Determinant and Inverse of a Triangular Matrix

Calling Sequence

CALL DTRDI	(DA, LDA, N, DDET, JOB, INFO)
CALL STRDI	(SA, LDA, N, SDET, JOB, INFO)
CALL ZTRDI	(ZA, LDA, N, ZDET, JOB, INFO)
CALL CTRDI	(CA, LDA, N, CDET, JOB, INFO)
void dtrdi	(double *da, int lda, int n, double *ddet, int job, int *info)
void strdi	(float *sa, int lda, int n, float *sdet, int job, int *info)
void ztrdi	(doublecomplex *za, int lda, int n, doublecomplex *zdet, int job, int *info)
void ctrdi	(complex *ca, int lda, int n, complex *cdet, int job, int *info)

Arguments

xA	On entry, the matrix A. On exit, the inverse of the original matrix A if the inverse was requested, otherwise unchanged.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA max(1,N).
N	Order of the original matrix A. N 0.
xDET	On exit, the determinant of the matrix A. The determinant is stored as b × 10expon where b is stored in DET(1) and expon is stored in DET(2). 1.0 |DET(1)| < 10.0 or DET(1) = 0.0.
JOB	Determines which operation the subroutine will perform:
	010	no determinant, inverse of lower triangular A
	011	no determinant, inverse of upper triangular A
	100	determinant, no inverse
	110	determinant, inverse of lower triangular A
	111	determinant, inverse of upper triangular A
INFO	On exit:
	INFO = 0	Subroutine completed normally.
	INFO > 0	Contains the index of a zero element of A if the inverse is requested and A is singular.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER INDTLO, LDA, N

PARAMETER (INDTLO = 110)

PARAMETER (N = 5)

PARAMETER (LDA = N)

C

DOUBLE PRECISION A(LDA,N), DET(2)

INTEGER ICOL, INFO, IROW, JOB

C

EXTERNAL DTRDI

C

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

C shown below.

C

C 1

C 1 -1

C A = 1 -2 1

C 1 -3 3 -1

C 1 -4 6 -4 1

C

DATA A / 5*1.0D0, 8D8, -1.0D0, -2.0D0, -3.0D0, -4.0D0,

$ 2*8D8, 1.0D0, 3.0D0, 6.0D0, 3*8D8, -1.0D0,

$ -4.0D0, 4*8D8, 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)

C

C Factor the matrix in banded form.

C

JOB = INDTLO

CALL DTRDI (A, LDA, N, DET, JOB, INFO)

IF (INFO .EQ. 0) THEN

PRINT 1030, DET(1) * (10.0 ** DET(2))

PRINT 1040

DO 110, IROW = 1, N

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

110 CONTINUE

ELSE

PRINT 1050, 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, `det(A) = `, F4.1)

1040 FORMAT (/1X, `A**(-1):')

1050 FORMAT (1X, `A appears singular at `, I2)

C

END

Sample Output

A in full form:
1.0
1.0 -1.0
1.0 -2.0 1.0
1.0 -3.0 3.0 -1.0
1.0 -4.0 6.0 -4.0 1.0
A in triangular form: (* in unused elements)
1.0 **** **** **** ****
1.0 -1.0 **** **** ****
1.0 -2.0 1.0 **** ****
1.0 -3.0 3.0 -1.0 ****
1.0 -4.0 6.0 -4.0 1.0
det(A) = 1.0
A**(-1):
1.0
1.0 -1.0
1.0 -2.0 1.0
1.0 -3.0 3.0 -1.0
1.0 -4.0 6.0 -4.0 1.0