UDU or LDL Factorization of a Symmetric Matrix in Packed Storage

Calling Sequence

CALL DSPTRF	(UPLO, N, DA, IPIVOT, INFO)
CALL SSPTRF	(UPLO, N, SA, IPIVOT, INFO)
CALL ZSPTRF	(UPLO, N, ZA, IPIVOT, INFO)
CALL CSPTRF	(UPLO, N, CA, IPIVOT, INFO)
void dsptrf	(char uplo, int n, double *da, int *ipivot, int *info)
void ssptrf	(char uplo, int n, float *sa, int *ipivot, int *info)
void zsptrf	(char uplo, int n, doublecomplex *za, int *ipivot, int *info)
void csptrf	(char uplo, int n, complex *ca, int *ipivot, 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 UDU or LDL factorization of the matrix A.
IPIVOT	On exit, an N-element array containing details of the row interchanges and block structure of D.
INFO	On exit:
	INFO = 0	Subroutine completed normally.
	INFO < 0	The ith argument, where i = |INFO|, had an illegal value.
	INFO > 0	D(i,i), where i = INFO, is exactly zero, and D is therefore singular. The factorization is complete, but division by zero will occur if this factorization is used to solve a linear system.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDA, LDB, N, NRHS

PARAMETER (N = 4)

PARAMETER (NRHS = 1)

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

PARAMETER (LDB = N)

C

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

INTEGER INFO, IPIVOT(N)

C

EXTERNAL DSPTRF, DSPTRS

INTRINSIC ABS

C

C Initialize the array A to store in packed symmetric form the

C 4x4 symmetric coefficient matrix A shown below. Initialize

C array B to store the right 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 LDL factor A.

C

CALL DSPTRF ('UPPER TRIANGLE OF A STORED', N, A, IPIVOT,

$ 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 DSPTRS ('UPPER TRIANGLE OF A STORED', N, NRHS, A,

$ IPIVOT, 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:')

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 DSPTRS, argument #', I1)

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

C

END

Sample Output

A:
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