*> \brief SSYCON_ROOK * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SSYCON_ROOK + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SSYCON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND, * WORK, IWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDA, N * REAL ANORM, RCOND * .. * .. Array Arguments .. * INTEGER IPIV( * ), IWORK( * ) * REAL A( LDA, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SSYCON_ROOK estimates the reciprocal of the condition number (in the *> 1-norm) of a real symmetric matrix A using the factorization *> A = U*D*U**T or A = L*D*L**T computed by SSYTRF_ROOK. *> *> 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] A *> \verbatim *> A is REAL array, dimension (LDA,N) *> The block diagonal matrix D and the multipliers used to *> obtain the factor U or L as computed by SSYTRF_ROOK. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> Details of the interchanges and the block structure of D *> as determined by SSYTRF_ROOK. *> \endverbatim *> *> \param[in] ANORM *> \verbatim *> ANORM is REAL *> The 1-norm of the original matrix A. *> \endverbatim *> *> \param[out] RCOND *> \verbatim *> RCOND is REAL *> 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 REAL array, dimension (2*N) *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (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 realSYcomputational * *> \par Contributors: * ================== *> \verbatim *> *> December 2016, Igor Kozachenko, *> Computer Science Division, *> University of California, Berkeley *> *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, *> School of Mathematics, *> University of Manchester *> *> \endverbatim * * ===================================================================== SUBROUTINE SSYCON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, $ IWORK, 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, LDA, N REAL ANORM, RCOND * .. * .. Array Arguments .. INTEGER IPIV( * ), IWORK( * ) REAL A( LDA, * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER I, KASE REAL AINVNM * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL SLACN2, SSYTRS_ROOK, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. 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( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 ELSE IF( ANORM.LT.ZERO ) THEN INFO = -6 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'SSYCON_ROOK', -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 * DO 10 I = N, 1, -1 IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO ) $ RETURN 10 CONTINUE ELSE * * Lower triangular storage: examine D from top to bottom. * DO 20 I = 1, N IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO ) $ RETURN 20 CONTINUE END IF * * Estimate the 1-norm of the inverse. * KASE = 0 30 CONTINUE CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE ) IF( KASE.NE.0 ) THEN * * Multiply by inv(L*D*L**T) or inv(U*D*U**T). * CALL SSYTRS_ROOK( UPLO, N, 1, A, LDA, 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 SSYCON_ROOK * END