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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 DGRQTS( M, P, N, A, AF, Q, R, LDA, TAUA, B, BF, Z, T, 00002 $ BWK, LDB, TAUB, WORK, LWORK, 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 LDA, LDB, LWORK, M, N, P 00010 * .. 00011 * .. Array Arguments .. 00012 DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), B( LDB, * ), 00013 $ BF( LDB, * ), BWK( LDB, * ), Q( LDA, * ), 00014 $ R( LDA, * ), RESULT( 4 ), RWORK( * ), 00015 $ T( LDB, * ), TAUA( * ), TAUB( * ), 00016 $ WORK( LWORK ), Z( LDB, * ) 00017 * .. 00018 * 00019 * Purpose 00020 * ======= 00021 * 00022 * DGRQTS tests DGGRQF, which computes the GRQ factorization of an 00023 * M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q. 00024 * 00025 * Arguments 00026 * ========= 00027 * 00028 * M (input) INTEGER 00029 * The number of rows of the matrix A. M >= 0. 00030 * 00031 * P (input) INTEGER 00032 * The number of rows of the matrix B. P >= 0. 00033 * 00034 * N (input) INTEGER 00035 * The number of columns of the matrices A and B. N >= 0. 00036 * 00037 * A (input) DOUBLE PRECISION array, dimension (LDA,N) 00038 * The M-by-N matrix A. 00039 * 00040 * AF (output) DOUBLE PRECISION array, dimension (LDA,N) 00041 * Details of the GRQ factorization of A and B, as returned 00042 * by DGGRQF, see SGGRQF for further details. 00043 * 00044 * Q (output) DOUBLE PRECISION array, dimension (LDA,N) 00045 * The N-by-N orthogonal matrix Q. 00046 * 00047 * R (workspace) DOUBLE PRECISION array, dimension (LDA,MAX(M,N)) 00048 * 00049 * LDA (input) INTEGER 00050 * The leading dimension of the arrays A, AF, R and Q. 00051 * LDA >= max(M,N). 00052 * 00053 * TAUA (output) DOUBLE PRECISION array, dimension (min(M,N)) 00054 * The scalar factors of the elementary reflectors, as returned 00055 * by DGGQRC. 00056 * 00057 * B (input) DOUBLE PRECISION array, dimension (LDB,N) 00058 * On entry, the P-by-N matrix A. 00059 * 00060 * BF (output) DOUBLE PRECISION array, dimension (LDB,N) 00061 * Details of the GQR factorization of A and B, as returned 00062 * by DGGRQF, see SGGRQF for further details. 00063 * 00064 * Z (output) DOUBLE PRECISION array, dimension (LDB,P) 00065 * The P-by-P orthogonal matrix Z. 00066 * 00067 * T (workspace) DOUBLE PRECISION array, dimension (LDB,max(P,N)) 00068 * 00069 * BWK (workspace) DOUBLE PRECISION array, dimension (LDB,N) 00070 * 00071 * LDB (input) INTEGER 00072 * The leading dimension of the arrays B, BF, Z and T. 00073 * LDB >= max(P,N). 00074 * 00075 * TAUB (output) DOUBLE PRECISION array, dimension (min(P,N)) 00076 * The scalar factors of the elementary reflectors, as returned 00077 * by DGGRQF. 00078 * 00079 * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) 00080 * 00081 * LWORK (input) INTEGER 00082 * The dimension of the array WORK, LWORK >= max(M,P,N)**2. 00083 * 00084 * RWORK (workspace) DOUBLE PRECISION array, dimension (M) 00085 * 00086 * RESULT (output) DOUBLE PRECISION array, dimension (4) 00087 * The test ratios: 00088 * RESULT(1) = norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP) 00089 * RESULT(2) = norm( T*Q - Z'*B ) / (MAX(P,N)*norm(B)*ULP) 00090 * RESULT(3) = norm( I - Q'*Q ) / ( N*ULP ) 00091 * RESULT(4) = norm( I - Z'*Z ) / ( P*ULP ) 00092 * 00093 * ===================================================================== 00094 * 00095 * .. Parameters .. 00096 DOUBLE PRECISION ZERO, ONE 00097 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00098 DOUBLE PRECISION ROGUE 00099 PARAMETER ( ROGUE = -1.0D+10 ) 00100 * .. 00101 * .. Local Scalars .. 00102 INTEGER INFO 00103 DOUBLE PRECISION ANORM, BNORM, RESID, ULP, UNFL 00104 * .. 00105 * .. External Functions .. 00106 DOUBLE PRECISION DLAMCH, DLANGE, DLANSY 00107 EXTERNAL DLAMCH, DLANGE, DLANSY 00108 * .. 00109 * .. External Subroutines .. 00110 EXTERNAL DGEMM, DGGRQF, DLACPY, DLASET, DORGQR, DORGRQ, 00111 $ DSYRK 00112 * .. 00113 * .. Intrinsic Functions .. 00114 INTRINSIC DBLE, MAX, MIN 00115 * .. 00116 * .. Executable Statements .. 00117 * 00118 ULP = DLAMCH( 'Precision' ) 00119 UNFL = DLAMCH( 'Safe minimum' ) 00120 * 00121 * Copy the matrix A to the array AF. 00122 * 00123 CALL DLACPY( 'Full', M, N, A, LDA, AF, LDA ) 00124 CALL DLACPY( 'Full', P, N, B, LDB, BF, LDB ) 00125 * 00126 ANORM = MAX( DLANGE( '1', M, N, A, LDA, RWORK ), UNFL ) 00127 BNORM = MAX( DLANGE( '1', P, N, B, LDB, RWORK ), UNFL ) 00128 * 00129 * Factorize the matrices A and B in the arrays AF and BF. 00130 * 00131 CALL DGGRQF( M, P, N, AF, LDA, TAUA, BF, LDB, TAUB, WORK, LWORK, 00132 $ INFO ) 00133 * 00134 * Generate the N-by-N matrix Q 00135 * 00136 CALL DLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA ) 00137 IF( M.LE.N ) THEN 00138 IF( M.GT.0 .AND. M.LT.N ) 00139 $ CALL DLACPY( 'Full', M, N-M, AF, LDA, Q( N-M+1, 1 ), LDA ) 00140 IF( M.GT.1 ) 00141 $ CALL DLACPY( 'Lower', M-1, M-1, AF( 2, N-M+1 ), LDA, 00142 $ Q( N-M+2, N-M+1 ), LDA ) 00143 ELSE 00144 IF( N.GT.1 ) 00145 $ CALL DLACPY( 'Lower', N-1, N-1, AF( M-N+2, 1 ), LDA, 00146 $ Q( 2, 1 ), LDA ) 00147 END IF 00148 CALL DORGRQ( N, N, MIN( M, N ), Q, LDA, TAUA, WORK, LWORK, INFO ) 00149 * 00150 * Generate the P-by-P matrix Z 00151 * 00152 CALL DLASET( 'Full', P, P, ROGUE, ROGUE, Z, LDB ) 00153 IF( P.GT.1 ) 00154 $ CALL DLACPY( 'Lower', P-1, N, BF( 2, 1 ), LDB, Z( 2, 1 ), LDB ) 00155 CALL DORGQR( P, P, MIN( P, N ), Z, LDB, TAUB, WORK, LWORK, INFO ) 00156 * 00157 * Copy R 00158 * 00159 CALL DLASET( 'Full', M, N, ZERO, ZERO, R, LDA ) 00160 IF( M.LE.N ) THEN 00161 CALL DLACPY( 'Upper', M, M, AF( 1, N-M+1 ), LDA, R( 1, N-M+1 ), 00162 $ LDA ) 00163 ELSE 00164 CALL DLACPY( 'Full', M-N, N, AF, LDA, R, LDA ) 00165 CALL DLACPY( 'Upper', N, N, AF( M-N+1, 1 ), LDA, R( M-N+1, 1 ), 00166 $ LDA ) 00167 END IF 00168 * 00169 * Copy T 00170 * 00171 CALL DLASET( 'Full', P, N, ZERO, ZERO, T, LDB ) 00172 CALL DLACPY( 'Upper', P, N, BF, LDB, T, LDB ) 00173 * 00174 * Compute R - A*Q' 00175 * 00176 CALL DGEMM( 'No transpose', 'Transpose', M, N, N, -ONE, A, LDA, Q, 00177 $ LDA, ONE, R, LDA ) 00178 * 00179 * Compute norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP ) . 00180 * 00181 RESID = DLANGE( '1', M, N, R, LDA, RWORK ) 00182 IF( ANORM.GT.ZERO ) THEN 00183 RESULT( 1 ) = ( ( RESID / DBLE( MAX( 1, M, N ) ) ) / ANORM ) / 00184 $ ULP 00185 ELSE 00186 RESULT( 1 ) = ZERO 00187 END IF 00188 * 00189 * Compute T*Q - Z'*B 00190 * 00191 CALL DGEMM( 'Transpose', 'No transpose', P, N, P, ONE, Z, LDB, B, 00192 $ LDB, ZERO, BWK, LDB ) 00193 CALL DGEMM( 'No transpose', 'No transpose', P, N, N, ONE, T, LDB, 00194 $ Q, LDA, -ONE, BWK, LDB ) 00195 * 00196 * Compute norm( T*Q - Z'*B ) / ( MAX(P,N)*norm(A)*ULP ) . 00197 * 00198 RESID = DLANGE( '1', P, N, BWK, LDB, RWORK ) 00199 IF( BNORM.GT.ZERO ) THEN 00200 RESULT( 2 ) = ( ( RESID / DBLE( MAX( 1, P, M ) ) ) / BNORM ) / 00201 $ ULP 00202 ELSE 00203 RESULT( 2 ) = ZERO 00204 END IF 00205 * 00206 * Compute I - Q*Q' 00207 * 00208 CALL DLASET( 'Full', N, N, ZERO, ONE, R, LDA ) 00209 CALL DSYRK( 'Upper', 'No Transpose', N, N, -ONE, Q, LDA, ONE, R, 00210 $ LDA ) 00211 * 00212 * Compute norm( I - Q'*Q ) / ( N * ULP ) . 00213 * 00214 RESID = DLANSY( '1', 'Upper', N, R, LDA, RWORK ) 00215 RESULT( 3 ) = ( RESID / DBLE( MAX( 1, N ) ) ) / ULP 00216 * 00217 * Compute I - Z'*Z 00218 * 00219 CALL DLASET( 'Full', P, P, ZERO, ONE, T, LDB ) 00220 CALL DSYRK( 'Upper', 'Transpose', P, P, -ONE, Z, LDB, ONE, T, 00221 $ LDB ) 00222 * 00223 * Compute norm( I - Z'*Z ) / ( P*ULP ) . 00224 * 00225 RESID = DLANSY( '1', 'Upper', P, T, LDB, RWORK ) 00226 RESULT( 4 ) = ( RESID / DBLE( MAX( 1, P ) ) ) / ULP 00227 * 00228 RETURN 00229 * 00230 * End of DGRQTS 00231 * 00232 END
1.7.3 
