Inverse of a Triangular Matrix

Calling Sequence

CALL DTRTRI	(UPLO, DIAG, N, DA, LDA, INFO)
CALL STRTRI	(UPLO, DIAG, N, SA, LDA, INFO)
CALL ZTRTRI	(UPLO, DIAG, N, ZA, LDA, INFO)
CALL CTRTRI	(UPLO, DIAG, N, CA, LDA, INFO)
void dtrtri	(char uplo, char diag, int n, double *da, int lda, int *info)
void strtri	(char uplo, char diag, int n, float *sa, int lda, int *info)
void ztrtri	(char uplo, char diag, int n, doublecomplex *za, int lda, int *info)
void ctrtri	(char uplo, char diag, int n, complex *ca, int lda, 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.
DIAG	Indicates whether or not A is unit triangular. The legal values for DIAG are listed below. Any values not listed below are illegal.
	'N' or 'n'	A is not unit triangular.
	'U' or 'u'	A is unit triangular.
N	Order of the matrix A. N 0.
xA	On entry, the upper or lower triangular matrix A. If DIAG = 'U' or 'u', the diagonal elements of A are assumed to be 1 and are not used. On exit, the triangular inverse of the matrix A.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA 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	A(i,i), where i = INFO, is exactly zero. The matrix is therefore singular and its inverse could not be computed.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDA, N

PARAMETER (N = 4)

PARAMETER (LDA = N)

C

DOUBLE PRECISION A(LDA,N)

INTEGER ICOL, INFO, IROW

C

EXTERNAL DTRTRI

C

C Initialize the array A to store the matrix A shown below.

C

C 1

C A = 1 1

C 1 1 1

C 1 1 1 1

C

DATA A / 1.0D0, 1.0D0, 1.0D0, 1.0D0,

$ 8.8D8, 1.0D0, 1.0D0, 1.0D0,

$ 8.8D8, 8.8D8, 1.0D0, 1.0D0,

$ 8.8D8, 8.8D8, 8.8D8, 1.0D0 /

C

C Print the A array.

C

PRINT 1000

DO 100, IROW = 1, N

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

$ (0.0D0, ICOL = IROW + 1, N)

100 CONTINUE

PRINT 1020

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

C

C Compute and print A**(-1).

C

CALL DTRTRI ('LOWER TRIANGULAR A', 'NO UNIT DIAGONAL A',

$ N, A, LDA, INFO)

IF (INFO .NE. 0) THEN

PRINT 1030, INFO

STOP 1

END IF

PRINT 1040

DO 110, IROW = 1, N

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

$ (0.0D0, ICOL = IROW + 1, N)

110 CONTINUE

C

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

1010 FORMAT (4(3X, F8.4))

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

1030 FORMAT (/1X, 'Error inverting A, INFO = ', I5)

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

C

END

Sample Output

A in full form:
1.0000 0.0000 0.0000 0.0000
1.0000 1.0000 0.0000 0.0000
1.0000 1.0000 1.0000 0.0000
1.0000 1.0000 1.0000 1.0000
A in triangular form: (* in unused elements)
1.0000 ******** ******** ********
1.0000 1.0000 ******** ********
1.0000 1.0000 1.0000 ********
1.0000 1.0000 1.0000 1.0000
A**(-1):
1.0000 0.0000 0.0000 0.0000
-1.0000 1.0000 0.0000 0.0000
0.0000 -1.0000 1.0000 0.0000
0.0000 0.0000 -1.0000 1.0000