spodi(3P)

NAME

spodi - compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO, xPOFA, or xQRDC.

SYNOPSIS

CALL DPODI (DA, LDA, N, DDET, JOB)

CALL SPODI (SA, LDA, N, SDET, JOB)

CALL ZPODI (ZA, LDA, N, DDET, JOB)

CALL CPODI (CA, LDA, N, SDET, JOB)

void dpodi(double ∗da, long int lda, long int n, double ∗det,
long int job)

void spodi(float ∗sa, long int lda, long int n, float ∗det,
long int job)

void cpodi(complex ∗ca, long int lda, long int n, float ∗det,
long int job)

void zpodi(doublecomplex ∗za, long int lda,
long int n, double ∗det, long int job)

ARGUMENTS

xAOn entry, the Cholesky factorization of the matrix A, as
computed by xPOCO, xPOFA, or xQRDC. On exit, the inverse of the original matrix A if the inverse was requested, otherwise A is unchanged. 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 original matrix A. N >= 0.

xDETOn exit, the determinant of the matrix A. The determinant is stored as b ∗ (10 ∗∗ expon) where b is stored in DET(1) and expon is stored in DET(2).
1.0 <= |DET(1)| <= 10.0 or DET(1) = 0.0.

JOBDetermines which operation the subroutine will perform:
11 both determinant and inverse
01 inverse only
10 determinant only

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           INVDET, LDA, N
      PARAMETER        (INVDET = 11)
      PARAMETER        (N = 4)
      PARAMETER        (LDA = N)
C
      DOUBLE PRECISION A(LDA,N), DET(2)
      INTEGER           ICOL, INFO, IROW, JOB
C
      EXTERNAL          DPODI, DPOFA
C
C     Initialize the array A to store in symmetric storage mode
C     the matrix A shown below.
C
C         4 3 2 1
C     A = 3 4 3 2
C         2 3 4 3
C         1 2 3 4
C
      DATA A / 4.0D0, 3∗8D8, 3.0D0, 4.0D0, 2∗8D8, 2.0D0, 3.0D0,
     $         4.0D0, 8D8, 1.0D0, 2.0D0, 3.0D0, 4.0D0 /
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)
      CALL DPOFA (A, LDA, N, INFO)
      IF (INFO .EQ. 0) THEN
        JOB = INVDET
        CALL DPODI (A, LDA, N, DET, JOB)
        PRINT 1050
        DO 110, IROW = 1, N
          PRINT 1010, (A(ICOL,IROW), ICOL = 1, IROW),
     $                (A(IROW,ICOL), ICOL = IROW + 1, N)
110   CONTINUE
        PRINT 1060, DET(1) ∗ (10.0D0 ∗∗ DET(2))
      ELSE
        PRINT 1070
      END IF
C
1000 FORMAT (1X, ’A in full form:’)
1010 FORMAT (4(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):’)
1060 FORMAT (/1X, ’The determinant of A is ’, F5.1)
1070 FORMAT (/1X, ’A is not positive definite.’)
C
      END

SAMPLE OUTPUT

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

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

A∗∗(-1):
     0.600    -0.500     0.000     0.100
    -0.500     1.000    -0.500     0.000
     0.000    -0.500     1.000    -0.500
     0.100     0.000    -0.500     0.600

The determinant of A is 20.0