Cholesky Factorization of a Symmetric Positive Definite Matrix in Packed Storage

Calling Sequence

CALL DPPTRF	(UPLO, N, DA, INFO)
CALL SPPTRF	(UPLO, N, SA, INFO)
CALL ZPPTRF	(UPLO, N, ZA, INFO)
CALL CPPTRF	(UPLO, N, CA, INFO)
void dpptrf	(char uplo, int n, double *da, int *info)
void spptrf	(char uplo, int n, float *sa, int *info)
void zpptrf	(char uplo, int n, doublecomplex *za, int *info)
void cpptrf	(char uplo, int n, complex *ca, int *info)

Arguments

UPLO	Indicates whether xA contains the upper or lower triangle of the matrix. The legal values for UPLO are listed below. Any values not listed below are illegal.
	'U' or 'u'	xA contains the upper triangle.
	'L' or 'l'	xA contains the lower triangle.
N	Order of the matrix A. N 0.
xA	On entry, the upper or lower triangle of the matrix A. The dimension of xA is (N × N + N) / 2. On exit, a Cholesky factorization of the matrix A.
INFO	On exit:
	INFO = 0	Subroutine completed normally.
	INFO < 0	The ith argument, where i = |INFO|, had an illegal value.
	INFO > 0	The leading minor of order i of A, where i = INFO, is not positive definite. The factorization could not be completed.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDA, LDB, N, NRHS

PARAMETER (N = 4)

PARAMETER (LDA = (N * (N + 1)) / 2)

PARAMETER (LDB = N)

PARAMETER (NRHS = 1)

C

DOUBLE PRECISION A(LDA), B(LDB,NRHS)

INTEGER INFO

C

EXTERNAL DPPTRF, DPPTRS

INTRINSIC ABS

C

C Initialize the array A to store in symmetric form the

C 4x4 symmetric positive definite coefficient matrix A

C shown below. Initialize the array B to store the right

C hand side vector b shown below.

C

C 2 -1 0 0 6

C A = -1 2 -1 0 b = 12

C 0 -1 2 -1 12

C 0 0 -1 2 6

C

DATA A / 2.0D0, -1.0D0, 2.0D0, 0.0D0, -1.0D0, 2.0D0,

$ 0.0D0, 0.0D0, -1.0D0, 2.0D0 /

DATA B / 6.0D0, 1.2D1, 1.2D1, 6.0D0 /

C

C Print the initial values of the arrays.

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

C

C Cholesky factor A.

C

CALL DPPTRF ('UPPER TRIANGLE OF A STORED', N, A, INFO)

IF (INFO .NE. 0) THEN

PRINT 1040, INFO

STOP 1

END IF

C

C Use the factored form of A to solve Ax=b then print

C the result.

C

CALL DPPTRS ('UPPER TRIANGLE OF A STORED', N, NRHS, A,

$ B, LDB, INFO)

IF (INFO .NE. 0) THEN

PRINT 1050, ABS(INFO)

STOP 2

END IF

PRINT 1060

PRINT 1030, B

C

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

1010 FORMAT (4(3X, F6.3))

1020 FORMAT (/1X, 'b:')

1030 FORMAT (1X, F6.2)

1040 FORMAT (1X, 'Error factoring A, INFO = ', I5)

1050 FORMAT (1X, 'Illegal argument to DPPTRS, argument #', I1)

1060 FORMAT (/1X, 'x:')

C

END

Sample Output

A in full form:
2.000 -1.000 0.000 0.000
-1.000 2.000 -1.000 0.000
0.000 -1.000 2.000 -1.000
0.000 0.000 -1.000 2.000
b:
6.00
12.00
12.00
6.00
x:
18.00
30.00
30.00
18.00