     4.000     5.000     4.000
     1.000     2.000     3.000     4.000     5.000

A in symmetric form: (∗ in unused entries)
     5.000     4.000     3.000     2.000     1.000
   ∗∗∗∗∗∗∗     5.000     4.000     3.000     2.000
   ∗∗∗∗∗∗∗   ∗∗∗∗∗∗∗     5.000     4.000     3.000
   ∗∗∗∗∗∗∗   ∗∗∗∗∗∗∗   ∗∗∗∗∗∗∗     5.000     4.000
   ∗∗∗∗∗∗∗   ∗∗∗∗∗∗∗   ∗∗∗∗∗∗∗   ∗∗∗∗∗∗∗     5.000

b:
   120.000
    60.000
    40.000
    60.000
   120.000

A∗∗(-1) ∗ b:
    50.000
   -20.000
   -20.000
   -20.000
    50.000