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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZQRT05 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 ZQRT05(M,N,L,NB,RESULT) 00012 * 00013 * .. Scalar Arguments .. 00014 * INTEGER LWORK, M, N, L, NB, LDT 00015 * .. Return values .. 00016 * DOUBLE PRECISION RESULT(6) 00017 * 00018 * 00019 *> \par Purpose: 00020 * ============= 00021 *> 00022 *> \verbatim 00023 *> 00024 *> ZQRT05 tests ZTPQRT and ZTPMQRT. 00025 *> \endverbatim 00026 * 00027 * Arguments: 00028 * ========== 00029 * 00030 *> \param[in] M 00031 *> \verbatim 00032 *> M is INTEGER 00033 *> Number of rows in lower part of the 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] L 00043 *> \verbatim 00044 *> L is INTEGER 00045 *> The number of rows of the upper trapezoidal part the 00046 *> lower test matrix. 0 <= L <= M. 00047 *> \endverbatim 00048 *> 00049 *> \param[in] NB 00050 *> \verbatim 00051 *> NB is INTEGER 00052 *> Block size of test matrix. NB <= N. 00053 *> \endverbatim 00054 *> 00055 *> \param[out] RESULT 00056 *> \verbatim 00057 *> RESULT is DOUBLE PRECISION array, dimension (6) 00058 *> Results of each of the six tests below. 00059 *> 00060 *> RESULT(1) = | A - Q R | 00061 *> RESULT(2) = | I - Q^H Q | 00062 *> RESULT(3) = | Q C - Q C | 00063 *> RESULT(4) = | Q^H C - Q^H C | 00064 *> RESULT(5) = | C Q - C Q | 00065 *> RESULT(6) = | C Q^H - C Q^H | 00066 *> \endverbatim 00067 * 00068 * Authors: 00069 * ======== 00070 * 00071 *> \author Univ. of Tennessee 00072 *> \author Univ. of California Berkeley 00073 *> \author Univ. of Colorado Denver 00074 *> \author NAG Ltd. 00075 * 00076 *> \date April 2012 00077 * 00078 *> \ingroup complex16_lin 00079 * 00080 * ===================================================================== 00081 SUBROUTINE ZQRT05(M,N,L,NB,RESULT) 00082 IMPLICIT NONE 00083 * 00084 * -- LAPACK test routine (version 3.4.1) -- 00085 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00086 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00087 * April 2012 00088 * 00089 * .. Scalar Arguments .. 00090 INTEGER LWORK, M, N, L, NB, LDT 00091 * .. Return values .. 00092 DOUBLE PRECISION RESULT(6) 00093 * 00094 * ===================================================================== 00095 * 00096 * .. 00097 * .. Local allocatable arrays 00098 COMPLEX*16, ALLOCATABLE :: AF(:,:), Q(:,:), 00099 $ R(:,:), RWORK(:), WORK( : ), T(:,:), 00100 $ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:) 00101 * 00102 * .. Parameters .. 00103 DOUBLE PRECISION ZERO 00104 COMPLEX*16 ONE, CZERO 00105 PARAMETER( ZERO = 0.0, ONE = (1.0,0.0), CZERO=(0.0,0.0) ) 00106 * .. 00107 * .. Local Scalars .. 00108 INTEGER INFO, J, K, M2, NP1 00109 DOUBLE PRECISION ANORM, EPS, RESID, CNORM, DNORM 00110 * .. 00111 * .. Local Arrays .. 00112 INTEGER ISEED( 4 ) 00113 * .. 00114 * .. External Functions .. 00115 DOUBLE PRECISION DLAMCH 00116 DOUBLE PRECISION ZLANGE, ZLANSY 00117 LOGICAL LSAME 00118 EXTERNAL DLAMCH, ZLANGE, ZLANSY, LSAME 00119 * .. 00120 * .. Data statements .. 00121 DATA ISEED / 1988, 1989, 1990, 1991 / 00122 * 00123 EPS = DLAMCH( 'Epsilon' ) 00124 K = N 00125 M2 = M+N 00126 IF( M.GT.0 ) THEN 00127 NP1 = N+1 00128 ELSE 00129 NP1 = 1 00130 END IF 00131 LWORK = M2*M2*NB 00132 * 00133 * Dynamically allocate all arrays 00134 * 00135 ALLOCATE(A(M2,N),AF(M2,N),Q(M2,M2),R(M2,M2),RWORK(M2), 00136 $ WORK(LWORK),T(NB,N),C(M2,N),CF(M2,N), 00137 $ D(N,M2),DF(N,M2) ) 00138 * 00139 * Put random stuff into A 00140 * 00141 LDT=NB 00142 CALL ZLASET( 'Full', M2, N, CZERO, CZERO, A, M2 ) 00143 CALL ZLASET( 'Full', NB, N, CZERO, CZERO, T, NB ) 00144 DO J=1,N 00145 CALL ZLARNV( 2, ISEED, J, A( 1, J ) ) 00146 END DO 00147 IF( M.GT.0 ) THEN 00148 DO J=1,N 00149 CALL ZLARNV( 2, ISEED, M-L, A( MIN(N+M,N+1), J ) ) 00150 END DO 00151 END IF 00152 IF( L.GT.0 ) THEN 00153 DO J=1,N 00154 CALL ZLARNV( 2, ISEED, MIN(J,L), A( MIN(N+M,N+M-L+1), J ) ) 00155 END DO 00156 END IF 00157 * 00158 * Copy the matrix A to the array AF. 00159 * 00160 CALL ZLACPY( 'Full', M2, N, A, M2, AF, M2 ) 00161 * 00162 * Factor the matrix A in the array AF. 00163 * 00164 CALL ZTPQRT( M,N,L,NB,AF,M2,AF(NP1,1),M2,T,LDT,WORK,INFO) 00165 * 00166 * Generate the (M+N)-by-(M+N) matrix Q by applying H to I 00167 * 00168 CALL ZLASET( 'Full', M2, M2, CZERO, ONE, Q, M2 ) 00169 CALL ZGEMQRT( 'R', 'N', M2, M2, K, NB, AF, M2, T, LDT, Q, M2, 00170 $ WORK, INFO ) 00171 * 00172 * Copy R 00173 * 00174 CALL ZLASET( 'Full', M2, N, CZERO, CZERO, R, M2 ) 00175 CALL ZLACPY( 'Upper', M2, N, AF, M2, R, M2 ) 00176 * 00177 * Compute |R - Q'*A| / |A| and store in RESULT(1) 00178 * 00179 CALL ZGEMM( 'C', 'N', M2, N, M2, -ONE, Q, M2, A, M2, ONE, R, M2 ) 00180 ANORM = ZLANGE( '1', M2, N, A, M2, RWORK ) 00181 RESID = ZLANGE( '1', M2, N, R, M2, RWORK ) 00182 IF( ANORM.GT.ZERO ) THEN 00183 RESULT( 1 ) = RESID / (EPS*ANORM*MAX(1,M2)) 00184 ELSE 00185 RESULT( 1 ) = ZERO 00186 END IF 00187 * 00188 * Compute |I - Q'*Q| and store in RESULT(2) 00189 * 00190 CALL ZLASET( 'Full', M2, M2, CZERO, ONE, R, M2 ) 00191 CALL ZHERK( 'U', 'C', M2, M2, DREAL(-ONE), Q, M2, DREAL(ONE), 00192 $ R, M2 ) 00193 RESID = ZLANSY( '1', 'Upper', M2, R, M2, RWORK ) 00194 RESULT( 2 ) = RESID / (EPS*MAX(1,M2)) 00195 * 00196 * Generate random m-by-n matrix C and a copy CF 00197 * 00198 DO J=1,N 00199 CALL ZLARNV( 2, ISEED, M2, C( 1, J ) ) 00200 END DO 00201 CNORM = ZLANGE( '1', M2, N, C, M2, RWORK) 00202 CALL ZLACPY( 'Full', M2, N, C, M2, CF, M2 ) 00203 * 00204 * Apply Q to C as Q*C 00205 * 00206 CALL ZTPMQRT( 'L','N', M,N,K,L,NB,AF(NP1,1),M2,T,LDT,CF,M2, 00207 $ CF(NP1,1),M2,WORK,INFO) 00208 * 00209 * Compute |Q*C - Q*C| / |C| 00210 * 00211 CALL ZGEMM( 'N', 'N', M2, N, M2, -ONE, Q, M2, C, M2, ONE, CF, M2 ) 00212 RESID = ZLANGE( '1', M2, N, CF, M2, RWORK ) 00213 IF( CNORM.GT.ZERO ) THEN 00214 RESULT( 3 ) = RESID / (EPS*MAX(1,M2)*CNORM) 00215 ELSE 00216 RESULT( 3 ) = ZERO 00217 END IF 00218 * 00219 * Copy C into CF again 00220 * 00221 CALL ZLACPY( 'Full', M2, N, C, M2, CF, M2 ) 00222 * 00223 * Apply Q to C as QT*C 00224 * 00225 CALL ZTPMQRT( 'L','C',M,N,K,L,NB,AF(NP1,1),M2,T,LDT,CF,M2, 00226 $ CF(NP1,1),M2,WORK,INFO) 00227 * 00228 * Compute |QT*C - QT*C| / |C| 00229 * 00230 CALL ZGEMM('C','N',M2,N,M2,-ONE,Q,M2,C,M2,ONE,CF,M2) 00231 RESID = ZLANGE( '1', M2, N, CF, M2, RWORK ) 00232 IF( CNORM.GT.ZERO ) THEN 00233 RESULT( 4 ) = RESID / (EPS*MAX(1,M2)*CNORM) 00234 ELSE 00235 RESULT( 4 ) = ZERO 00236 END IF 00237 * 00238 * Generate random n-by-m matrix D and a copy DF 00239 * 00240 DO J=1,M2 00241 CALL ZLARNV( 2, ISEED, N, D( 1, J ) ) 00242 END DO 00243 DNORM = ZLANGE( '1', N, M2, D, N, RWORK) 00244 CALL ZLACPY( 'Full', N, M2, D, N, DF, N ) 00245 * 00246 * Apply Q to D as D*Q 00247 * 00248 CALL ZTPMQRT('R','N',N,M,N,L,NB,AF(NP1,1),M2,T,LDT,DF,N, 00249 $ DF(1,NP1),N,WORK,INFO) 00250 * 00251 * Compute |D*Q - D*Q| / |D| 00252 * 00253 CALL ZGEMM('N','N',N,M2,M2,-ONE,D,N,Q,M2,ONE,DF,N) 00254 RESID = ZLANGE('1',N, M2,DF,N,RWORK ) 00255 IF( CNORM.GT.ZERO ) THEN 00256 RESULT( 5 ) = RESID / (EPS*MAX(1,M2)*DNORM) 00257 ELSE 00258 RESULT( 5 ) = ZERO 00259 END IF 00260 * 00261 * Copy D into DF again 00262 * 00263 CALL ZLACPY('Full',N,M2,D,N,DF,N ) 00264 * 00265 * Apply Q to D as D*QT 00266 * 00267 CALL ZTPMQRT('R','C',N,M,N,L,NB,AF(NP1,1),M2,T,LDT,DF,N, 00268 $ DF(1,NP1),N,WORK,INFO) 00269 00270 * 00271 * Compute |D*QT - D*QT| / |D| 00272 * 00273 CALL ZGEMM( 'N', 'C', N, M2, M2, -ONE, D, N, Q, M2, ONE, DF, N ) 00274 RESID = ZLANGE( '1', N, M2, DF, N, RWORK ) 00275 IF( CNORM.GT.ZERO ) THEN 00276 RESULT( 6 ) = RESID / (EPS*MAX(1,M2)*DNORM) 00277 ELSE 00278 RESULT( 6 ) = ZERO 00279 END IF 00280 * 00281 * Deallocate all arrays 00282 * 00283 DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF) 00284 RETURN 00285 END 00286