*> \brief \b ZSPCON * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZSPCON + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, N * DOUBLE PRECISION ANORM, RCOND * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX*16 AP( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZSPCON estimates the reciprocal of the condition number (in the *> 1-norm) of a complex symmetric packed matrix A using the *> factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF. *> *> An estimate is obtained for norm(inv(A)), and the reciprocal of the *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the details of the factorization are stored *> as an upper or lower triangular matrix. *> = 'U': Upper triangular, form is A = U*D*U**T; *> = 'L': Lower triangular, form is A = L*D*L**T. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] AP *> \verbatim *> AP is COMPLEX*16 array, dimension (N*(N+1)/2) *> The block diagonal matrix D and the multipliers used to *> obtain the factor U or L as computed by ZSPTRF, stored as a *> packed triangular matrix. *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> Details of the interchanges and the block structure of D *> as determined by ZSPTRF. *> \endverbatim *> *> \param[in] ANORM *> \verbatim *> ANORM is DOUBLE PRECISION *> The 1-norm of the original matrix A. *> \endverbatim *> *> \param[out] RCOND *> \verbatim *> RCOND is DOUBLE PRECISION *> The reciprocal of the condition number of the matrix A, *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an *> estimate of the 1-norm of inv(A) computed in this routine. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (2*N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, N DOUBLE PRECISION ANORM, RCOND * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 AP( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER I, IP, KASE DOUBLE PRECISION AINVNM * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLACN2, ZSPTRS * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( ANORM.LT.ZERO ) THEN INFO = -5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZSPCON', -INFO ) RETURN END IF * * Quick return if possible * RCOND = ZERO IF( N.EQ.0 ) THEN RCOND = ONE RETURN ELSE IF( ANORM.LE.ZERO ) THEN RETURN END IF * * Check that the diagonal matrix D is nonsingular. * IF( UPPER ) THEN * * Upper triangular storage: examine D from bottom to top * IP = N*( N+1 ) / 2 DO 10 I = N, 1, -1 IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO ) \$ RETURN IP = IP - I 10 CONTINUE ELSE * * Lower triangular storage: examine D from top to bottom. * IP = 1 DO 20 I = 1, N IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO ) \$ RETURN IP = IP + N - I + 1 20 CONTINUE END IF * * Estimate the 1-norm of the inverse. * KASE = 0 30 CONTINUE CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) IF( KASE.NE.0 ) THEN * * Multiply by inv(L*D*L**T) or inv(U*D*U**T). * CALL ZSPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO ) GO TO 30 END IF * * Compute the estimate of the reciprocal condition number. * IF( AINVNM.NE.ZERO ) \$ RCOND = ( ONE / AINVNM ) / ANORM * RETURN * * End of ZSPCON * END