*> \brief \b SPPCON * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SPPCON + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SPPCON( UPLO, N, AP, ANORM, RCOND, WORK, IWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, N * REAL ANORM, RCOND * .. * .. Array Arguments .. * INTEGER IWORK( * ) * REAL AP( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SPPCON estimates the reciprocal of the condition number (in the *> 1-norm) of a real symmetric positive definite packed matrix using *> the Cholesky factorization A = U**T*U or A = L*L**T computed by *> SPPTRF. *> *> 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 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] AP *> \verbatim *> AP is REAL array, dimension (N*(N+1)/2) *> The triangular factor U or L from the Cholesky factorization *> A = U**T*U or A = L*L**T, packed columnwise in a linear *> array. The j-th column of U or L is stored in the array AP *> as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. *> \endverbatim *> *> \param[in] ANORM *> \verbatim *> ANORM is REAL *> The 1-norm (or infinity-norm) of the symmetric 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 (3*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. * *> \date December 2016 * *> \ingroup realOTHERcomputational * * ===================================================================== SUBROUTINE SPPCON( UPLO, N, AP, ANORM, RCOND, WORK, IWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, N REAL ANORM, RCOND * .. * .. Array Arguments .. INTEGER IWORK( * ) REAL AP( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. LOGICAL UPPER CHARACTER NORMIN INTEGER IX, KASE REAL AINVNM, SCALE, SCALEL, SCALEU, SMLNUM * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME INTEGER ISAMAX REAL SLAMCH EXTERNAL LSAME, ISAMAX, SLAMCH * .. * .. External Subroutines .. EXTERNAL SLACN2, SLATPS, SRSCL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS * .. * .. 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 = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'SPPCON', -INFO ) RETURN END IF * * Quick return if possible * RCOND = ZERO IF( N.EQ.0 ) THEN RCOND = ONE RETURN ELSE IF( ANORM.EQ.ZERO ) THEN RETURN END IF * SMLNUM = SLAMCH( 'Safe minimum' ) * * Estimate the 1-norm of the inverse. * KASE = 0 NORMIN = 'N' 10 CONTINUE CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE ) IF( KASE.NE.0 ) THEN IF( UPPER ) THEN * * Multiply by inv(U**T). * CALL SLATPS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, \$ AP, WORK, SCALEL, WORK( 2*N+1 ), INFO ) NORMIN = 'Y' * * Multiply by inv(U). * CALL SLATPS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N, \$ AP, WORK, SCALEU, WORK( 2*N+1 ), INFO ) ELSE * * Multiply by inv(L). * CALL SLATPS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N, \$ AP, WORK, SCALEL, WORK( 2*N+1 ), INFO ) NORMIN = 'Y' * * Multiply by inv(L**T). * CALL SLATPS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N, \$ AP, WORK, SCALEU, WORK( 2*N+1 ), INFO ) END IF * * Multiply by 1/SCALE if doing so will not cause overflow. * SCALE = SCALEL*SCALEU IF( SCALE.NE.ONE ) THEN IX = ISAMAX( N, WORK, 1 ) IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO ) \$ GO TO 20 CALL SRSCL( N, SCALE, WORK, 1 ) END IF GO TO 10 END IF * * Compute the estimate of the reciprocal condition number. * IF( AINVNM.NE.ZERO ) \$ RCOND = ( ONE / AINVNM ) / ANORM * 20 CONTINUE RETURN * * End of SPPCON * END