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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b SQRT04 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 SQRT04(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 *> SQRT04 tests SGEQRT and SGEMQRT. 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 single_lin 00072 * 00073 * ===================================================================== 00074 SUBROUTINE SQRT04(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 REAL, ALLOCATABLE :: AF(:,:), Q(:,:), 00092 $ R(:,:), RWORK(:), WORK( : ), T(:,:), 00093 $ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:) 00094 * 00095 * .. Parameters .. 00096 REAL ONE, ZERO 00097 PARAMETER( ZERO = 0.0, ONE = 1.0 ) 00098 * .. 00099 * .. Local Scalars .. 00100 INTEGER INFO, J, K, L, LWORK 00101 REAL ANORM, EPS, RESID, CNORM, DNORM 00102 * .. 00103 * .. Local Arrays .. 00104 INTEGER ISEED( 4 ) 00105 * .. 00106 * .. External Functions .. 00107 REAL SLAMCH 00108 REAL SLANGE, SLANSY 00109 LOGICAL LSAME 00110 EXTERNAL SLAMCH, SLANGE, SLANSY, LSAME 00111 * .. 00112 * .. Intrinsic Functions .. 00113 INTRINSIC MAX, MIN 00114 * .. 00115 * .. Data statements .. 00116 DATA ISEED / 1988, 1989, 1990, 1991 / 00117 * 00118 EPS = SLAMCH( 'Epsilon' ) 00119 K = MIN(M,N) 00120 L = MAX(M,N) 00121 LWORK = MAX(2,L)*MAX(2,L)*NB 00122 * 00123 * Dynamically allocate local arrays 00124 * 00125 ALLOCATE ( A(M,N), AF(M,N), Q(M,M), R(M,L), RWORK(L), 00126 $ WORK(LWORK), T(NB,N), C(M,N), CF(M,N), 00127 $ D(N,M), DF(N,M) ) 00128 * 00129 * Put random numbers into A and copy to AF 00130 * 00131 LDT=NB 00132 DO J=1,N 00133 CALL SLARNV( 2, ISEED, M, A( 1, J ) ) 00134 END DO 00135 CALL SLACPY( 'Full', M, N, A, M, AF, M ) 00136 * 00137 * Factor the matrix A in the array AF. 00138 * 00139 CALL SGEQRT( M, N, NB, AF, M, T, LDT, WORK, INFO ) 00140 * 00141 * Generate the m-by-m matrix Q 00142 * 00143 CALL SLASET( 'Full', M, M, ZERO, ONE, Q, M ) 00144 CALL SGEMQRT( 'R', 'N', M, M, K, NB, AF, M, T, LDT, Q, M, 00145 $ WORK, INFO ) 00146 * 00147 * Copy R 00148 * 00149 CALL SLASET( 'Full', M, N, ZERO, ZERO, R, M ) 00150 CALL SLACPY( 'Upper', M, N, AF, M, R, M ) 00151 * 00152 * Compute |R - Q'*A| / |A| and store in RESULT(1) 00153 * 00154 CALL SGEMM( 'T', 'N', M, N, M, -ONE, Q, M, A, M, ONE, R, M ) 00155 ANORM = SLANGE( '1', M, N, A, M, RWORK ) 00156 RESID = SLANGE( '1', M, N, R, M, RWORK ) 00157 IF( ANORM.GT.ZERO ) THEN 00158 RESULT( 1 ) = RESID / (EPS*MAX(1,M)*ANORM) 00159 ELSE 00160 RESULT( 1 ) = ZERO 00161 END IF 00162 * 00163 * Compute |I - Q'*Q| and store in RESULT(2) 00164 * 00165 CALL SLASET( 'Full', M, M, ZERO, ONE, R, M ) 00166 CALL SSYRK( 'U', 'C', M, M, -ONE, Q, M, ONE, R, M ) 00167 RESID = SLANSY( '1', 'Upper', M, R, M, RWORK ) 00168 RESULT( 2 ) = RESID / (EPS*MAX(1,M)) 00169 * 00170 * Generate random m-by-n matrix C and a copy CF 00171 * 00172 DO J=1,N 00173 CALL SLARNV( 2, ISEED, M, C( 1, J ) ) 00174 END DO 00175 CNORM = SLANGE( '1', M, N, C, M, RWORK) 00176 CALL SLACPY( 'Full', M, N, C, M, CF, M ) 00177 * 00178 * Apply Q to C as Q*C 00179 * 00180 CALL SGEMQRT( 'L', 'N', M, N, K, NB, AF, M, T, NB, CF, M, 00181 $ WORK, INFO) 00182 * 00183 * Compute |Q*C - Q*C| / |C| 00184 * 00185 CALL SGEMM( 'N', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M ) 00186 RESID = SLANGE( '1', M, N, CF, M, RWORK ) 00187 IF( CNORM.GT.ZERO ) THEN 00188 RESULT( 3 ) = RESID / (EPS*MAX(1,M)*CNORM) 00189 ELSE 00190 RESULT( 3 ) = ZERO 00191 END IF 00192 * 00193 * Copy C into CF again 00194 * 00195 CALL SLACPY( 'Full', M, N, C, M, CF, M ) 00196 * 00197 * Apply Q to C as QT*C 00198 * 00199 CALL SGEMQRT( 'L', 'T', M, N, K, NB, AF, M, T, NB, CF, M, 00200 $ WORK, INFO) 00201 * 00202 * Compute |QT*C - QT*C| / |C| 00203 * 00204 CALL SGEMM( 'T', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M ) 00205 RESID = SLANGE( '1', M, N, CF, M, RWORK ) 00206 IF( CNORM.GT.ZERO ) THEN 00207 RESULT( 4 ) = RESID / (EPS*MAX(1,M)*CNORM) 00208 ELSE 00209 RESULT( 4 ) = ZERO 00210 END IF 00211 * 00212 * Generate random n-by-m matrix D and a copy DF 00213 * 00214 DO J=1,M 00215 CALL SLARNV( 2, ISEED, N, D( 1, J ) ) 00216 END DO 00217 DNORM = SLANGE( '1', N, M, D, N, RWORK) 00218 CALL SLACPY( 'Full', N, M, D, N, DF, N ) 00219 * 00220 * Apply Q to D as D*Q 00221 * 00222 CALL SGEMQRT( 'R', 'N', N, M, K, NB, AF, M, T, NB, DF, N, 00223 $ WORK, INFO) 00224 * 00225 * Compute |D*Q - D*Q| / |D| 00226 * 00227 CALL SGEMM( 'N', 'N', N, M, M, -ONE, D, N, Q, M, ONE, DF, N ) 00228 RESID = SLANGE( '1', N, M, DF, N, RWORK ) 00229 IF( CNORM.GT.ZERO ) THEN 00230 RESULT( 5 ) = RESID / (EPS*MAX(1,M)*DNORM) 00231 ELSE 00232 RESULT( 5 ) = ZERO 00233 END IF 00234 * 00235 * Copy D into DF again 00236 * 00237 CALL SLACPY( 'Full', N, M, D, N, DF, N ) 00238 * 00239 * Apply Q to D as D*QT 00240 * 00241 CALL SGEMQRT( 'R', 'T', N, M, K, NB, AF, M, T, NB, DF, N, 00242 $ WORK, INFO) 00243 * 00244 * Compute |D*QT - D*QT| / |D| 00245 * 00246 CALL SGEMM( 'N', 'T', N, M, M, -ONE, D, N, Q, M, ONE, DF, N ) 00247 RESID = SLANGE( '1', N, M, DF, N, RWORK ) 00248 IF( CNORM.GT.ZERO ) THEN 00249 RESULT( 6 ) = RESID / (EPS*MAX(1,M)*DNORM) 00250 ELSE 00251 RESULT( 6 ) = ZERO 00252 END IF 00253 * 00254 * Deallocate all arrays 00255 * 00256 DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF) 00257 * 00258 RETURN 00259 END 00260