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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DORGL2 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DORGL2 + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorgl2.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorgl2.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgl2.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DORGL2( M, N, K, A, LDA, TAU, WORK, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * INTEGER INFO, K, LDA, M, N 00025 * .. 00026 * .. Array Arguments .. 00027 * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) 00028 * .. 00029 * 00030 * 00031 *> \par Purpose: 00032 * ============= 00033 *> 00034 *> \verbatim 00035 *> 00036 *> DORGL2 generates an m by n real matrix Q with orthonormal rows, 00037 *> which is defined as the first m rows of a product of k elementary 00038 *> reflectors of order n 00039 *> 00040 *> Q = H(k) . . . H(2) H(1) 00041 *> 00042 *> as returned by DGELQF. 00043 *> \endverbatim 00044 * 00045 * Arguments: 00046 * ========== 00047 * 00048 *> \param[in] M 00049 *> \verbatim 00050 *> M is INTEGER 00051 *> The number of rows of the matrix Q. M >= 0. 00052 *> \endverbatim 00053 *> 00054 *> \param[in] N 00055 *> \verbatim 00056 *> N is INTEGER 00057 *> The number of columns of the matrix Q. N >= M. 00058 *> \endverbatim 00059 *> 00060 *> \param[in] K 00061 *> \verbatim 00062 *> K is INTEGER 00063 *> The number of elementary reflectors whose product defines the 00064 *> matrix Q. M >= K >= 0. 00065 *> \endverbatim 00066 *> 00067 *> \param[in,out] A 00068 *> \verbatim 00069 *> A is DOUBLE PRECISION array, dimension (LDA,N) 00070 *> On entry, the i-th row must contain the vector which defines 00071 *> the elementary reflector H(i), for i = 1,2,...,k, as returned 00072 *> by DGELQF in the first k rows of its array argument A. 00073 *> On exit, the m-by-n matrix Q. 00074 *> \endverbatim 00075 *> 00076 *> \param[in] LDA 00077 *> \verbatim 00078 *> LDA is INTEGER 00079 *> The first dimension of the array A. LDA >= max(1,M). 00080 *> \endverbatim 00081 *> 00082 *> \param[in] TAU 00083 *> \verbatim 00084 *> TAU is DOUBLE PRECISION array, dimension (K) 00085 *> TAU(i) must contain the scalar factor of the elementary 00086 *> reflector H(i), as returned by DGELQF. 00087 *> \endverbatim 00088 *> 00089 *> \param[out] WORK 00090 *> \verbatim 00091 *> WORK is DOUBLE PRECISION array, dimension (M) 00092 *> \endverbatim 00093 *> 00094 *> \param[out] INFO 00095 *> \verbatim 00096 *> INFO is INTEGER 00097 *> = 0: successful exit 00098 *> < 0: if INFO = -i, the i-th argument has an illegal value 00099 *> \endverbatim 00100 * 00101 * Authors: 00102 * ======== 00103 * 00104 *> \author Univ. of Tennessee 00105 *> \author Univ. of California Berkeley 00106 *> \author Univ. of Colorado Denver 00107 *> \author NAG Ltd. 00108 * 00109 *> \date November 2011 00110 * 00111 *> \ingroup doubleOTHERcomputational 00112 * 00113 * ===================================================================== 00114 SUBROUTINE DORGL2( M, N, K, A, LDA, TAU, WORK, INFO ) 00115 * 00116 * -- LAPACK computational routine (version 3.4.0) -- 00117 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00118 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00119 * November 2011 00120 * 00121 * .. Scalar Arguments .. 00122 INTEGER INFO, K, LDA, M, N 00123 * .. 00124 * .. Array Arguments .. 00125 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) 00126 * .. 00127 * 00128 * ===================================================================== 00129 * 00130 * .. Parameters .. 00131 DOUBLE PRECISION ONE, ZERO 00132 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00133 * .. 00134 * .. Local Scalars .. 00135 INTEGER I, J, L 00136 * .. 00137 * .. External Subroutines .. 00138 EXTERNAL DLARF, DSCAL, XERBLA 00139 * .. 00140 * .. Intrinsic Functions .. 00141 INTRINSIC MAX 00142 * .. 00143 * .. Executable Statements .. 00144 * 00145 * Test the input arguments 00146 * 00147 INFO = 0 00148 IF( M.LT.0 ) THEN 00149 INFO = -1 00150 ELSE IF( N.LT.M ) THEN 00151 INFO = -2 00152 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN 00153 INFO = -3 00154 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00155 INFO = -5 00156 END IF 00157 IF( INFO.NE.0 ) THEN 00158 CALL XERBLA( 'DORGL2', -INFO ) 00159 RETURN 00160 END IF 00161 * 00162 * Quick return if possible 00163 * 00164 IF( M.LE.0 ) 00165 $ RETURN 00166 * 00167 IF( K.LT.M ) THEN 00168 * 00169 * Initialise rows k+1:m to rows of the unit matrix 00170 * 00171 DO 20 J = 1, N 00172 DO 10 L = K + 1, M 00173 A( L, J ) = ZERO 00174 10 CONTINUE 00175 IF( J.GT.K .AND. J.LE.M ) 00176 $ A( J, J ) = ONE 00177 20 CONTINUE 00178 END IF 00179 * 00180 DO 40 I = K, 1, -1 00181 * 00182 * Apply H(i) to A(i:m,i:n) from the right 00183 * 00184 IF( I.LT.N ) THEN 00185 IF( I.LT.M ) THEN 00186 A( I, I ) = ONE 00187 CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, 00188 $ TAU( I ), A( I+1, I ), LDA, WORK ) 00189 END IF 00190 CALL DSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA ) 00191 END IF 00192 A( I, I ) = ONE - TAU( I ) 00193 * 00194 * Set A(i,1:i-1) to zero 00195 * 00196 DO 30 L = 1, I - 1 00197 A( I, L ) = ZERO 00198 30 CONTINUE 00199 40 CONTINUE 00200 RETURN 00201 * 00202 * End of DORGL2 00203 * 00204 END