Reciprocal Condition Number of a Triangular Matrix in Packed Storage

Calling Sequence

CALL DTPCON	(NORM, UPLO, DIAG, N, DA, DRCOND, DWORK, IWORK2, INFO)
CALL STPCON	(NORM, UPLO, DIAG, N, SA, SRCOND, SWORK, IWORK2, INFO)
CALL ZTPCON	(NORM, UPLO, DIAG, N, ZA, DRCOND, ZWORK, DWORK2, INFO)
CALL CTPCON	(NORM, UPLO, DIAG, N, CA, SRCOND, CWORK, SWORK2, INFO)
void dtpcon	(char norm, char uplo, char diag, int n, double *da, double *drcond, int *info)
void stpcon	(char norm, char uplo, char diag, int n, float *sa, float *srcond, int *info)
void ztpcon	(char norm, char uplo, char diag, int n, doublecomplex *za, double *drcond, int *info)
void ctpcon	(char norm, char uplo, char diag, int n, complex *ca, 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. The dimension of xA is (N × N + N) / 2.
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 + 1) * N) / 2)

PARAMETER (LDIWRK = N)

PARAMETER (LDWORK = 3 * N)

PARAMETER (ZERO = 0.0D0)

C

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

INTEGER INFO, IWORK(LDIWRK)

C

EXTERNAL DTPCON

INTRINSIC ABS

C

C Initialize A to store in packed triangular form the matrix A

C shown below.

C

C 1 2 4

C A = 0 3 5

C 0 0 6

C

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

C

PRINT 1000

PRINT 1010, A(1), A(2), A(4)

PRINT 1010, ZERO, ZERO, A(5)

PRINT 1010, ZERO, A(5), A(6)

C

CALL DTPCON ('ONE-NORM OF A', 'UPPER TRIANGULAR A',

$ 'NO UNIT DIAGONAL A', N, A, RCOND, WORK, IWORK,

$ INFO)

IF (INFO .NE. 0) THEN

PRINT 1020, ABS(INFO)

STOP 1

END IF

PRINT 1030, 1.0D0 / RCOND

C

1000 FORMAT ('A:')

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

1020 FORMAT (1X, 'Illegal argument to DTPCON, argument #', I2)

1030 FORMAT (/1X, 'Estimated condition number of A: ', F7.4)

C

END

Sample Output

A:
1.00 2.00 2.00
0.00 0.00 3.00
0.00 3.00 3.00
Estimated condition number of A: 8.0000