zppfa(3P)

NAME

zppfa - 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

CALL DPPFA (DA, N, INFO)

CALL SPPFA (SA, N, INFO)

CALL ZPPFA (ZA, N, INFO)

CALL CPPFA (CA, N, INFO)

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

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

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

void cppfa(complex ∗cap, 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.

NOrder of the matrix A. N >= 0.

INFOOn 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