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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DQRT05 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 DQRT05(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 *> DQRT05 tests DTPQRT and DTPMQRT. 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 double_lin 00079 * 00080 * ===================================================================== 00081 SUBROUTINE DQRT05(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 DOUBLE PRECISION, ALLOCATABLE :: AF(:,:), Q(:,:), 00099 $ R(:,:), RWORK(:), WORK( : ), T(:,:), 00100 $ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:) 00101 * 00102 * .. Parameters .. 00103 DOUBLE PRECISION ONE, ZERO 00104 PARAMETER( ZERO = 0.0, ONE = 1.0 ) 00105 * .. 00106 * .. Local Scalars .. 00107 INTEGER INFO, J, K, M2, NP1 00108 DOUBLE PRECISION ANORM, EPS, RESID, CNORM, DNORM 00109 * .. 00110 * .. Local Arrays .. 00111 INTEGER ISEED( 4 ) 00112 * .. 00113 * .. External Functions .. 00114 DOUBLE PRECISION DLAMCH, DLANGE, DLANSY 00115 LOGICAL LSAME 00116 EXTERNAL DLAMCH, DLANGE, DLANSY, LSAME 00117 * .. 00118 * .. Data statements .. 00119 DATA ISEED / 1988, 1989, 1990, 1991 / 00120 * 00121 EPS = DLAMCH( 'Epsilon' ) 00122 K = N 00123 M2 = M+N 00124 IF( M.GT.0 ) THEN 00125 NP1 = N+1 00126 ELSE 00127 NP1 = 1 00128 END IF 00129 LWORK = M2*M2*NB 00130 * 00131 * Dynamically allocate all arrays 00132 * 00133 ALLOCATE(A(M2,N),AF(M2,N),Q(M2,M2),R(M2,M2),RWORK(M2), 00134 $ WORK(LWORK),T(NB,N),C(M2,N),CF(M2,N), 00135 $ D(N,M2),DF(N,M2) ) 00136 * 00137 * Put random stuff into A 00138 * 00139 LDT=NB 00140 CALL DLASET( 'Full', M2, N, ZERO, ZERO, A, M2 ) 00141 CALL DLASET( 'Full', NB, N, ZERO, ZERO, T, NB ) 00142 DO J=1,N 00143 CALL DLARNV( 2, ISEED, J, A( 1, J ) ) 00144 END DO 00145 IF( M.GT.0 ) THEN 00146 DO J=1,N 00147 CALL DLARNV( 2, ISEED, M-L, A( MIN(N+M,N+1), J ) ) 00148 END DO 00149 END IF 00150 IF( L.GT.0 ) THEN 00151 DO J=1,N 00152 CALL DLARNV( 2, ISEED, MIN(J,L), A( MIN(N+M,N+M-L+1), J ) ) 00153 END DO 00154 END IF 00155 * 00156 * Copy the matrix A to the array AF. 00157 * 00158 CALL DLACPY( 'Full', M2, N, A, M2, AF, M2 ) 00159 * 00160 * Factor the matrix A in the array AF. 00161 * 00162 CALL DTPQRT( M,N,L,NB,AF,M2,AF(NP1,1),M2,T,LDT,WORK,INFO) 00163 * 00164 * Generate the (M+N)-by-(M+N) matrix Q by applying H to I 00165 * 00166 CALL DLASET( 'Full', M2, M2, ZERO, ONE, Q, M2 ) 00167 CALL DGEMQRT( 'R', 'N', M2, M2, K, NB, AF, M2, T, LDT, Q, M2, 00168 $ WORK, INFO ) 00169 * 00170 * Copy R 00171 * 00172 CALL DLASET( 'Full', M2, N, ZERO, ZERO, R, M2 ) 00173 CALL DLACPY( 'Upper', M2, N, AF, M2, R, M2 ) 00174 * 00175 * Compute |R - Q'*A| / |A| and store in RESULT(1) 00176 * 00177 CALL DGEMM( 'T', 'N', M2, N, M2, -ONE, Q, M2, A, M2, ONE, R, M2 ) 00178 ANORM = DLANGE( '1', M2, N, A, M2, RWORK ) 00179 RESID = DLANGE( '1', M2, N, R, M2, RWORK ) 00180 IF( ANORM.GT.ZERO ) THEN 00181 RESULT( 1 ) = RESID / (EPS*ANORM*MAX(1,M2)) 00182 ELSE 00183 RESULT( 1 ) = ZERO 00184 END IF 00185 * 00186 * Compute |I - Q'*Q| and store in RESULT(2) 00187 * 00188 CALL DLASET( 'Full', M2, M2, ZERO, ONE, R, M2 ) 00189 CALL DSYRK( 'U', 'C', M2, M2, -ONE, Q, M2, ONE, R, M2 ) 00190 RESID = DLANSY( '1', 'Upper', M2, R, M2, RWORK ) 00191 RESULT( 2 ) = RESID / (EPS*MAX(1,M2)) 00192 * 00193 * Generate random m-by-n matrix C and a copy CF 00194 * 00195 DO J=1,N 00196 CALL DLARNV( 2, ISEED, M2, C( 1, J ) ) 00197 END DO 00198 CNORM = DLANGE( '1', M2, N, C, M2, RWORK) 00199 CALL DLACPY( 'Full', M2, N, C, M2, CF, M2 ) 00200 * 00201 * Apply Q to C as Q*C 00202 * 00203 CALL DTPMQRT( 'L','N', M,N,K,L,NB,AF(NP1,1),M2,T,LDT,CF,M2, 00204 $ CF(NP1,1),M2,WORK,INFO) 00205 * 00206 * Compute |Q*C - Q*C| / |C| 00207 * 00208 CALL DGEMM( 'N', 'N', M2, N, M2, -ONE, Q, M2, C, M2, ONE, CF, M2 ) 00209 RESID = DLANGE( '1', M2, N, CF, M2, RWORK ) 00210 IF( CNORM.GT.ZERO ) THEN 00211 RESULT( 3 ) = RESID / (EPS*MAX(1,M2)*CNORM) 00212 ELSE 00213 RESULT( 3 ) = ZERO 00214 END IF 00215 * 00216 * Copy C into CF again 00217 * 00218 CALL DLACPY( 'Full', M2, N, C, M2, CF, M2 ) 00219 * 00220 * Apply Q to C as QT*C 00221 * 00222 CALL DTPMQRT( 'L','T',M,N,K,L,NB,AF(NP1,1),M2,T,LDT,CF,M2, 00223 $ CF(NP1,1),M2,WORK,INFO) 00224 * 00225 * Compute |QT*C - QT*C| / |C| 00226 * 00227 CALL DGEMM('T','N',M2,N,M2,-ONE,Q,M2,C,M2,ONE,CF,M2) 00228 RESID = DLANGE( '1', M2, N, CF, M2, RWORK ) 00229 IF( CNORM.GT.ZERO ) THEN 00230 RESULT( 4 ) = RESID / (EPS*MAX(1,M2)*CNORM) 00231 ELSE 00232 RESULT( 4 ) = ZERO 00233 END IF 00234 * 00235 * Generate random n-by-m matrix D and a copy DF 00236 * 00237 DO J=1,M2 00238 CALL DLARNV( 2, ISEED, N, D( 1, J ) ) 00239 END DO 00240 DNORM = DLANGE( '1', N, M2, D, N, RWORK) 00241 CALL DLACPY( 'Full', N, M2, D, N, DF, N ) 00242 * 00243 * Apply Q to D as D*Q 00244 * 00245 CALL DTPMQRT('R','N',N,M,N,L,NB,AF(NP1,1),M2,T,LDT,DF,N, 00246 $ DF(1,NP1),N,WORK,INFO) 00247 * 00248 * Compute |D*Q - D*Q| / |D| 00249 * 00250 CALL DGEMM('N','N',N,M2,M2,-ONE,D,N,Q,M2,ONE,DF,N) 00251 RESID = DLANGE('1',N, M2,DF,N,RWORK ) 00252 IF( CNORM.GT.ZERO ) THEN 00253 RESULT( 5 ) = RESID / (EPS*MAX(1,M2)*DNORM) 00254 ELSE 00255 RESULT( 5 ) = ZERO 00256 END IF 00257 * 00258 * Copy D into DF again 00259 * 00260 CALL DLACPY('Full',N,M2,D,N,DF,N ) 00261 * 00262 * Apply Q to D as D*QT 00263 * 00264 CALL DTPMQRT('R','T',N,M,N,L,NB,AF(NP1,1),M2,T,LDT,DF,N, 00265 $ DF(1,NP1),N,WORK,INFO) 00266 00267 * 00268 * Compute |D*QT - D*QT| / |D| 00269 * 00270 CALL DGEMM( 'N', 'T', N, M2, M2, -ONE, D, N, Q, M2, ONE, DF, N ) 00271 RESID = DLANGE( '1', N, M2, DF, N, RWORK ) 00272 IF( CNORM.GT.ZERO ) THEN 00273 RESULT( 6 ) = RESID / (EPS*MAX(1,M2)*DNORM) 00274 ELSE 00275 RESULT( 6 ) = ZERO 00276 END IF 00277 * 00278 * Deallocate all arrays 00279 * 00280 DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF) 00281 RETURN 00282 END 00283