LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cqrt12.f
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00001 *> \brief \b CQRT12
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *  Definition:
00009 *  ===========
00010 *
00011 *       REAL             FUNCTION CQRT12( M, N, A, LDA, S, WORK, LWORK,
00012 *                        RWORK )
00013 * 
00014 *       .. Scalar Arguments ..
00015 *       INTEGER            LDA, LWORK, M, N
00016 *       ..
00017 *       .. Array Arguments ..
00018 *       REAL               RWORK( * ), S( * )
00019 *       COMPLEX            A( LDA, * ), WORK( LWORK )
00020 *       ..
00021 *  
00022 *
00023 *> \par Purpose:
00024 *  =============
00025 *>
00026 *> \verbatim
00027 *>
00028 *> CQRT12 computes the singular values `svlues' of the upper trapezoid
00029 *> of A(1:M,1:N) and returns the ratio
00030 *>
00031 *>      || s - svlues||/(||svlues||*eps*max(M,N))
00032 *> \endverbatim
00033 *
00034 *  Arguments:
00035 *  ==========
00036 *
00037 *> \param[in] M
00038 *> \verbatim
00039 *>          M is INTEGER
00040 *>          The number of rows of the matrix A.
00041 *> \endverbatim
00042 *>
00043 *> \param[in] N
00044 *> \verbatim
00045 *>          N is INTEGER
00046 *>          The number of columns of the matrix A.
00047 *> \endverbatim
00048 *>
00049 *> \param[in] A
00050 *> \verbatim
00051 *>          A is COMPLEX array, dimension (LDA,N)
00052 *>          The M-by-N matrix A. Only the upper trapezoid is referenced.
00053 *> \endverbatim
00054 *>
00055 *> \param[in] LDA
00056 *> \verbatim
00057 *>          LDA is INTEGER
00058 *>          The leading dimension of the array A.
00059 *> \endverbatim
00060 *>
00061 *> \param[in] S
00062 *> \verbatim
00063 *>          S is REAL array, dimension (min(M,N))
00064 *>          The singular values of the matrix A.
00065 *> \endverbatim
00066 *>
00067 *> \param[out] WORK
00068 *> \verbatim
00069 *>          WORK is COMPLEX array, dimension (LWORK)
00070 *> \endverbatim
00071 *>
00072 *> \param[in] LWORK
00073 *> \verbatim
00074 *>          LWORK is INTEGER
00075 *>          The length of the array WORK. LWORK >= M*N + 2*min(M,N) +
00076 *>          max(M,N).
00077 *> \endverbatim
00078 *>
00079 *> \param[out] RWORK
00080 *> \verbatim
00081 *>          RWORK is REAL array, dimension (4*min(M,N))
00082 *> \endverbatim
00083 *
00084 *  Authors:
00085 *  ========
00086 *
00087 *> \author Univ. of Tennessee 
00088 *> \author Univ. of California Berkeley 
00089 *> \author Univ. of Colorado Denver 
00090 *> \author NAG Ltd. 
00091 *
00092 *> \date November 2011
00093 *
00094 *> \ingroup complex_lin
00095 *
00096 *  =====================================================================
00097       REAL             FUNCTION CQRT12( M, N, A, LDA, S, WORK, LWORK,
00098      $                 RWORK )
00099 *
00100 *  -- LAPACK test routine (version 3.4.0) --
00101 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00102 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00103 *     November 2011
00104 *
00105 *     .. Scalar Arguments ..
00106       INTEGER            LDA, LWORK, M, N
00107 *     ..
00108 *     .. Array Arguments ..
00109       REAL               RWORK( * ), S( * )
00110       COMPLEX            A( LDA, * ), WORK( LWORK )
00111 *     ..
00112 *
00113 *  =====================================================================
00114 *
00115 *     .. Parameters ..
00116       REAL               ZERO, ONE
00117       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
00118 *     ..
00119 *     .. Local Scalars ..
00120       INTEGER            I, INFO, ISCL, J, MN
00121       REAL               ANRM, BIGNUM, NRMSVL, SMLNUM
00122 *     ..
00123 *     .. Local Arrays ..
00124       REAL               DUMMY( 1 )
00125 *     ..
00126 *     .. External Functions ..
00127       REAL               CLANGE, SASUM, SLAMCH, SNRM2
00128       EXTERNAL           CLANGE, SASUM, SLAMCH, SNRM2
00129 *     ..
00130 *     .. External Subroutines ..
00131       EXTERNAL           CGEBD2, CLASCL, CLASET, SAXPY, SBDSQR, SLABAD,
00132      $                   SLASCL, XERBLA
00133 *     ..
00134 *     .. Intrinsic Functions ..
00135       INTRINSIC          CMPLX, MAX, MIN, REAL
00136 *     ..
00137 *     .. Executable Statements ..
00138 *
00139       CQRT12 = ZERO
00140 *
00141 *     Test that enough workspace is supplied
00142 *
00143       IF( LWORK.LT.M*N+2*MIN( M, N )+MAX( M, N ) ) THEN
00144          CALL XERBLA( 'CQRT12', 7 )
00145          RETURN
00146       END IF
00147 *
00148 *     Quick return if possible
00149 *
00150       MN = MIN( M, N )
00151       IF( MN.LE.ZERO )
00152      $   RETURN
00153 *
00154       NRMSVL = SNRM2( MN, S, 1 )
00155 *
00156 *     Copy upper triangle of A into work
00157 *
00158       CALL CLASET( 'Full', M, N, CMPLX( ZERO ), CMPLX( ZERO ), WORK, M )
00159       DO 20 J = 1, N
00160          DO 10 I = 1, MIN( J, M )
00161             WORK( ( J-1 )*M+I ) = A( I, J )
00162    10    CONTINUE
00163    20 CONTINUE
00164 *
00165 *     Get machine parameters
00166 *
00167       SMLNUM = SLAMCH( 'S' ) / SLAMCH( 'P' )
00168       BIGNUM = ONE / SMLNUM
00169       CALL SLABAD( SMLNUM, BIGNUM )
00170 *
00171 *     Scale work if max entry outside range [SMLNUM,BIGNUM]
00172 *
00173       ANRM = CLANGE( 'M', M, N, WORK, M, DUMMY )
00174       ISCL = 0
00175       IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
00176 *
00177 *        Scale matrix norm up to SMLNUM
00178 *
00179          CALL CLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, WORK, M, INFO )
00180          ISCL = 1
00181       ELSE IF( ANRM.GT.BIGNUM ) THEN
00182 *
00183 *        Scale matrix norm down to BIGNUM
00184 *
00185          CALL CLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, WORK, M, INFO )
00186          ISCL = 1
00187       END IF
00188 *
00189       IF( ANRM.NE.ZERO ) THEN
00190 *
00191 *        Compute SVD of work
00192 *
00193          CALL CGEBD2( M, N, WORK, M, RWORK( 1 ), RWORK( MN+1 ),
00194      $                WORK( M*N+1 ), WORK( M*N+MN+1 ),
00195      $                WORK( M*N+2*MN+1 ), INFO )
00196          CALL SBDSQR( 'Upper', MN, 0, 0, 0, RWORK( 1 ), RWORK( MN+1 ),
00197      $                DUMMY, MN, DUMMY, 1, DUMMY, MN, RWORK( 2*MN+1 ),
00198      $                INFO )
00199 *
00200          IF( ISCL.EQ.1 ) THEN
00201             IF( ANRM.GT.BIGNUM ) THEN
00202                CALL SLASCL( 'G', 0, 0, BIGNUM, ANRM, MN, 1, RWORK( 1 ),
00203      $                      MN, INFO )
00204             END IF
00205             IF( ANRM.LT.SMLNUM ) THEN
00206                CALL SLASCL( 'G', 0, 0, SMLNUM, ANRM, MN, 1, RWORK( 1 ),
00207      $                      MN, INFO )
00208             END IF
00209          END IF
00210 *
00211       ELSE
00212 *
00213          DO 30 I = 1, MN
00214             RWORK( I ) = ZERO
00215    30    CONTINUE
00216       END IF
00217 *
00218 *     Compare s and singular values of work
00219 *
00220       CALL SAXPY( MN, -ONE, S, 1, RWORK( 1 ), 1 )
00221       CQRT12 = SASUM( MN, RWORK( 1 ), 1 ) /
00222      $         ( SLAMCH( 'Epsilon' )*REAL( MAX( M, N ) ) )
00223       IF( NRMSVL.NE.ZERO )
00224      $   CQRT12 = CQRT12 / NRMSVL
00225 *
00226       RETURN
00227 *
00228 *     End of CQRT12
00229 *
00230       END
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