LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
crqt01.f
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00001 *> \brief \b CRQT01
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *  Definition:
00009 *  ===========
00010 *
00011 *       SUBROUTINE CRQT01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
00012 *                          RWORK, RESULT )
00013 * 
00014 *       .. Scalar Arguments ..
00015 *       INTEGER            LDA, LWORK, M, N
00016 *       ..
00017 *       .. Array Arguments ..
00018 *       REAL               RESULT( * ), RWORK( * )
00019 *       COMPLEX            A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
00020 *      $                   R( LDA, * ), TAU( * ), WORK( LWORK )
00021 *       ..
00022 *  
00023 *
00024 *> \par Purpose:
00025 *  =============
00026 *>
00027 *> \verbatim
00028 *>
00029 *> CRQT01 tests CGERQF, which computes the RQ factorization of an m-by-n
00030 *> matrix A, and partially tests CUNGRQ which forms the n-by-n
00031 *> orthogonal matrix Q.
00032 *>
00033 *> CRQT01 compares R with A*Q', and checks that Q is orthogonal.
00034 *> \endverbatim
00035 *
00036 *  Arguments:
00037 *  ==========
00038 *
00039 *> \param[in] M
00040 *> \verbatim
00041 *>          M is INTEGER
00042 *>          The number of rows of the matrix A.  M >= 0.
00043 *> \endverbatim
00044 *>
00045 *> \param[in] N
00046 *> \verbatim
00047 *>          N is INTEGER
00048 *>          The number of columns of the matrix A.  N >= 0.
00049 *> \endverbatim
00050 *>
00051 *> \param[in] A
00052 *> \verbatim
00053 *>          A is COMPLEX array, dimension (LDA,N)
00054 *>          The m-by-n matrix A.
00055 *> \endverbatim
00056 *>
00057 *> \param[out] AF
00058 *> \verbatim
00059 *>          AF is COMPLEX array, dimension (LDA,N)
00060 *>          Details of the RQ factorization of A, as returned by CGERQF.
00061 *>          See CGERQF for further details.
00062 *> \endverbatim
00063 *>
00064 *> \param[out] Q
00065 *> \verbatim
00066 *>          Q is COMPLEX array, dimension (LDA,N)
00067 *>          The n-by-n orthogonal matrix Q.
00068 *> \endverbatim
00069 *>
00070 *> \param[out] R
00071 *> \verbatim
00072 *>          R is COMPLEX array, dimension (LDA,max(M,N))
00073 *> \endverbatim
00074 *>
00075 *> \param[in] LDA
00076 *> \verbatim
00077 *>          LDA is INTEGER
00078 *>          The leading dimension of the arrays A, AF, Q and L.
00079 *>          LDA >= max(M,N).
00080 *> \endverbatim
00081 *>
00082 *> \param[out] TAU
00083 *> \verbatim
00084 *>          TAU is COMPLEX array, dimension (min(M,N))
00085 *>          The scalar factors of the elementary reflectors, as returned
00086 *>          by CGERQF.
00087 *> \endverbatim
00088 *>
00089 *> \param[out] WORK
00090 *> \verbatim
00091 *>          WORK is COMPLEX array, dimension (LWORK)
00092 *> \endverbatim
00093 *>
00094 *> \param[in] LWORK
00095 *> \verbatim
00096 *>          LWORK is INTEGER
00097 *>          The dimension of the array WORK.
00098 *> \endverbatim
00099 *>
00100 *> \param[out] RWORK
00101 *> \verbatim
00102 *>          RWORK is REAL array, dimension (max(M,N))
00103 *> \endverbatim
00104 *>
00105 *> \param[out] RESULT
00106 *> \verbatim
00107 *>          RESULT is REAL array, dimension (2)
00108 *>          The test ratios:
00109 *>          RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
00110 *>          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
00111 *> \endverbatim
00112 *
00113 *  Authors:
00114 *  ========
00115 *
00116 *> \author Univ. of Tennessee 
00117 *> \author Univ. of California Berkeley 
00118 *> \author Univ. of Colorado Denver 
00119 *> \author NAG Ltd. 
00120 *
00121 *> \date November 2011
00122 *
00123 *> \ingroup complex_lin
00124 *
00125 *  =====================================================================
00126       SUBROUTINE CRQT01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
00127      $                   RWORK, RESULT )
00128 *
00129 *  -- LAPACK test routine (version 3.4.0) --
00130 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00131 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00132 *     November 2011
00133 *
00134 *     .. Scalar Arguments ..
00135       INTEGER            LDA, LWORK, M, N
00136 *     ..
00137 *     .. Array Arguments ..
00138       REAL               RESULT( * ), RWORK( * )
00139       COMPLEX            A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
00140      $                   R( LDA, * ), TAU( * ), WORK( LWORK )
00141 *     ..
00142 *
00143 *  =====================================================================
00144 *
00145 *     .. Parameters ..
00146       REAL               ZERO, ONE
00147       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00148       COMPLEX            ROGUE
00149       PARAMETER          ( ROGUE = ( -1.0E+10, -1.0E+10 ) )
00150 *     ..
00151 *     .. Local Scalars ..
00152       INTEGER            INFO, MINMN
00153       REAL               ANORM, EPS, RESID
00154 *     ..
00155 *     .. External Functions ..
00156       REAL               CLANGE, CLANSY, SLAMCH
00157       EXTERNAL           CLANGE, CLANSY, SLAMCH
00158 *     ..
00159 *     .. External Subroutines ..
00160       EXTERNAL           CGEMM, CGERQF, CHERK, CLACPY, CLASET, CUNGRQ
00161 *     ..
00162 *     .. Intrinsic Functions ..
00163       INTRINSIC          CMPLX, MAX, MIN, REAL
00164 *     ..
00165 *     .. Scalars in Common ..
00166       CHARACTER*32       SRNAMT
00167 *     ..
00168 *     .. Common blocks ..
00169       COMMON             / SRNAMC / SRNAMT
00170 *     ..
00171 *     .. Executable Statements ..
00172 *
00173       MINMN = MIN( M, N )
00174       EPS = SLAMCH( 'Epsilon' )
00175 *
00176 *     Copy the matrix A to the array AF.
00177 *
00178       CALL CLACPY( 'Full', M, N, A, LDA, AF, LDA )
00179 *
00180 *     Factorize the matrix A in the array AF.
00181 *
00182       SRNAMT = 'CGERQF'
00183       CALL CGERQF( M, N, AF, LDA, TAU, WORK, LWORK, INFO )
00184 *
00185 *     Copy details of Q
00186 *
00187       CALL CLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA )
00188       IF( M.LE.N ) THEN
00189          IF( M.GT.0 .AND. M.LT.N )
00190      $      CALL CLACPY( 'Full', M, N-M, AF, LDA, Q( N-M+1, 1 ), LDA )
00191          IF( M.GT.1 )
00192      $      CALL CLACPY( 'Lower', M-1, M-1, AF( 2, N-M+1 ), LDA,
00193      $                   Q( N-M+2, N-M+1 ), LDA )
00194       ELSE
00195          IF( N.GT.1 )
00196      $      CALL CLACPY( 'Lower', N-1, N-1, AF( M-N+2, 1 ), LDA,
00197      $                   Q( 2, 1 ), LDA )
00198       END IF
00199 *
00200 *     Generate the n-by-n matrix Q
00201 *
00202       SRNAMT = 'CUNGRQ'
00203       CALL CUNGRQ( N, N, MINMN, Q, LDA, TAU, WORK, LWORK, INFO )
00204 *
00205 *     Copy R
00206 *
00207       CALL CLASET( 'Full', M, N, CMPLX( ZERO ), CMPLX( ZERO ), R, LDA )
00208       IF( M.LE.N ) THEN
00209          IF( M.GT.0 )
00210      $      CALL CLACPY( 'Upper', M, M, AF( 1, N-M+1 ), LDA,
00211      $                   R( 1, N-M+1 ), LDA )
00212       ELSE
00213          IF( M.GT.N .AND. N.GT.0 )
00214      $      CALL CLACPY( 'Full', M-N, N, AF, LDA, R, LDA )
00215          IF( N.GT.0 )
00216      $      CALL CLACPY( 'Upper', N, N, AF( M-N+1, 1 ), LDA,
00217      $                   R( M-N+1, 1 ), LDA )
00218       END IF
00219 *
00220 *     Compute R - A*Q'
00221 *
00222       CALL CGEMM( 'No transpose', 'Conjugate transpose', M, N, N,
00223      $            CMPLX( -ONE ), A, LDA, Q, LDA, CMPLX( ONE ), R, LDA )
00224 *
00225 *     Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) .
00226 *
00227       ANORM = CLANGE( '1', M, N, A, LDA, RWORK )
00228       RESID = CLANGE( '1', M, N, R, LDA, RWORK )
00229       IF( ANORM.GT.ZERO ) THEN
00230          RESULT( 1 ) = ( ( RESID / REAL( MAX( 1, N ) ) ) / ANORM ) / EPS
00231       ELSE
00232          RESULT( 1 ) = ZERO
00233       END IF
00234 *
00235 *     Compute I - Q*Q'
00236 *
00237       CALL CLASET( 'Full', N, N, CMPLX( ZERO ), CMPLX( ONE ), R, LDA )
00238       CALL CHERK( 'Upper', 'No transpose', N, N, -ONE, Q, LDA, ONE, R,
00239      $            LDA )
00240 *
00241 *     Compute norm( I - Q*Q' ) / ( N * EPS ) .
00242 *
00243       RESID = CLANSY( '1', 'Upper', N, R, LDA, RWORK )
00244 *
00245       RESULT( 2 ) = ( RESID / REAL( MAX( 1, N ) ) ) / EPS
00246 *
00247       RETURN
00248 *
00249 *     End of CRQT01
00250 *
00251       END
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