Inverse of a Triangular Matrix in Packed Storage

Calling Sequence

CALL DTPTRI	(UPLO, DIAG, N, DA, INFO)
CALL STPTRI	(UPLO, DIAG, N, SA, INFO)
CALL ZTPTRI	(UPLO, DIAG, N, ZA, INFO)
CALL CTPTRI	(UPLO, DIAG, N, CA, INFO)
void dtptri	(char uplo, char diag, int n, double *da, int *info)
void stptri	(char uplo, char diag, int n, float *sa, int *info)
void ztptri	(char uplo, char diag, int n, doublecomplex *za, int *info)
void ctptri	(char uplo, char diag, int n, complex *ca, 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. The dimension of xA is (N × N + N) / 2. On exit, the triangular inverse of A.
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

DOUBLE PRECISION ZERO

INTEGER LDA, N

PARAMETER (N = 4)

PARAMETER (LDA = ((N + 1) * N) / 2)

PARAMETER (ZERO = 0.0D0)

C

DOUBLE PRECISION A(LDA)

INTEGER INFO

C

EXTERNAL DTPTRI

C

C Initialize the array A to store in packed triangular form

C the matrix A shown below.

C

C 1

C A = 1 1

C 1 1 1

C 1 1 1 1

C

DATA A / LDA*1.0D0 /

C

C Print the A array.

C

PRINT 1000

PRINT 1010, A(1), ZERO, ZERO, ZERO

PRINT 1010, A(2), A(5), ZERO, ZERO

PRINT 1010, A(3), A(6), A(8), ZERO

PRINT 1010, A(4), A(7), A(9), A(10)

C

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

C

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

$ N, A, INFO)

IF (INFO .NE. 0) THEN

PRINT 1020, INFO

STOP 1

END IF

PRINT 1030

PRINT 1010, A(1), ZERO, ZERO, ZERO

PRINT 1010, A(2), A(5), ZERO, ZERO

PRINT 1010, A(3), A(6), A(8), ZERO

PRINT 1010, A(4), A(7), A(9), A(10)

C

1000 FORMAT (1X, 'A:')

1010 FORMAT (4(3X, F5.2))

1020 FORMAT (/1X, 'Error inverting A, INFO = ', I5)

1030 FORMAT (/1X, 'A**(-1):')

C

END

Sample Output

A:
1.00 0.00 0.00 0.00
1.00 1.00 0.00 0.00
1.00 1.00 1.00 0.00
1.00 1.00 1.00 1.00
A**(-1):
1.00 0.00 0.00 0.00
-1.00 1.00 0.00 0.00
0.00 -1.00 1.00 0.00
0.00 0.00 -1.00 1.00