Reciprocal Condition Number of a Triangular Matrix

Calling Sequence

CALL DTRCON	(NORM, UPLO, DIAG, N, DA, LDA, DRCOND, DWORK, IWORK2, INFO)
CALL STRCON	(NORM, UPLO, DIAG, N, SA, LDA, SRCOND, SWORK, IWORK2, INFO)
CALL ZTRCON	(NORM, UPLO, DIAG, N, ZA, LDA, DRCOND, ZWORK, DWORK2, INFO)
CALL CTRCON	(NORM, UPLO, DIAG, N, CA, LDA, SRCOND, CWORK, SWORK2, INFO)
void dtrcon	(char norm, char uplo, char diag, int n, double *da, int lda, double *drcond, int *info)
void strcon	(char norm, char uplo, char diag, int n, float *sa, int lda, float *srcond, int *info)
void ztrcon	(char norm, char uplo, char diag, int n, doublecomplex *za, int lda, double *drcond, int *info)
void ctrcon	(char norm, char uplo, char diag, int n, complex *ca, int lda, float *srcond, int *info)

Arguments

NORM	Indicates whether the 1-norm condition number or the -norm condition number is required. The legal values for NORM are listed below. Any values not listed below are illegal.
	'O', 'o', or '1'	1-norm condition number is required.
	'I' or 'i'	-norm condition number is required.
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	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.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA max(1, N).
xRCOND	On exit, the estimated reciprocal of the condition number of the matrix A where the reciprocal condition number of A is defined to be 1 / (||A|| × ||A-1||). The reciprocal of the condition number is estimated instead of the condition number itself to avoid overflow or division by zero. If RCOND is less than machine precision (in particular, if RCOND = 0) then A is singular to working precision.
xWORK	Scratch array with a dimension of 3 × N for real subroutines or 2 × N for complex subroutines.
xWORK2	Scratch array with a dimension of N.
INFO	On exit:
	INFO = 0	Subroutine completed normally.
	INFO < 0	The ith argument, where i = |INFO|, had an illegal value.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

DOUBLE PRECISION ZERO

INTEGER LDA, LDIWRK, LDWORK, N

PARAMETER (N = 3)

PARAMETER (LDA = N)

PARAMETER (LDIWRK = N)

PARAMETER (LDWORK = 3 * N)

PARAMETER (ZERO = 0.0D0)

C

DOUBLE PRECISION A(LDA,N), RCOND, WORK(LDWORK)

INTEGER ICOL, INFO, IROW, IWORK(LDIWRK)

C

EXTERNAL DTRCON

INTRINSIC ABS

C

C Initialize A to store in triangular form the matrix A

C shown below.

C

C 1

C A = 2 2

C 3 3 3

C

DATA A / 1.0D0, 2.0D0, 3.0D0, 8D8, 2.0D0, 3.0D0, 8D8, 8D8,

$ 3.0D0 /

C

C Print the initial value of A.

C

PRINT 1000

DO 100, IROW = 1, N

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

$ (ZERO, ICOL = IROW + 1, N)

100 CONTINUE

PRINT 1020

DO 110, IROW = 1, LDA

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

110 CONTINUE

C

CALL DTRCON ('ONE-NORM OF A', 'LOWER TRIANGULAR A',

$ 'NO UNIT DIAGONAL A', N, A, LDA, RCOND,

$ WORK, IWORK, INFO)

IF (INFO .NE. 0) THEN

PRINT 1030, ABS(INFO)

STOP 1

END IF

PRINT 1040, 1.0D0 / RCOND

C

1000 FORMAT ('A in full form:')

1010 FORMAT (3(3X, F19.16))

1020 FORMAT (/1X, 'A in triangular form: ',

$ ' (* in unused positions)')

1030 FORMAT (1X, 'Illegal argument to DTRCON, argument #', I2)

1040 FORMAT (/1X, 'Estimated condition number of A: ', F7.4)

C

END

Sample Output

A in full form:
1.0000000000000000 0.0000000000000000 0.0000000000000000
2.0000000000000000 2.0000000000000000 0.0000000000000000
3.0000000000000000 3.0000000000000000 3.0000000000000000
A in triangular form: (* in unused positions)
1.0000000000000000 ******************* *******************
2.0000000000000000 2.0000000000000000 *******************
3.0000000000000000 3.0000000000000000 3.0000000000000000
Estimated condition number of A: 12.0000