1*> \brief \b SQRT01P 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 SQRT01P( M, N, A, AF, Q, R, 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, * ), Q( LDA, * ), 19* $ R( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ), 20* $ WORK( LWORK ) 21* .. 22* 23* 24*> \par Purpose: 25* ============= 26*> 27*> \verbatim 28*> 29*> SQRT01P tests SGEQRFP, which computes the QR factorization of an m-by-n 30*> matrix A, and partially tests SORGQR which forms the m-by-m 31*> orthogonal matrix Q. 32*> 33*> SQRT01P compares R with Q'*A, 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 QR factorization of A, as returned by SGEQRFP. 61*> See SGEQRFP for further details. 62*> \endverbatim 63*> 64*> \param[out] Q 65*> \verbatim 66*> Q is REAL array, dimension (LDA,M) 67*> The m-by-m orthogonal matrix Q. 68*> \endverbatim 69*> 70*> \param[out] R 71*> \verbatim 72*> R 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 R. 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 SGEQRFP. 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 (M) 103*> \endverbatim 104*> 105*> \param[out] RESULT 106*> \verbatim 107*> RESULT is REAL array, dimension (2) 108*> The test ratios: 109*> RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS ) 110*> RESULT(2) = norm( I - Q'*Q ) / ( M * 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 November 2011 122* 123*> \ingroup single_lin 124* 125* ===================================================================== 126 SUBROUTINE SQRT01P( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, 127 $ RWORK, RESULT ) 128* 129* -- LAPACK test routine (version 3.4.0) -- 130* -- LAPACK is a software package provided by Univ. of Tennessee, -- 131* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 132* November 2011 133* 134* .. Scalar Arguments .. 135 INTEGER LDA, LWORK, M, N 136* .. 137* .. Array Arguments .. 138 REAL A( LDA, * ), AF( LDA, * ), Q( LDA, * ), 139 $ R( 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 SGEMM, SGEQRFP, SLACPY, SLASET, SORGQR, 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 = 'SGEQRFP' 183 CALL SGEQRFP( M, N, AF, LDA, TAU, WORK, LWORK, INFO ) 184* 185* Copy details of Q 186* 187 CALL SLASET( 'Full', M, M, ROGUE, ROGUE, Q, LDA ) 188 CALL SLACPY( 'Lower', M-1, N, AF( 2, 1 ), LDA, Q( 2, 1 ), LDA ) 189* 190* Generate the m-by-m matrix Q 191* 192 SRNAMT = 'SORGQR' 193 CALL SORGQR( M, M, MINMN, Q, LDA, TAU, WORK, LWORK, INFO ) 194* 195* Copy R 196* 197 CALL SLASET( 'Full', M, N, ZERO, ZERO, R, LDA ) 198 CALL SLACPY( 'Upper', M, N, AF, LDA, R, LDA ) 199* 200* Compute R - Q'*A 201* 202 CALL SGEMM( 'Transpose', 'No transpose', M, N, M, -ONE, Q, LDA, A, 203 $ LDA, ONE, R, LDA ) 204* 205* Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) . 206* 207 ANORM = SLANGE( '1', M, N, A, LDA, RWORK ) 208 RESID = SLANGE( '1', M, N, R, LDA, RWORK ) 209 IF( ANORM.GT.ZERO ) THEN 210 RESULT( 1 ) = ( ( RESID / REAL( MAX( 1, M ) ) ) / ANORM ) / EPS 211 ELSE 212 RESULT( 1 ) = ZERO 213 END IF 214* 215* Compute I - Q'*Q 216* 217 CALL SLASET( 'Full', M, M, ZERO, ONE, R, LDA ) 218 CALL SSYRK( 'Upper', 'Transpose', M, M, -ONE, Q, LDA, ONE, R, 219 $ LDA ) 220* 221* Compute norm( I - Q'*Q ) / ( M * EPS ) . 222* 223 RESID = SLANSY( '1', 'Upper', M, R, LDA, RWORK ) 224* 225 RESULT( 2 ) = ( RESID / REAL( MAX( 1, M ) ) ) / EPS 226* 227 RETURN 228* 229* End of SQRT01P 230* 231 END 232