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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b SGEQRS 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 * Definition: 00009 * =========== 00010 * 00011 * SUBROUTINE SGEQRS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, 00012 * INFO ) 00013 * 00014 * .. Scalar Arguments .. 00015 * INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS 00016 * .. 00017 * .. Array Arguments .. 00018 * REAL A( LDA, * ), B( LDB, * ), TAU( * ), 00019 * $ WORK( LWORK ) 00020 * .. 00021 * 00022 * 00023 *> \par Purpose: 00024 * ============= 00025 *> 00026 *> \verbatim 00027 *> 00028 *> Solve the least squares problem 00029 *> min || A*X - B || 00030 *> using the QR factorization 00031 *> A = Q*R 00032 *> computed by SGEQRF. 00033 *> \endverbatim 00034 * 00035 * Arguments: 00036 * ========== 00037 * 00038 *> \param[in] M 00039 *> \verbatim 00040 *> M is INTEGER 00041 *> The number of rows of the matrix A. M >= 0. 00042 *> \endverbatim 00043 *> 00044 *> \param[in] N 00045 *> \verbatim 00046 *> N is INTEGER 00047 *> The number of columns of the matrix A. M >= N >= 0. 00048 *> \endverbatim 00049 *> 00050 *> \param[in] NRHS 00051 *> \verbatim 00052 *> NRHS is INTEGER 00053 *> The number of columns of B. NRHS >= 0. 00054 *> \endverbatim 00055 *> 00056 *> \param[in] A 00057 *> \verbatim 00058 *> A is REAL array, dimension (LDA,N) 00059 *> Details of the QR factorization of the original matrix A as 00060 *> returned by SGEQRF. 00061 *> \endverbatim 00062 *> 00063 *> \param[in] LDA 00064 *> \verbatim 00065 *> LDA is INTEGER 00066 *> The leading dimension of the array A. LDA >= M. 00067 *> \endverbatim 00068 *> 00069 *> \param[in] TAU 00070 *> \verbatim 00071 *> TAU is REAL array, dimension (N) 00072 *> Details of the orthogonal matrix Q. 00073 *> \endverbatim 00074 *> 00075 *> \param[in,out] B 00076 *> \verbatim 00077 *> B is REAL array, dimension (LDB,NRHS) 00078 *> On entry, the m-by-nrhs right hand side matrix B. 00079 *> On exit, the n-by-nrhs solution matrix X. 00080 *> \endverbatim 00081 *> 00082 *> \param[in] LDB 00083 *> \verbatim 00084 *> LDB is INTEGER 00085 *> The leading dimension of the array B. LDB >= M. 00086 *> \endverbatim 00087 *> 00088 *> \param[out] WORK 00089 *> \verbatim 00090 *> WORK is REAL array, dimension (LWORK) 00091 *> \endverbatim 00092 *> 00093 *> \param[in] LWORK 00094 *> \verbatim 00095 *> LWORK is INTEGER 00096 *> The length of the array WORK. LWORK must be at least NRHS, 00097 *> and should be at least NRHS*NB, where NB is the block size 00098 *> for this environment. 00099 *> \endverbatim 00100 *> 00101 *> \param[out] INFO 00102 *> \verbatim 00103 *> INFO is INTEGER 00104 *> = 0: successful exit 00105 *> < 0: if INFO = -i, the i-th argument had an illegal value 00106 *> \endverbatim 00107 * 00108 * Authors: 00109 * ======== 00110 * 00111 *> \author Univ. of Tennessee 00112 *> \author Univ. of California Berkeley 00113 *> \author Univ. of Colorado Denver 00114 *> \author NAG Ltd. 00115 * 00116 *> \date November 2011 00117 * 00118 *> \ingroup single_lin 00119 * 00120 * ===================================================================== 00121 SUBROUTINE SGEQRS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, 00122 $ INFO ) 00123 * 00124 * -- LAPACK test routine (version 3.4.0) -- 00125 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00126 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00127 * November 2011 00128 * 00129 * .. Scalar Arguments .. 00130 INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS 00131 * .. 00132 * .. Array Arguments .. 00133 REAL A( LDA, * ), B( LDB, * ), TAU( * ), 00134 $ WORK( LWORK ) 00135 * .. 00136 * 00137 * ===================================================================== 00138 * 00139 * .. Parameters .. 00140 REAL ONE 00141 PARAMETER ( ONE = 1.0E+0 ) 00142 * .. 00143 * .. External Subroutines .. 00144 EXTERNAL SORMQR, STRSM, XERBLA 00145 * .. 00146 * .. Intrinsic Functions .. 00147 INTRINSIC MAX 00148 * .. 00149 * .. Executable Statements .. 00150 * 00151 * Test the input arguments. 00152 * 00153 INFO = 0 00154 IF( M.LT.0 ) THEN 00155 INFO = -1 00156 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN 00157 INFO = -2 00158 ELSE IF( NRHS.LT.0 ) THEN 00159 INFO = -3 00160 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00161 INFO = -5 00162 ELSE IF( LDB.LT.MAX( 1, M ) ) THEN 00163 INFO = -8 00164 ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 ) 00165 $ THEN 00166 INFO = -10 00167 END IF 00168 IF( INFO.NE.0 ) THEN 00169 CALL XERBLA( 'SGEQRS', -INFO ) 00170 RETURN 00171 END IF 00172 * 00173 * Quick return if possible 00174 * 00175 IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 ) 00176 $ RETURN 00177 * 00178 * B := Q' * B 00179 * 00180 CALL SORMQR( 'Left', 'Transpose', M, NRHS, N, A, LDA, TAU, B, LDB, 00181 $ WORK, LWORK, INFO ) 00182 * 00183 * Solve R*X = B(1:n,:) 00184 * 00185 CALL STRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N, NRHS, 00186 $ ONE, A, LDA, B, LDB ) 00187 * 00188 RETURN 00189 * 00190 * End of SGEQRS 00191 * 00192 END