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