Reciprocal Condition Number of a UDU- or LDL-Factored Symmetric Matrix

Calling Sequence

CALL DSYCON	(UPLO, N, DA, LDA, IPIVOT, DANORM, DRCOND, DWORK, IWORK2, INFO)
CALL SSYCON	(UPLO, N, SA, LDA, IPIVOT, SANORM, SRCOND, SWORK, IWORK2, INFO)
CALL ZSYCON	(UPLO, N, ZA, LDA, IPIVOT, DANORM, DRCOND, ZWORK, INFO)
CALL CSYCON	(UPLO, N, CA, LDA, IPIVOT, SANORM, SRCOND, CWORK, INFO)
void dsycon	(char uplo, int n, double *da, int lda, int *ipivot, double danorm, double *drcond, int *info)
void ssycon	(char uplo, int n, float *sa, int lda, int *ipivot, float sanorm, float *srcond, int *info)
void zsycon	(char uplo, int n, doublecomplex *za, int lda, int *ipivot, double danorm, double *drcond, int *info)
void csycon	(char uplo, int n, complex *ca, int lda, int *ipivot, float sanorm, float *srcond, 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.
N	Order of the matrix A. N 0.
xA	UDU or LDL factorization of the matrix A as computed by xSYTRF.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA max(1, N).
IPIVOT	Pivot indices as computed by xSYTRF.
xANORM	The 1-norm or -norm of matrix A.
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 / (ANORM × ||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 2 × N.
IWORK2	Scratch array with a dimension of N for real subroutines.
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

INTEGER LDA, LDIWRK, LDWORK, N

PARAMETER (N = 3)

PARAMETER (LDA = N)

PARAMETER (LDIWRK = N)

PARAMETER (LDWORK = 2 * N)

C

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

INTEGER ICOL, INFO, IROW, IPIVOT(N), IWORK(LDIWRK)

C

EXTERNAL DSYCON, DSYTRF

C

C Initialize the array A to store the coefficient matrix A

C shown below.

C

C 1 2 2

C A = 2 1 2

C 2 2 1

C

DATA A / 1.0D0, 2*8D8, 2.0D0, 1.0D0, 8D8, 2.0D0, 2.0D0,

$ 1.0D0 /

C

PRINT 1000

DO 100, IROW = 1, N

PRINT 1010, (0.0D0, ICOL = 1, IROW - 1),

$ (A(IROW, ICOL), ICOL = IROW, N)

100 CONTINUE

PRINT 1020

DO 110, IROW = 1, LDA

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

110 CONTINUE

C

CALL DSYTRF ('UPPER TRIANGULAR A', N, A, LDA, IPIVOT,

$ WORK, LDWORK, INFO)

IF (INFO .EQ. 0) THEN

ANORM = 5.0D0

CALL DSYCON ('UPPER TRIANGULAR A', N, A, LDA, IPIVOT,

$ ANORM, RCOND, WORK, IWORK, INFO)

IF (INFO .EQ. 0) THEN

PRINT 1030, 1.0D0 / RCOND

ELSE

PRINT 1040, INFO

END IF

ELSE

PRINT 1050, INFO

END IF

C

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

1010 FORMAT (3(3X, F4.1))

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

1030 FORMAT (/1X, 'Estimated condition number: ', F6.2)

1040 FORMAT (1X, 'Error computing condition number, INFO = ', I6)

1050 FORMAT (1X, 'Factorization failed with INFO = ', I6)

C

END

Sample Output

A in full form:
1.0 2.0 2.0
0.0 1.0 2.0
0.0 0.0 1.0
A in symmetric form: (* in unused elements)
1.0 2.0 2.0
**** 1.0 2.0
**** **** 1.0
Estimated condition number: 7.00