1*> \brief \b SLQT01 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8* Definition: 9* =========== 10* 11* SUBROUTINE SLQT01( M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, 12* RWORK, RESULT ) 13* 14* .. Scalar Arguments .. 15* INTEGER LDA, LWORK, M, N 16* .. 17* .. Array Arguments .. 18* REAL A( LDA, * ), AF( LDA, * ), L( LDA, * ), 19* $ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ), 20* $ WORK( LWORK ) 21* .. 22* 23* 24*> \par Purpose: 25* ============= 26*> 27*> \verbatim 28*> 29*> SLQT01 tests SGELQF, which computes the LQ factorization of an m-by-n 30*> matrix A, and partially tests SORGLQ which forms the n-by-n 31*> orthogonal matrix Q. 32*> 33*> SLQT01 compares L with A*Q', and checks that Q is orthogonal. 34*> \endverbatim 35* 36* Arguments: 37* ========== 38* 39*> \param[in] M 40*> \verbatim 41*> M is INTEGER 42*> The number of rows of the matrix A. M >= 0. 43*> \endverbatim 44*> 45*> \param[in] N 46*> \verbatim 47*> N is INTEGER 48*> The number of columns of the matrix A. N >= 0. 49*> \endverbatim 50*> 51*> \param[in] A 52*> \verbatim 53*> A is REAL array, dimension (LDA,N) 54*> The m-by-n matrix A. 55*> \endverbatim 56*> 57*> \param[out] AF 58*> \verbatim 59*> AF is REAL array, dimension (LDA,N) 60*> Details of the LQ factorization of A, as returned by SGELQF. 61*> See SGELQF for further details. 62*> \endverbatim 63*> 64*> \param[out] Q 65*> \verbatim 66*> Q is REAL array, dimension (LDA,N) 67*> The n-by-n orthogonal matrix Q. 68*> \endverbatim 69*> 70*> \param[out] L 71*> \verbatim 72*> L is REAL array, dimension (LDA,max(M,N)) 73*> \endverbatim 74*> 75*> \param[in] LDA 76*> \verbatim 77*> LDA is INTEGER 78*> The leading dimension of the arrays A, AF, Q and L. 79*> LDA >= max(M,N). 80*> \endverbatim 81*> 82*> \param[out] TAU 83*> \verbatim 84*> TAU is REAL array, dimension (min(M,N)) 85*> The scalar factors of the elementary reflectors, as returned 86*> by SGELQF. 87*> \endverbatim 88*> 89*> \param[out] WORK 90*> \verbatim 91*> WORK is REAL array, dimension (LWORK) 92*> \endverbatim 93*> 94*> \param[in] LWORK 95*> \verbatim 96*> LWORK is INTEGER 97*> The dimension of the array WORK. 98*> \endverbatim 99*> 100*> \param[out] RWORK 101*> \verbatim 102*> RWORK is REAL array, dimension (max(M,N)) 103*> \endverbatim 104*> 105*> \param[out] RESULT 106*> \verbatim 107*> RESULT is REAL array, dimension (2) 108*> The test ratios: 109*> RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS ) 110*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS ) 111*> \endverbatim 112* 113* Authors: 114* ======== 115* 116*> \author Univ. of Tennessee 117*> \author Univ. of California Berkeley 118*> \author Univ. of Colorado Denver 119*> \author NAG Ltd. 120* 121*> \date December 2016 122* 123*> \ingroup single_lin 124* 125* ===================================================================== 126 SUBROUTINE SLQT01( M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, 127 $ RWORK, RESULT ) 128* 129* -- LAPACK test routine (version 3.7.0) -- 130* -- LAPACK is a software package provided by Univ. of Tennessee, -- 131* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 132* December 2016 133* 134* .. Scalar Arguments .. 135 INTEGER LDA, LWORK, M, N 136* .. 137* .. Array Arguments .. 138 REAL A( LDA, * ), AF( LDA, * ), L( LDA, * ), 139 $ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ), 140 $ WORK( LWORK ) 141* .. 142* 143* ===================================================================== 144* 145* .. Parameters .. 146 REAL ZERO, ONE 147 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 148 REAL ROGUE 149 PARAMETER ( ROGUE = -1.0E+10 ) 150* .. 151* .. Local Scalars .. 152 INTEGER INFO, MINMN 153 REAL ANORM, EPS, RESID 154* .. 155* .. External Functions .. 156 REAL SLAMCH, SLANGE, SLANSY 157 EXTERNAL SLAMCH, SLANGE, SLANSY 158* .. 159* .. External Subroutines .. 160 EXTERNAL SGELQF, SGEMM, SLACPY, SLASET, SORGLQ, SSYRK 161* .. 162* .. Intrinsic Functions .. 163 INTRINSIC MAX, MIN, REAL 164* .. 165* .. Scalars in Common .. 166 CHARACTER*32 SRNAMT 167* .. 168* .. Common blocks .. 169 COMMON / SRNAMC / SRNAMT 170* .. 171* .. Executable Statements .. 172* 173 MINMN = MIN( M, N ) 174 EPS = SLAMCH( 'Epsilon' ) 175* 176* Copy the matrix A to the array AF. 177* 178 CALL SLACPY( 'Full', M, N, A, LDA, AF, LDA ) 179* 180* Factorize the matrix A in the array AF. 181* 182 SRNAMT = 'SGELQF' 183 CALL SGELQF( M, N, AF, LDA, TAU, WORK, LWORK, INFO ) 184* 185* Copy details of Q 186* 187 CALL SLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA ) 188 IF( N.GT.1 ) 189 $ CALL SLACPY( 'Upper', M, N-1, AF( 1, 2 ), LDA, Q( 1, 2 ), LDA ) 190* 191* Generate the n-by-n matrix Q 192* 193 SRNAMT = 'SORGLQ' 194 CALL SORGLQ( N, N, MINMN, Q, LDA, TAU, WORK, LWORK, INFO ) 195* 196* Copy L 197* 198 CALL SLASET( 'Full', M, N, ZERO, ZERO, L, LDA ) 199 CALL SLACPY( 'Lower', M, N, AF, LDA, L, LDA ) 200* 201* Compute L - A*Q' 202* 203 CALL SGEMM( 'No transpose', 'Transpose', M, N, N, -ONE, A, LDA, Q, 204 $ LDA, ONE, L, LDA ) 205* 206* Compute norm( L - Q'*A ) / ( N * norm(A) * EPS ) . 207* 208 ANORM = SLANGE( '1', M, N, A, LDA, RWORK ) 209 RESID = SLANGE( '1', M, N, L, LDA, RWORK ) 210 IF( ANORM.GT.ZERO ) THEN 211 RESULT( 1 ) = ( ( RESID / REAL( MAX( 1, N ) ) ) / ANORM ) / EPS 212 ELSE 213 RESULT( 1 ) = ZERO 214 END IF 215* 216* Compute I - Q*Q' 217* 218 CALL SLASET( 'Full', N, N, ZERO, ONE, L, LDA ) 219 CALL SSYRK( 'Upper', 'No transpose', N, N, -ONE, Q, LDA, ONE, L, 220 $ LDA ) 221* 222* Compute norm( I - Q*Q' ) / ( N * EPS ) . 223* 224 RESID = SLANSY( '1', 'Upper', N, L, LDA, RWORK ) 225* 226 RESULT( 2 ) = ( RESID / REAL( MAX( 1, N ) ) ) / EPS 227* 228 RETURN 229* 230* End of SLQT01 231* 232 END 233