LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
spocon.f
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00001 *> \brief \b SPOCON
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download SPOCON + dependencies 
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00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/spocon.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/spocon.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE SPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK,
00022 *                          INFO )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          UPLO
00026 *       INTEGER            INFO, LDA, N
00027 *       REAL               ANORM, RCOND
00028 *       ..
00029 *       .. Array Arguments ..
00030 *       INTEGER            IWORK( * )
00031 *       REAL               A( LDA, * ), WORK( * )
00032 *       ..
00033 *  
00034 *
00035 *> \par Purpose:
00036 *  =============
00037 *>
00038 *> \verbatim
00039 *>
00040 *> SPOCON estimates the reciprocal of the condition number (in the 
00041 *> 1-norm) of a real symmetric positive definite matrix using the
00042 *> Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF.
00043 *>
00044 *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
00045 *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
00046 *> \endverbatim
00047 *
00048 *  Arguments:
00049 *  ==========
00050 *
00051 *> \param[in] UPLO
00052 *> \verbatim
00053 *>          UPLO is CHARACTER*1
00054 *>          = 'U':  Upper triangle of A is stored;
00055 *>          = 'L':  Lower triangle of A is stored.
00056 *> \endverbatim
00057 *>
00058 *> \param[in] N
00059 *> \verbatim
00060 *>          N is INTEGER
00061 *>          The order of the matrix A.  N >= 0.
00062 *> \endverbatim
00063 *>
00064 *> \param[in] A
00065 *> \verbatim
00066 *>          A is REAL array, dimension (LDA,N)
00067 *>          The triangular factor U or L from the Cholesky factorization
00068 *>          A = U**T*U or A = L*L**T, as computed by SPOTRF.
00069 *> \endverbatim
00070 *>
00071 *> \param[in] LDA
00072 *> \verbatim
00073 *>          LDA is INTEGER
00074 *>          The leading dimension of the array A.  LDA >= max(1,N).
00075 *> \endverbatim
00076 *>
00077 *> \param[in] ANORM
00078 *> \verbatim
00079 *>          ANORM is REAL
00080 *>          The 1-norm (or infinity-norm) of the symmetric matrix A.
00081 *> \endverbatim
00082 *>
00083 *> \param[out] RCOND
00084 *> \verbatim
00085 *>          RCOND is REAL
00086 *>          The reciprocal of the condition number of the matrix A,
00087 *>          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
00088 *>          estimate of the 1-norm of inv(A) computed in this routine.
00089 *> \endverbatim
00090 *>
00091 *> \param[out] WORK
00092 *> \verbatim
00093 *>          WORK is REAL array, dimension (3*N)
00094 *> \endverbatim
00095 *>
00096 *> \param[out] IWORK
00097 *> \verbatim
00098 *>          IWORK is INTEGER array, dimension (N)
00099 *> \endverbatim
00100 *>
00101 *> \param[out] INFO
00102 *> \verbatim
00103 *>          INFO is INTEGER
00104 *>          = 0:  successful exit
00105 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00106 *> \endverbatim
00107 *
00108 *  Authors:
00109 *  ========
00110 *
00111 *> \author Univ. of Tennessee 
00112 *> \author Univ. of California Berkeley 
00113 *> \author Univ. of Colorado Denver 
00114 *> \author NAG Ltd. 
00115 *
00116 *> \date November 2011
00117 *
00118 *> \ingroup realPOcomputational
00119 *
00120 *  =====================================================================
00121       SUBROUTINE SPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK,
00122      $                   INFO )
00123 *
00124 *  -- LAPACK computational routine (version 3.4.0) --
00125 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00126 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00127 *     November 2011
00128 *
00129 *     .. Scalar Arguments ..
00130       CHARACTER          UPLO
00131       INTEGER            INFO, LDA, N
00132       REAL               ANORM, RCOND
00133 *     ..
00134 *     .. Array Arguments ..
00135       INTEGER            IWORK( * )
00136       REAL               A( LDA, * ), WORK( * )
00137 *     ..
00138 *
00139 *  =====================================================================
00140 *
00141 *     .. Parameters ..
00142       REAL               ONE, ZERO
00143       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00144 *     ..
00145 *     .. Local Scalars ..
00146       LOGICAL            UPPER
00147       CHARACTER          NORMIN
00148       INTEGER            IX, KASE
00149       REAL               AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
00150 *     ..
00151 *     .. Local Arrays ..
00152       INTEGER            ISAVE( 3 )
00153 *     ..
00154 *     .. External Functions ..
00155       LOGICAL            LSAME
00156       INTEGER            ISAMAX
00157       REAL               SLAMCH
00158       EXTERNAL           LSAME, ISAMAX, SLAMCH
00159 *     ..
00160 *     .. External Subroutines ..
00161       EXTERNAL           SLACN2, SLATRS, SRSCL, XERBLA
00162 *     ..
00163 *     .. Intrinsic Functions ..
00164       INTRINSIC          ABS, MAX
00165 *     ..
00166 *     .. Executable Statements ..
00167 *
00168 *     Test the input parameters.
00169 *
00170       INFO = 0
00171       UPPER = LSAME( UPLO, 'U' )
00172       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00173          INFO = -1
00174       ELSE IF( N.LT.0 ) THEN
00175          INFO = -2
00176       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00177          INFO = -4
00178       ELSE IF( ANORM.LT.ZERO ) THEN
00179          INFO = -5
00180       END IF
00181       IF( INFO.NE.0 ) THEN
00182          CALL XERBLA( 'SPOCON', -INFO )
00183          RETURN
00184       END IF
00185 *
00186 *     Quick return if possible
00187 *
00188       RCOND = ZERO
00189       IF( N.EQ.0 ) THEN
00190          RCOND = ONE
00191          RETURN
00192       ELSE IF( ANORM.EQ.ZERO ) THEN
00193          RETURN
00194       END IF
00195 *
00196       SMLNUM = SLAMCH( 'Safe minimum' )
00197 *
00198 *     Estimate the 1-norm of inv(A).
00199 *
00200       KASE = 0
00201       NORMIN = 'N'
00202    10 CONTINUE
00203       CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
00204       IF( KASE.NE.0 ) THEN
00205          IF( UPPER ) THEN
00206 *
00207 *           Multiply by inv(U**T).
00208 *
00209             CALL SLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, A,
00210      $                   LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO )
00211             NORMIN = 'Y'
00212 *
00213 *           Multiply by inv(U).
00214 *
00215             CALL SLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
00216      $                   A, LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO )
00217          ELSE
00218 *
00219 *           Multiply by inv(L).
00220 *
00221             CALL SLATRS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
00222      $                   A, LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO )
00223             NORMIN = 'Y'
00224 *
00225 *           Multiply by inv(L**T).
00226 *
00227             CALL SLATRS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N, A,
00228      $                   LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO )
00229          END IF
00230 *
00231 *        Multiply by 1/SCALE if doing so will not cause overflow.
00232 *
00233          SCALE = SCALEL*SCALEU
00234          IF( SCALE.NE.ONE ) THEN
00235             IX = ISAMAX( N, WORK, 1 )
00236             IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
00237      $         GO TO 20
00238             CALL SRSCL( N, SCALE, WORK, 1 )
00239          END IF
00240          GO TO 10
00241       END IF
00242 *
00243 *     Compute the estimate of the reciprocal condition number.
00244 *
00245       IF( AINVNM.NE.ZERO )
00246      $   RCOND = ( ONE / AINVNM ) / ANORM
00247 *
00248    20 CONTINUE
00249       RETURN
00250 *
00251 *     End of SPOCON
00252 *
00253       END
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