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

Calling Sequence

CALL DPTTRS	(UPLO, N, NRHS, DDIAG, DOFFD, DB, LDB, INFO)
CALL SPTTRS	(UPLO, N, NRHS, SDIAG, SOFFD, SB, LDB, INFO)
CALL ZPTTRS	(N, NRHS, DDIAG, ZOFFD, ZB, LDB, INFO)
CALL CPTTRS	(N, NRHS, SDIAG, COFFD, CB, LDB, INFO)
void dpttrs	(int n, int nrhs, double *ddiag, double *doffd, double *db, int ldb, int *info)
void spttrs	(int n, int nrhs, float *sdiag, float *soffd, float *sb, int ldb, int *info)
void zpttrs	(char uplo, int n, int nrhs, double *ddiag, doublecomplex *zoffd, doublecomplex *zb, int ldb, int *info)
void cpttrs	(char uplo, int n, int nrhs, float *sdiag, complex *coffd, complex *cb, int ldb, int *info)

Arguments

UPLO	(For real matrices)
	Indicates whether OFFD contains the superdiagonal or the subdiagonal of the matrix A and the form of the factorization. The legal values for UPLO are listed below. Any values not listed are illegal.
	'U' or 'u'	xOFFD contains the superdiagonal and the factorization is UDU.
	'L' or 'l'	xOFFD contains the subdiagonal and the factorization is LDL.
	(The two forms are equivalent if A if real.)
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.
xDIAG	The N diagonal elements of the matrix D from the UDU or LDL factorization of the matrix A, as computed by xPTTRF.
xOFFD	The N-1 off-diagonal elements of the unit bidiagonal factor U or L from the UDU or LDL factorization of the matrix A, as computed by xPTTRF.
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 LDB, N, NRHS

PARAMETER (N = 4)

PARAMETER (NRHS = 1)

PARAMETER (LDB = N)

C

DOUBLE PRECISION B(LDB,NRHS), DIAG(N), DLOWER(N-1)

INTEGER ICOL, INFO, IROW

C

EXTERNAL DPTTRF, DPTTRS

INTRINSIC ABS

C

C Initialize the arrays DIAG and DLOWER to store in symmetric

C tridiagonal form the 4x4 symmetric positive definite

C coefficient matrix A shown below. Initialize the array B

C 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 DIAG / 2.0D0, 2.0D0, 2.0D0, 2.0D0 /

DATA DLOWER / -1.0D0, -1.0D0, -1.0D0 /

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

C

C Print the initial values of the arrays.

C

PRINT 1000

DO 100, IROW = 1, N

PRINT 1010, (0.0D0, ICOL = 1, IROW - 2),

$ (DLOWER(ICOL + 1), ICOL = ABS(IROW - 2), IROW - 2),

$ DIAG(IROW),

$ (DLOWER(IROW), ICOL = 1, MIN(1, N - IROW)),

$ (0.0D0, ICOL = IROW + 2, N)

100 CONTINUE

PRINT 1020

PRINT 1030, B

C

C LDL factor A.

C

CALL DPTTRF (N, DIAG, DLOWER, 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 DPTTRS (N, NRHS, DIAG, DLOWER, 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 DPTTRS, 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