Reciprocal Condition Number of a Cholesky-Factored Symmetric Positive Definite Matrix in Packed Storage

Calling Sequence

CALL DPPCON	(UPLO, N, DA, DANORM, DRCOND, DWORK, IWORK2, INFO)
CALL SPPCON	(UPLO, N, SA, SANORM, SRCOND, SWORK, IWORK2, INFO)
CALL ZPPCON	(UPLO, N, ZA, DANORM, DRCOND, ZWORK, DWORK2, INFO)
CALL CPPCON	(UPLO, N, CA, SANORM, SRCOND, CWORK, SWORK2, INFO)
void dppcon	(char uplo, int n, double *da, double danorm, double *drcond, int *info)
void sppcon	(char uplo, int n, float *sa, float sanorm, float *srcond, int *info)
void zppcon	(char uplo, int n, doublecomplex *za, double danorm, double *drcond, int *info)
void cppcon	(char uplo, int n, complex *ca, 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	Cholesky factorization of the matrix A, as computed by xPPTRF. The dimension of xA is (N × N + N) / 2.
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 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

INTEGER LDA, LDIWRK, LDWORK, N

PARAMETER (N = 4)

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

PARAMETER (LDIWRK = N)

PARAMETER (LDWORK = 3 * N)

C

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

INTEGER INFO, IWORK(LDIWRK)

C

EXTERNAL DPPCON, DPPTRF

INTRINSIC ABS

C

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

C 4x4 symmetric positive definite 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 Cholesky factor A.

C

CALL DPPTRF ('UPPER TRIANGLE OF A STORED', N, A, 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 DPPCON ('UPPER TRIANGLE FACTOR STORED', N, A,

$ 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 DPPCON, 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