Solution to a Linear System in a Triangular Matrix

Calling Sequence

CALL DTRSL	(DA, LDA, N, DB, JOB, INFO)
CALL STRSL	(SA, LDA, N, SB, JOB, INFO)
CALL ZTRSL	(ZA, LDA, N, ZB, JOB, INFO)
CALL CTRSL	(CA, LDA, N, CB, JOB, INFO)
void dtrsl	(double *da, int lda, int n, double *db, int job, int *info)
void strsl	(float *sa, int lda, int n, float *sb, int job, int *info)
void ztrsl	(doublecomplex *za, int lda, int n, doublecomplex *zb, int job, int *info)
void ctrsl	(complex *ca, int lda, int n, complex *cb, int job, int *info)

Arguments

xA	Matrix A.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA max(1,N).
N	Order of the matrix A. N 0.
xB	On entry, the right-hand side vector b. On exit, the solution vector x.
JOB	Determines which operation the subroutine will perform:
	00	solve Ax = b, A lower triangular
	01	solve Ax = b, A upper triangular
	10	solve AHx = b, A lower triangular
	11	solve AHx = b, A upper triangular
		Note that ATx = AHx for real matrices.
INFO	On exit:
	INFO = 0	Subroutine completed normally.
	INFO > 0	Returns the index of the first zero diagonal element of A.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDA, LOTRAN, N

PARAMETER (LOTRAN = 10)

PARAMETER (N = 5)

PARAMETER (LDA = N)

C

DOUBLE PRECISION A(LDA,N), B(N)

INTEGER ICOL, INFO, IROW, JOB

C

EXTERNAL DTRSL

C

C Initialize the array A to store the 5x5 triangular matrix A

C shown below.

C

C 1 5

C 1 1 4

C A = 1 1 1 b = 3

C 1 1 1 1 2

C 1 1 1 1 1 1

C

DATA A / 5*1.0D0, 8D8, 4*1.0D0, 2*8D8, 3*1.0D0, 3*8D8,

$ 2*1.0D0, 4*8D8, 1.0D0 /

DATA B / 5.0D0, 4.0D0, 3.0D0, 2.0D0, 1.0D0 /

C

C Print the initial values of the arrays.

C

PRINT 1000

DO 100, IROW = 1, N

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

100 CONTINUE

PRINT 1020

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

PRINT 1030

PRINT 1040, B

C

C Solve the matrix in banded form.

C

JOB = LOTRAN

CALL DTRSL (A, LDA, N, B, JOB, INFO)

IF (INFO .EQ. 0) THEN

PRINT 1050

PRINT 1040, B

ELSE

PRINT 1060, INFO

END IF

C

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

1010 FORMAT (5(3X, F4.1))

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

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

1040 FORMAT (3X, F4.1)

1050 FORMAT (/1X, 'A''**(-1) * b:')

1060 FORMAT (1X, 'A appears singular at ', I2)

C

END

Sample Output

A in full form:
1.0
1.0 1.0
1.0 1.0 1.0
1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0
A in triangular form: (* in unused elements)
1.0 **** **** **** ****
1.0 1.0 **** **** ****
1.0 1.0 1.0 **** ****
1.0 1.0 1.0 1.0 ****
1.0 1.0 1.0 1.0 1.0
b:
5.0
4.0
3.0
2.0
1.0
A'**(-1) * b:
1.0
1.0
1.0
1.0
1.0