Solution to a Linear System in a General Tridiagonal Matrix (Simple Driver)

Calling Sequence

CALL DGTSV	(N, NRHS, DLOW, DDIAG, DUP, DB, LDB, INFO)
CALL SGTSV	(N, NRHS, SLOW, SDIAG, SUP, SB, LDB, INFO)
CALL ZGTSV	(N, NRHS, ZLOW, ZDIAG, ZUP, ZB, LDB, INFO)
CALL CGTSV	(N, NRHS, CLOW, CDIAG, CUP, CB, LDB, INFO)
void dgtsv	(int n, int nrhs, double *dlow, double *ddiag, double *dup, double *db, int ldb, int *info)
void sgtsv	(int n, int nrhs, float *slow, float *sdiag, float *sup, float *sb, int ldb, int *info)
void zgtsv	(int n, int nrhs, doublecomplex *zlow, doublecomplex *zdiag, doublecomplex *zup, doublecomplex *zb, int ldb, int *info)
void cgtsv	(int n, int nrhs, complex *clow, complex *cdiag, complex *cup, complex *cb, int ldb, int *info)

Arguments

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.
xLOW	On entry, the N-1 subdiagonal elements of A. On exit, LOW is overwritten by the N-2 elements of the second superdiagonal of the upper triangular matrix U from the LU factorization of A, stored in elements 1 through N-2.
xDIAG	On entry, the N diagonal elements of A. On exit, DIAG is overwritten by the N diagonal elements of U.
xUP	On entry, the N-1 superdiagonal elements of A. On exit, UP is overwritten by the N-1 elements of the first superdiagonal of U.
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.
	INFO > 0	U(i,i), where i = INFO, is exactly zero, and U is therefore singular. The factorization has not been completed, unless i = N, and the solution could not be computed.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDB, LDIWRK, LDWORK, N, NRHS

PARAMETER (N = 4)

PARAMETER (LDB = N)

PARAMETER (LDIWRK = N)

PARAMETER (LDWORK = N)

PARAMETER (NRHS = 1)

C

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

DOUBLE PRECISION DUPPER(N-1)

INTEGER ICOL, INFO, IROW

C

EXTERNAL DGTSV

INTRINSIC ABS, MAX

C

C Initialize the arrays DLOWER, DIAG, and DUPPER to store the

C first subdiagonal, the diagonal, and the first superdiagonal

C of the coefficient matrix A shown below. Initialize the

C array B to store the right hand side matrix b shown below.

C

C 2 -1 0

C A = 1 2 -1 b = 2

C 1 2 -1 4

C 1 2 11

C

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

DATA DIAG / 2.0D0, 2.0D0, 2.0D0, 2.0D0 /

DATA DUPPER / -1.0D0, -1.0D0, -1.0D0 /

DATA B / 0.0D0, 2.0D0, 4.0D0, 1.1D1 /

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),

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

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

100 CONTINUE

PRINT 1020

PRINT 1030, B

C

CALL DGTSV (N, NRHS, DLOWER, DIAG, DUPPER, B, LDB, INFO)

IF (INFO .LT. 0) THEN

PRINT 1040, INFO

STOP 1

ELSE IF (INFO .GT. 0) THEN

PRINT 1050

STOP 2

END IF

PRINT 1060

PRINT 1030, B

C

1000 FORMAT (1X, 'A:')

1010 FORMAT (5(3X, F5.2))

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

1030 FORMAT (1X, F8.2)

1040 FORMAT (1X, 'Illegal argument to DGTSV, argument #', I2)

1050 FORMAT (1X, 'A is singular to working precision.')

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

C

END

Sample Output

A:
2.00 -1.00 0.00 0.00
1.00 2.00 -1.00 0.00
0.00 1.00 2.00 -1.00
0.00 0.00 1.00 2.00
b:
0.00
2.00
4.00
11.00
x:
1.00
2.00
3.00
4.00