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

Calling Sequence

CALL DSYTRS	(UPLO, N, NRHS, DA, LDA, IPIVOT, DB, LDB, INFO)
CALL SSYTRS	(UPLO, N, NRHS, SA, LDA, IPIVOT, SB, LDB, INFO)
CALL ZSYTRS	(UPLO, N, NRHS, ZA, LDA, IPIVOT, ZB, LDB, INFO)
CALL CSYTRS	(UPLO, N, NRHS, CA, LDA, IPIVOT, CB, LDB, INFO)
void dsytrs	(char uplo, int n, int nrhs, double *da, int lda, int *ipivot, double *db, int ldb, int *info)
void ssytrs	(char uplo, int n, int nrhs, float *sa, int lda, int *ipivot, float *sb, int ldb, int *info)
void zsytrs	(char uplo, int n, int nrhs, doublecomplex *za, int lda, int *ipivot, doublecomplex *zb, int ldb, int *info)
void csytrs	(char uplo, int n, int nrhs, complex *ca, int lda, 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 xSYTRF.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA max(1, N).
IPIVOT	Pivot indices as computed by xSYTRF.
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, LDWORK, N, NRHS

PARAMETER (N = 3)

PARAMETER (NRHS = 1)

PARAMETER (LDA = N)

PARAMETER (LDB = LDA)

PARAMETER (LDWORK = 1)

C

DOUBLE PRECISION A(LDA,N), B(LDB,NRHS), WORK(LDWORK)

INTEGER ICOL, INFO, IROW, IPIVOT(N)

C

EXTERNAL DSYTRF, DSYTRS

C

C Initialize the array A to store the coefficient matrix A

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

C hand side vector b shown below.

C

C 1 2 2 15

C A = 2 1 2 b = 15

C 2 2 1 15

C

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

$ 1.0D0 /

DATA B / N*1.5D1 /

C

C Print the initial values of the arrays.

C

PRINT 1000

DO 100, IROW = 1, N

PRINT 1010, (A(ICOL,IROW), ICOL = 1, IROW - 1),

$ (A(IROW,ICOL), ICOL = IROW, N)

100 CONTINUE

PRINT 1020

DO 110, IROW = 1, LDA

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

110 CONTINUE

PRINT 1030

PRINT 1040, B

C

C Solve the system Ax=b, then print the result.

C

CALL DSYTRF ('UPPER TRIANGLE OF A STORED', N, A, LDA,

$ IPIVOT, WORK, LDWORK, INFO)

IF (INFO .EQ. 0) THEN

CALL DSYTRS ('UPPER TRIANGULAR FACTOR', N, NRHS, A, LDA,

$ IPIVOT, B, LDB, INFO)

IF (INFO .EQ. 0) THEN

PRINT 1050

PRINT 1040, B

ELSE

PRINT 1060, INFO

END IF

ELSE

PRINT 1070, INFO

END IF

C

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

1010 FORMAT (3(3X, F4.1))

1020 FORMAT (/1X, 'A in symmetric form: (* in unused elements)')

1030 FORMAT (/1X, 'b:')

1040 FORMAT (1X, 2X, F4.1)

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

1060 FORMAT (1X, 'Solve failed with INFO = ', I6)

1070 FORMAT (1X, 'Factorization failed with INFO = ', I6)

C

END

Sample Output

A in full form:
1.0 2.0 2.0
2.0 1.0 2.0
2.0 2.0 1.0
A in symmetric form: (* in unused elements)
1.0 2.0 2.0
**** 1.0 2.0
**** **** 1.0
b:
15.0
15.0
15.0
x:
3.0
3.0
3.0