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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b SQRT05 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 SQRT05(M,N,L,NB,RESULT) 00012 * 00013 * .. Scalar Arguments .. 00014 * INTEGER LWORK, M, N, L, NB, LDT 00015 * .. Return values .. 00016 * REAL RESULT(6) 00017 * 00018 * 00019 *> \par Purpose: 00020 * ============= 00021 *> 00022 *> \verbatim 00023 *> 00024 *> SQRT05 tests STPQRT and STPMQRT. 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 REAL 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 single_lin 00079 * 00080 * ===================================================================== 00081 SUBROUTINE SQRT05(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 REAL RESULT(6) 00093 * 00094 * ===================================================================== 00095 * 00096 * .. 00097 * .. Local allocatable arrays 00098 REAL, ALLOCATABLE :: AF(:,:), Q(:,:), 00099 $ R(:,:), RWORK(:), WORK( : ), T(:,:), 00100 $ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:) 00101 * 00102 * .. Parameters .. 00103 REAL ZERO, ONE 00104 PARAMETER( ZERO = 0.0, ONE = 1.0 ) 00105 * .. 00106 * .. Local Scalars .. 00107 INTEGER INFO, J, K, M2, NP1 00108 REAL ANORM, EPS, RESID, CNORM, DNORM 00109 * .. 00110 * .. Local Arrays .. 00111 INTEGER ISEED( 4 ) 00112 * .. 00113 * .. External Functions .. 00114 REAL SLAMCH 00115 REAL SLANGE, SLANSY 00116 LOGICAL LSAME 00117 EXTERNAL SLAMCH, SLANGE, SLANSY, LSAME 00118 * .. 00119 * .. Data statements .. 00120 DATA ISEED / 1988, 1989, 1990, 1991 / 00121 * 00122 EPS = SLAMCH( 'Epsilon' ) 00123 K = N 00124 M2 = M+N 00125 IF( M.GT.0 ) THEN 00126 NP1 = N+1 00127 ELSE 00128 NP1 = 1 00129 END IF 00130 LWORK = M2*M2*NB 00131 * 00132 * Dynamically allocate all arrays 00133 * 00134 ALLOCATE(A(M2,N),AF(M2,N),Q(M2,M2),R(M2,M2),RWORK(M2), 00135 $ WORK(LWORK),T(NB,N),C(M2,N),CF(M2,N), 00136 $ D(N,M2),DF(N,M2) ) 00137 * 00138 * Put random stuff into A 00139 * 00140 LDT=NB 00141 CALL SLASET( 'Full', M2, N, ZERO, ZERO, A, M2 ) 00142 CALL SLASET( 'Full', NB, N, ZERO, ZERO, T, NB ) 00143 DO J=1,N 00144 CALL SLARNV( 2, ISEED, J, A( 1, J ) ) 00145 END DO 00146 IF( M.GT.0 ) THEN 00147 DO J=1,N 00148 CALL SLARNV( 2, ISEED, M-L, A( N+1, J ) ) 00149 END DO 00150 END IF 00151 IF( L.GT.0 ) THEN 00152 DO J=1,N 00153 CALL SLARNV( 2, ISEED, MIN(J,L), A( N+M-L+1, J ) ) 00154 END DO 00155 END IF 00156 * 00157 * Copy the matrix A to the array AF. 00158 * 00159 CALL SLACPY( 'Full', M2, N, A, M2, AF, M2 ) 00160 * 00161 * Factor the matrix A in the array AF. 00162 * 00163 CALL STPQRT( M,N,L,NB,AF,M2,AF(NP1,1),M2,T,LDT,WORK,INFO) 00164 * 00165 * Generate the (M+N)-by-(M+N) matrix Q by applying H to I 00166 * 00167 CALL SLASET( 'Full', M2, M2, ZERO, ONE, Q, M2 ) 00168 CALL SGEMQRT( 'R', 'N', M2, M2, K, NB, AF, M2, T, LDT, Q, M2, 00169 $ WORK, INFO ) 00170 * 00171 * Copy R 00172 * 00173 CALL SLASET( 'Full', M2, N, ZERO, ZERO, R, M2 ) 00174 CALL SLACPY( 'Upper', M2, N, AF, M2, R, M2 ) 00175 * 00176 * Compute |R - Q'*A| / |A| and store in RESULT(1) 00177 * 00178 CALL SGEMM( 'T', 'N', M2, N, M2, -ONE, Q, M2, A, M2, ONE, R, M2 ) 00179 ANORM = SLANGE( '1', M2, N, A, M2, RWORK ) 00180 RESID = SLANGE( '1', M2, N, R, M2, RWORK ) 00181 IF( ANORM.GT.ZERO ) THEN 00182 RESULT( 1 ) = RESID / (EPS*ANORM*MAX(1,M2)) 00183 ELSE 00184 RESULT( 1 ) = ZERO 00185 END IF 00186 * 00187 * Compute |I - Q'*Q| and store in RESULT(2) 00188 * 00189 CALL SLASET( 'Full', M2, M2, ZERO, ONE, R, M2 ) 00190 CALL SSYRK( 'U', 'C', M2, M2, -ONE, Q, M2, ONE, 00191 $ R, M2 ) 00192 RESID = SLANSY( '1', 'Upper', M2, R, M2, RWORK ) 00193 RESULT( 2 ) = RESID / (EPS*MAX(1,M2)) 00194 * 00195 * Generate random m-by-n matrix C and a copy CF 00196 * 00197 DO J=1,N 00198 CALL SLARNV( 2, ISEED, M2, C( 1, J ) ) 00199 END DO 00200 CNORM = SLANGE( '1', M2, N, C, M2, RWORK) 00201 CALL SLACPY( 'Full', M2, N, C, M2, CF, M2 ) 00202 * 00203 * Apply Q to C as Q*C 00204 * 00205 CALL STPMQRT( 'L','N', M,N,K,L,NB,AF(NP1,1),M2,T,LDT,CF, 00206 $ M2,CF(NP1,1),M2,WORK,INFO) 00207 * 00208 * Compute |Q*C - Q*C| / |C| 00209 * 00210 CALL SGEMM( 'N', 'N', M2, N, M2, -ONE, Q,M2,C,M2,ONE,CF,M2) 00211 RESID = SLANGE( '1', M2, N, CF, M2, RWORK ) 00212 IF( CNORM.GT.ZERO ) THEN 00213 RESULT( 3 ) = RESID / (EPS*MAX(1,M2)*CNORM) 00214 ELSE 00215 RESULT( 3 ) = ZERO 00216 END IF 00217 * 00218 * Copy C into CF again 00219 * 00220 CALL SLACPY( 'Full', M2, N, C, M2, CF, M2 ) 00221 * 00222 * Apply Q to C as QT*C 00223 * 00224 CALL STPMQRT('L','T',M,N,K,L,NB,AF(NP1,1),M2,T,LDT,CF,M2, 00225 $ CF(NP1,1),M2,WORK,INFO) 00226 * 00227 * Compute |QT*C - QT*C| / |C| 00228 * 00229 CALL SGEMM('T','N',M2,N,M2,-ONE,Q,M2,C,M2,ONE,CF,M2) 00230 RESID = SLANGE( '1', M2, N, CF, M2, RWORK ) 00231 IF( CNORM.GT.ZERO ) THEN 00232 RESULT( 4 ) = RESID / (EPS*MAX(1,M2)*CNORM) 00233 ELSE 00234 RESULT( 4 ) = ZERO 00235 END IF 00236 * 00237 * Generate random n-by-m matrix D and a copy DF 00238 * 00239 DO J=1,M2 00240 CALL SLARNV( 2, ISEED, N, D( 1, J ) ) 00241 END DO 00242 DNORM = SLANGE( '1', N, M2, D, N, RWORK) 00243 CALL SLACPY( 'Full', N, M2, D, N, DF, N ) 00244 * 00245 * Apply Q to D as D*Q 00246 * 00247 CALL STPMQRT('R','N',N,M,N,L,NB,AF(NP1,1),M2,T,LDT,DF,N, 00248 $ DF(1,NP1),N,WORK,INFO) 00249 * 00250 * Compute |D*Q - D*Q| / |D| 00251 * 00252 CALL SGEMM('N','N',N,M2,M2,-ONE,D,N,Q,M2,ONE,DF,N) 00253 RESID = SLANGE('1',N, M2,DF,N,RWORK ) 00254 IF( CNORM.GT.ZERO ) THEN 00255 RESULT( 5 ) = RESID / (EPS*MAX(1,M2)*DNORM) 00256 ELSE 00257 RESULT( 5 ) = ZERO 00258 END IF 00259 * 00260 * Copy D into DF again 00261 * 00262 CALL SLACPY('Full',N,M2,D,N,DF,N ) 00263 * 00264 * Apply Q to D as D*QT 00265 * 00266 CALL STPMQRT('R','T',N,M,N,L,NB,AF(NP1,1),M2,T,LDT,DF,N, 00267 $ DF(1,NP1),N,WORK,INFO) 00268 00269 * 00270 * Compute |D*QT - D*QT| / |D| 00271 * 00272 CALL SGEMM( 'N', 'T', N, M2, M2, -ONE, D, N, Q, M2, ONE, DF, N ) 00273 RESID = SLANGE( '1', N, M2, DF, N, RWORK ) 00274 IF( CNORM.GT.ZERO ) THEN 00275 RESULT( 6 ) = RESID / (EPS*MAX(1,M2)*DNORM) 00276 ELSE 00277 RESULT( 6 ) = ZERO 00278 END IF 00279 * 00280 * Deallocate all arrays 00281 * 00282 DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF) 00283 RETURN 00284 END 00285