Solution to a Linear System in a UDU- or LDL-Factored Symmetric Matrix in Packed Storage

Calling Sequence

CALL DSPTRS	(UPLO, N, NRHS, DA, IPIVOT, DB, LDB, INFO)
CALL SSPTRS	(UPLO, N, NRHS, SA, IPIVOT, SB, LDB, INFO)
CALL ZSPTRS	(UPLO, N, NRHS, ZA, IPIVOT, ZB, LDB, INFO)
CALL CSPTRS	(UPLO, N, NRHS, CA, IPIVOT, CB, LDB, INFO)
void dsptrs	(char uplo, int n, int nrhs, double *da, int *ipivot, double *db, int ldb, int *info)
void ssptrs	(char uplo, int n, int nrhs, float *sa, int *ipivot, float *sb, int ldb, int *info)
void zsptrs	(char uplo, int n, int nrhs, doublecomplex *za, int *ipivot, doublecomplex *zb, int ldb, int *info)
void csptrs	(char uplo, int n, int nrhs, complex *ca, int *ipivot, complex *cb, int ldb, 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.
NRHS	Number of right-hand sides, equal to the number of columns of the matrix B. NRHS 0.
xA	UDU or LDL factorization of the matrix A, as computed by xSPTRF. The dimension of xA is (N × N + N) / 2.
IPIVOT	Pivot indices as computed by xSPTRF.
xB	On entry, the N×NRHS right-hand side matrix B. On exit, the N×NRHS solution matrix X.
LDB	Leading dimension of the array B as specified in a dimension or type statement. LDB max(1, N).
INFO	On exit:
	INFO = 0	Subroutine completed normally.
	INFO < 0	The ith argument, where i = |INFO|, had an illegal value.

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 the array B to store the right hand side vector b shown

C 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 2

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 1

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