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

Calling Sequence

CALL DSPCON	(UPLO, N, DA, IPIVOT, DANORM, DRCOND, DWORK, IWORK2, INFO)
CALL SSPCON	(UPLO, N, SA, IPIVOT, SANORM, SRCOND, SWORK, IWORK2, INFO)
CALL ZSPCON	(UPLO, N, ZA, IPIVOT, DANORM, DRCOND, ZWORK, INFO)
CALL CSPCON	(UPLO, N, CA, IPIVOT, SANORM, SRCOND, CWORK, INFO)
void dspcon	(char uplo, int n, double *da, int *ipivot, double danorm, double *drcond, int *info)
void sspcon	(char uplo, int n, float *sa, int *ipivot, float sanorm, float *srcond, int *info)
void zspcon	(char uplo, int n, doublecomplex *za, int *ipivot, double danorm, double *drcond, int *info)
void cspcon	(char uplo, int n, complex *ca, 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 xSPTRF. The dimension of xA is (N × N + N) / 2.
IPIVOT	Pivot indices as computed by xSPTRF.
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 = 4)

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

PARAMETER (LDIWRK = N)

PARAMETER (LDWORK = 2 * N)

C

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

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

C

EXTERNAL DSPCON, DSPTRF

INTRINSIC ABS

C

C Initialize the array A to store in packed symmetric form the

C 4x4 symmetric matrix A shown below.

C

C 2 -1 0 0

C A = -1 2 -1 0

C 0 -1 2 -1

C 0 0 -1 2

C

DATA A / 2.0D0, -1.0D0, 2.0D0, 0.0D0, -1.0D0, 2.0D0,

$ 0.0D0, 0.0D0, -1.0D0, 2.0D0 /

C

C Print the initial values of the arrays.

C

PRINT 1000

PRINT 1010, A(1), A(2), A(4), A(7)

PRINT 1010, A(2), A(3), A(5), A(8)

PRINT 1010, A(4), A(5), A(6), A(9)

PRINT 1010, A(7), A(8), A(9), A(10)

C

C LDL factor A.

C

CALL DSPTRF ('UPPER TRIANGLE OF A STORED', N, A, IPIVOT,

$ INFO)

IF (INFO .NE. 0) THEN

PRINT 1020, INFO

STOP 1

END IF

C

C Compute and print the condition number of A.

C

ANORM = 4.0D0

CALL DSPCON ('UPPER TRIANGLE FACTOR STORED', N, A, IPIVOT,

$ ANORM, RCOND, WORK, IWORK, INFO)

IF (INFO .NE. 0) THEN

PRINT 1030, ABS(INFO)

STOP 2

END IF

PRINT 1040, 1.0D0 / RCOND

C

1000 FORMAT (1X, 'A:')

1010 FORMAT (4(3X, F6.3))

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

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

1040 FORMAT (/1X, 'Estimated condition number of A = ', F8.4)

C

END

Sample Output

A:
2.000 -1.000 0.000 0.000
-1.000 2.000 -1.000 0.000
0.000 -1.000 2.000 -1.000
0.000 0.000 -1.000 2.000
Estimated condition number of A = 12.0000