Cholesky Factorization of a Symmetric Positive Definite Matrix in Banded Storage

Calling Sequence

CALL DPBFA	(DA, LDA, N, NDIAG, INFO)
CALL SPBFA	(SA, LDA, N, NDIAG, INFO)
CALL ZPBFA	(ZA, LDA, N, NDIAG, INFO)
CALL CPBFA	(CA, LDA, N, NDIAG, INFO)
void dpbfa	(double *da, int lda, int n, int ndiag, int *info)
void spbfa	(float *sa, int lda, int n, int ndiag, int *info)
void zpbfa	(doublecomplex *za, int lda, int n, int ndiag, int *info)
void cpbfa	(complex *ca, int lda, int n, int ndiag, int *info)

Arguments

xA	On entry, the upper triangle of the matrix A. On exit, a Cholesky factorization of the matrix A.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA NDIAG + 1.
N	Order of the matrix A. N 0.
NDIAG	Number of diagonals. N-1 NDIAG 0 but if N = 0 then NDIAG = 0.
INFO	On exit:
	INFO = 0	Subroutine completed normally.
	INFO > 0	Returns a value of k if the leading minor of order k is not positive definite.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDA, N, NDIAG

PARAMETER (N = 4)

PARAMETER (NDIAG = 1)

PARAMETER (LDA = NDIAG + 1)

C

DOUBLE PRECISION A(LDA,N), B(N)

INTEGER ICOL, INFO, IROW

C

EXTERNAL DPBFA, DPBSL

C

C Initialize the array A to store in banded storage mode

C the matrix A shown below. Initialize the array B to

C store the vector B shown below.

C

C 2 -1 0 0 60

C A = -1 2 -1 0 b = 60

C 0 -1 2 -1 60

C 0 0 -1 2 60

C

DATA A / 8D8, 2.0D0, -1.0D0, 2.0D0, -1.0D0, 2.0D0, -1.0D0,

$ 2.0D0 /

DATA B / 4*6.0D1 /

C

PRINT 1000

PRINT 1010, A(2,1), A(1,2)

PRINT 1010, A(3,1), A(2,2), A(1,3)

PRINT 1020, A(3,2), A(2,3), A(1,4)

PRINT 1030, A(3,3), A(2,4)

PRINT 1040

PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, LDA)

PRINT 1050

PRINT 1060, B

CALL DPBFA (A, LDA, N, NDIAG, INFO)

IF (INFO .EQ. 0) THEN

CALL DPBSL (A, LDA, N, NDIAG, B)

PRINT 1070

PRINT 1060, B

ELSE

PRINT 1080

END IF

C

1000 FORMAT (1X, 'A in full form:')

1010 FORMAT (4(3X, F5.1))

1020 FORMAT (8X, 3(3X, F5.1))

1030 FORMAT (16X, 3(3X, F5.1))

1040 FORMAT (/1X, 'A in banded form: (* in unused entries)')

1050 FORMAT (/1X, 'b:')

1060 FORMAT (3X, F5.1)

1070 FORMAT (/1X, 'A**(-1) * b:')

1080 FORMAT (/1X, 'A is not positive definite.')

C

END

Sample Output

A in full form:
2.0 -1.0
-1.0 2.0 -1.0
-1.0 2.0 -1.0
-1.0 2.0
A in banded form: (* in unused entries)
***** -1.0 -1.0 -1.0
2.0 2.0 2.0 2.0
b:
60.0
60.0
60.0
60.0
A**(-1) * b:
120.0
180.0
180.0
120.0