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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE CRQT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, 00002 $ RWORK, RESULT ) 00003 * 00004 * -- LAPACK test routine (version 3.1) -- 00005 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 INTEGER K, LDA, LWORK, M, N 00010 * .. 00011 * .. Array Arguments .. 00012 REAL RESULT( * ), RWORK( * ) 00013 COMPLEX AF( LDA, * ), C( LDA, * ), CC( LDA, * ), 00014 $ Q( LDA, * ), TAU( * ), WORK( LWORK ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * CRQT03 tests CUNMRQ, which computes Q*C, Q'*C, C*Q or C*Q'. 00021 * 00022 * CRQT03 compares the results of a call to CUNMRQ with the results of 00023 * forming Q explicitly by a call to CUNGRQ and then performing matrix 00024 * multiplication by a call to CGEMM. 00025 * 00026 * Arguments 00027 * ========= 00028 * 00029 * M (input) INTEGER 00030 * The number of rows or columns of the matrix C; C is n-by-m if 00031 * Q is applied from the left, or m-by-n if Q is applied from 00032 * the right. M >= 0. 00033 * 00034 * N (input) INTEGER 00035 * The order of the orthogonal matrix Q. N >= 0. 00036 * 00037 * K (input) INTEGER 00038 * The number of elementary reflectors whose product defines the 00039 * orthogonal matrix Q. N >= K >= 0. 00040 * 00041 * AF (input) COMPLEX array, dimension (LDA,N) 00042 * Details of the RQ factorization of an m-by-n matrix, as 00043 * returned by CGERQF. See CGERQF for further details. 00044 * 00045 * C (workspace) COMPLEX array, dimension (LDA,N) 00046 * 00047 * CC (workspace) COMPLEX array, dimension (LDA,N) 00048 * 00049 * Q (workspace) COMPLEX array, dimension (LDA,N) 00050 * 00051 * LDA (input) INTEGER 00052 * The leading dimension of the arrays AF, C, CC, and Q. 00053 * 00054 * TAU (input) COMPLEX array, dimension (min(M,N)) 00055 * The scalar factors of the elementary reflectors corresponding 00056 * to the RQ factorization in AF. 00057 * 00058 * WORK (workspace) COMPLEX array, dimension (LWORK) 00059 * 00060 * LWORK (input) INTEGER 00061 * The length of WORK. LWORK must be at least M, and should be 00062 * M*NB, where NB is the blocksize for this environment. 00063 * 00064 * RWORK (workspace) REAL array, dimension (M) 00065 * 00066 * RESULT (output) REAL array, dimension (4) 00067 * The test ratios compare two techniques for multiplying a 00068 * random matrix C by an n-by-n orthogonal matrix Q. 00069 * RESULT(1) = norm( Q*C - Q*C ) / ( N * norm(C) * EPS ) 00070 * RESULT(2) = norm( C*Q - C*Q ) / ( N * norm(C) * EPS ) 00071 * RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS ) 00072 * RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS ) 00073 * 00074 * ===================================================================== 00075 * 00076 * .. Parameters .. 00077 REAL ZERO, ONE 00078 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00079 COMPLEX ROGUE 00080 PARAMETER ( ROGUE = ( -1.0E+10, -1.0E+10 ) ) 00081 * .. 00082 * .. Local Scalars .. 00083 CHARACTER SIDE, TRANS 00084 INTEGER INFO, ISIDE, ITRANS, J, MC, MINMN, NC 00085 REAL CNORM, EPS, RESID 00086 * .. 00087 * .. External Functions .. 00088 LOGICAL LSAME 00089 REAL CLANGE, SLAMCH 00090 EXTERNAL LSAME, CLANGE, SLAMCH 00091 * .. 00092 * .. External Subroutines .. 00093 EXTERNAL CGEMM, CLACPY, CLARNV, CLASET, CUNGRQ, CUNMRQ 00094 * .. 00095 * .. Local Arrays .. 00096 INTEGER ISEED( 4 ) 00097 * .. 00098 * .. Intrinsic Functions .. 00099 INTRINSIC CMPLX, MAX, MIN, REAL 00100 * .. 00101 * .. Scalars in Common .. 00102 CHARACTER*32 SRNAMT 00103 * .. 00104 * .. Common blocks .. 00105 COMMON / SRNAMC / SRNAMT 00106 * .. 00107 * .. Data statements .. 00108 DATA ISEED / 1988, 1989, 1990, 1991 / 00109 * .. 00110 * .. Executable Statements .. 00111 * 00112 EPS = SLAMCH( 'Epsilon' ) 00113 MINMN = MIN( M, N ) 00114 * 00115 * Quick return if possible 00116 * 00117 IF( MINMN.EQ.0 ) THEN 00118 RESULT( 1 ) = ZERO 00119 RESULT( 2 ) = ZERO 00120 RESULT( 3 ) = ZERO 00121 RESULT( 4 ) = ZERO 00122 RETURN 00123 END IF 00124 * 00125 * Copy the last k rows of the factorization to the array Q 00126 * 00127 CALL CLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA ) 00128 IF( K.GT.0 .AND. N.GT.K ) 00129 $ CALL CLACPY( 'Full', K, N-K, AF( M-K+1, 1 ), LDA, 00130 $ Q( N-K+1, 1 ), LDA ) 00131 IF( K.GT.1 ) 00132 $ CALL CLACPY( 'Lower', K-1, K-1, AF( M-K+2, N-K+1 ), LDA, 00133 $ Q( N-K+2, N-K+1 ), LDA ) 00134 * 00135 * Generate the n-by-n matrix Q 00136 * 00137 SRNAMT = 'CUNGRQ' 00138 CALL CUNGRQ( N, N, K, Q, LDA, TAU( MINMN-K+1 ), WORK, LWORK, 00139 $ INFO ) 00140 * 00141 DO 30 ISIDE = 1, 2 00142 IF( ISIDE.EQ.1 ) THEN 00143 SIDE = 'L' 00144 MC = N 00145 NC = M 00146 ELSE 00147 SIDE = 'R' 00148 MC = M 00149 NC = N 00150 END IF 00151 * 00152 * Generate MC by NC matrix C 00153 * 00154 DO 10 J = 1, NC 00155 CALL CLARNV( 2, ISEED, MC, C( 1, J ) ) 00156 10 CONTINUE 00157 CNORM = CLANGE( '1', MC, NC, C, LDA, RWORK ) 00158 IF( CNORM.EQ.ZERO ) 00159 $ CNORM = ONE 00160 * 00161 DO 20 ITRANS = 1, 2 00162 IF( ITRANS.EQ.1 ) THEN 00163 TRANS = 'N' 00164 ELSE 00165 TRANS = 'C' 00166 END IF 00167 * 00168 * Copy C 00169 * 00170 CALL CLACPY( 'Full', MC, NC, C, LDA, CC, LDA ) 00171 * 00172 * Apply Q or Q' to C 00173 * 00174 SRNAMT = 'CUNMRQ' 00175 IF( K.GT.0 ) 00176 $ CALL CUNMRQ( SIDE, TRANS, MC, NC, K, AF( M-K+1, 1 ), LDA, 00177 $ TAU( MINMN-K+1 ), CC, LDA, WORK, LWORK, 00178 $ INFO ) 00179 * 00180 * Form explicit product and subtract 00181 * 00182 IF( LSAME( SIDE, 'L' ) ) THEN 00183 CALL CGEMM( TRANS, 'No transpose', MC, NC, MC, 00184 $ CMPLX( -ONE ), Q, LDA, C, LDA, CMPLX( ONE ), 00185 $ CC, LDA ) 00186 ELSE 00187 CALL CGEMM( 'No transpose', TRANS, MC, NC, NC, 00188 $ CMPLX( -ONE ), C, LDA, Q, LDA, CMPLX( ONE ), 00189 $ CC, LDA ) 00190 END IF 00191 * 00192 * Compute error in the difference 00193 * 00194 RESID = CLANGE( '1', MC, NC, CC, LDA, RWORK ) 00195 RESULT( ( ISIDE-1 )*2+ITRANS ) = RESID / 00196 $ ( REAL( MAX( 1, N ) )*CNORM*EPS ) 00197 * 00198 20 CONTINUE 00199 30 CONTINUE 00200 * 00201 RETURN 00202 * 00203 * End of CRQT03 00204 * 00205 END
1.7.3 
