LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cqrt04.f
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00001 *> \brief \b CQRT04
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 CQRT04(M,N,NB,RESULT)
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       INTEGER M, N, NB, LDT
00015 *       .. Return values ..
00016 *       REAL RESULT(6)
00017 *  
00018 *
00019 *> \par Purpose:
00020 *  =============
00021 *>
00022 *> \verbatim
00023 *>
00024 *> CQRT04 tests CGEQRT and CGEMQRT.
00025 *> \endverbatim
00026 *
00027 *  Arguments:
00028 *  ==========
00029 *
00030 *> \param[in] M
00031 *> \verbatim
00032 *>          M is INTEGER
00033 *>          Number of rows in test matrix.
00034 *> \endverbatim
00035 *>
00036 *> \param[in] N
00037 *> \verbatim
00038 *>          N is INTEGER
00039 *>          Number of columns in test matrix.
00040 *> \endverbatim
00041 *>
00042 *> \param[in] NB
00043 *> \verbatim
00044 *>          NB is INTEGER
00045 *>          Block size of test matrix.  NB <= Min(M,N).
00046 *> \endverbatim
00047 *>
00048 *> \param[out] RESULT
00049 *> \verbatim
00050 *>          RESULT is REAL array, dimension (6)
00051 *>          Results of each of the six tests below.
00052 *>
00053 *>          RESULT(1) = | A - Q R |
00054 *>          RESULT(2) = | I - Q^H Q |
00055 *>          RESULT(3) = | Q C - Q C |
00056 *>          RESULT(4) = | Q^H C - Q^H C |
00057 *>          RESULT(5) = | C Q - C Q | 
00058 *>          RESULT(6) = | C Q^H - C Q^H |
00059 *> \endverbatim
00060 *
00061 *  Authors:
00062 *  ========
00063 *
00064 *> \author Univ. of Tennessee 
00065 *> \author Univ. of California Berkeley 
00066 *> \author Univ. of Colorado Denver 
00067 *> \author NAG Ltd. 
00068 *
00069 *> \date April 2012
00070 *
00071 *> \ingroup complex_lin
00072 *
00073 *  =====================================================================
00074       SUBROUTINE CQRT04(M,N,NB,RESULT)
00075       IMPLICIT NONE
00076 *
00077 *  -- LAPACK test routine (version 3.4.1) --
00078 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00079 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00080 *     April 2012
00081 *
00082 *     .. Scalar Arguments ..
00083       INTEGER M, N, NB, LDT
00084 *     .. Return values ..
00085       REAL RESULT(6)
00086 *
00087 *  =====================================================================
00088 *
00089 *     ..
00090 *     .. Local allocatable arrays 
00091       COMPLEX, ALLOCATABLE :: AF(:,:), Q(:,:),
00092      $  R(:,:), RWORK(:), WORK( : ), T(:,:), 
00093      $  CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
00094 *
00095 *     .. Parameters ..
00096       REAL ZERO
00097       COMPLEX ONE, CZERO
00098       PARAMETER( ZERO = 0.0, ONE = (1.0,0.0), CZERO=(0.0,0.0) )
00099 *     ..
00100 *     .. Local Scalars ..
00101       INTEGER INFO, J, K, L, LWORK
00102       REAL   ANORM, EPS, RESID, CNORM, DNORM
00103 *     ..
00104 *     .. Local Arrays ..
00105       INTEGER            ISEED( 4 )
00106 *     ..
00107 *     .. External Functions ..
00108       REAL SLAMCH 
00109       REAL CLANGE, CLANSY
00110       LOGICAL  LSAME
00111       EXTERNAL SLAMCH, CLANGE, CLANSY, LSAME
00112 *     ..
00113 *     .. Intrinsic Functions ..
00114       INTRINSIC  MAX, MIN      
00115 *     ..
00116 *     .. Data statements ..
00117       DATA ISEED / 1988, 1989, 1990, 1991 /      
00118 *      
00119       EPS = SLAMCH( 'Epsilon' )
00120       K = MIN(M,N)
00121       L = MAX(M,N)
00122       LWORK = MAX(2,L)*MAX(2,L)*NB
00123 *
00124 *     Dynamically allocate local arrays
00125 *
00126       ALLOCATE ( A(M,N), AF(M,N), Q(M,M), R(M,L), RWORK(L), 
00127      $           WORK(LWORK), T(NB,N), C(M,N), CF(M,N), 
00128      $           D(N,M), DF(N,M) )
00129 *
00130 *     Put random numbers into A and copy to AF
00131 *
00132       LDT=NB
00133       DO J=1,N
00134          CALL CLARNV( 2, ISEED, M, A( 1, J ) )
00135       END DO
00136       CALL CLACPY( 'Full', M, N, A, M, AF, M )
00137 *
00138 *     Factor the matrix A in the array AF.
00139 *
00140       CALL CGEQRT( M, N, NB, AF, M, T, LDT, WORK, INFO )
00141 *
00142 *     Generate the m-by-m matrix Q
00143 *
00144       CALL CLASET( 'Full', M, M, CZERO, ONE, Q, M )
00145       CALL CGEMQRT( 'R', 'N', M, M, K, NB, AF, M, T, LDT, Q, M, 
00146      $              WORK, INFO )
00147 *
00148 *     Copy R
00149 *
00150       CALL CLASET( 'Full', M, N, CZERO, CZERO, R, M )
00151       CALL CLACPY( 'Upper', M, N, AF, M, R, M )
00152 *
00153 *     Compute |R - Q'*A| / |A| and store in RESULT(1)
00154 *
00155       CALL CGEMM( 'C', 'N', M, N, M, -ONE, Q, M, A, M, ONE, R, M )
00156       ANORM = CLANGE( '1', M, N, A, M, RWORK )
00157       RESID = CLANGE( '1', M, N, R, M, RWORK )
00158       IF( ANORM.GT.ZERO ) THEN
00159          RESULT( 1 ) = RESID / (EPS*MAX(1,M)*ANORM)
00160       ELSE
00161          RESULT( 1 ) = ZERO
00162       END IF
00163 *
00164 *     Compute |I - Q'*Q| and store in RESULT(2)
00165 *
00166       CALL CLASET( 'Full', M, M, CZERO, ONE, R, M )
00167       CALL CHERK( 'U', 'C', M, M, REAL(-ONE), Q, M, REAL(ONE), R, M )
00168       RESID = CLANSY( '1', 'Upper', M, R, M, RWORK )
00169       RESULT( 2 ) = RESID / (EPS*MAX(1,M))
00170 *
00171 *     Generate random m-by-n matrix C and a copy CF
00172 *
00173       DO J=1,N
00174          CALL CLARNV( 2, ISEED, M, C( 1, J ) )
00175       END DO
00176       CNORM = CLANGE( '1', M, N, C, M, RWORK)
00177       CALL CLACPY( 'Full', M, N, C, M, CF, M )
00178 *
00179 *     Apply Q to C as Q*C
00180 *
00181       CALL CGEMQRT( 'L', 'N', M, N, K, NB, AF, M, T, NB, CF, M, 
00182      $             WORK, INFO)
00183 *
00184 *     Compute |Q*C - Q*C| / |C|
00185 *
00186       CALL CGEMM( 'N', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
00187       RESID = CLANGE( '1', M, N, CF, M, RWORK )
00188       IF( CNORM.GT.ZERO ) THEN
00189          RESULT( 3 ) = RESID / (EPS*MAX(1,M)*CNORM)
00190       ELSE
00191          RESULT( 3 ) = ZERO
00192       END IF
00193 *
00194 *     Copy C into CF again
00195 *
00196       CALL CLACPY( 'Full', M, N, C, M, CF, M )
00197 *
00198 *     Apply Q to C as QT*C
00199 *
00200       CALL CGEMQRT( 'L', 'C', M, N, K, NB, AF, M, T, NB, CF, M, 
00201      $             WORK, INFO)
00202 *
00203 *     Compute |QT*C - QT*C| / |C|
00204 *
00205       CALL CGEMM( 'C', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
00206       RESID = CLANGE( '1', M, N, CF, M, RWORK )
00207       IF( CNORM.GT.ZERO ) THEN
00208          RESULT( 4 ) = RESID / (EPS*MAX(1,M)*CNORM)
00209       ELSE
00210          RESULT( 4 ) = ZERO
00211       END IF     
00212 *
00213 *     Generate random n-by-m matrix D and a copy DF
00214 *
00215       DO J=1,M
00216          CALL CLARNV( 2, ISEED, N, D( 1, J ) )
00217       END DO
00218       DNORM = CLANGE( '1', N, M, D, N, RWORK)
00219       CALL CLACPY( 'Full', N, M, D, N, DF, N )
00220 *
00221 *     Apply Q to D as D*Q
00222 *
00223       CALL CGEMQRT( 'R', 'N', N, M, K, NB, AF, M, T, NB, DF, N, 
00224      $             WORK, INFO)      
00225 *
00226 *     Compute |D*Q - D*Q| / |D|
00227 *
00228       CALL CGEMM( 'N', 'N', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
00229       RESID = CLANGE( '1', N, M, DF, N, RWORK )
00230       IF( CNORM.GT.ZERO ) THEN
00231          RESULT( 5 ) = RESID / (EPS*MAX(1,M)*DNORM)
00232       ELSE
00233          RESULT( 5 ) = ZERO
00234       END IF
00235 *
00236 *     Copy D into DF again
00237 *
00238       CALL CLACPY( 'Full', N, M, D, N, DF, N )
00239 *
00240 *     Apply Q to D as D*QT
00241 *
00242       CALL CGEMQRT( 'R', 'C', N, M, K, NB, AF, M, T, NB, DF, N, 
00243      $             WORK, INFO)      
00244 *
00245 *     Compute |D*QT - D*QT| / |D|
00246 *
00247       CALL CGEMM( 'N', 'C', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
00248       RESID = CLANGE( '1', N, M, DF, N, RWORK )
00249       IF( CNORM.GT.ZERO ) THEN
00250          RESULT( 6 ) = RESID / (EPS*MAX(1,M)*DNORM)
00251       ELSE
00252          RESULT( 6 ) = ZERO
00253       END IF
00254 *
00255 *     Deallocate all arrays
00256 *
00257       DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
00258 *
00259       RETURN
00260       END
00261 
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