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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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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