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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DORG2L 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DORG2L + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorg2l.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorg2l.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorg2l.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DORG2L( 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 *> DORG2L generates an m by n real matrix Q with orthonormal columns, 00037 *> which is defined as the last n columns of a product of k elementary 00038 *> reflectors of order m 00039 *> 00040 *> Q = H(k) . . . H(2) H(1) 00041 *> 00042 *> as returned by DGEQLF. 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. M >= N >= 0. 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. N >= 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 (n-k+i)-th column must contain the vector which 00071 *> defines the elementary reflector H(i), for i = 1,2,...,k, as 00072 *> returned by DGEQLF in the last k columns of its array 00073 *> argument A. 00074 *> On exit, the m by n matrix Q. 00075 *> \endverbatim 00076 *> 00077 *> \param[in] LDA 00078 *> \verbatim 00079 *> LDA is INTEGER 00080 *> The first dimension of the array A. LDA >= max(1,M). 00081 *> \endverbatim 00082 *> 00083 *> \param[in] TAU 00084 *> \verbatim 00085 *> TAU is DOUBLE PRECISION array, dimension (K) 00086 *> TAU(i) must contain the scalar factor of the elementary 00087 *> reflector H(i), as returned by DGEQLF. 00088 *> \endverbatim 00089 *> 00090 *> \param[out] WORK 00091 *> \verbatim 00092 *> WORK is DOUBLE PRECISION array, dimension (N) 00093 *> \endverbatim 00094 *> 00095 *> \param[out] INFO 00096 *> \verbatim 00097 *> INFO is INTEGER 00098 *> = 0: successful exit 00099 *> < 0: if INFO = -i, the i-th argument has an illegal value 00100 *> \endverbatim 00101 * 00102 * Authors: 00103 * ======== 00104 * 00105 *> \author Univ. of Tennessee 00106 *> \author Univ. of California Berkeley 00107 *> \author Univ. of Colorado Denver 00108 *> \author NAG Ltd. 00109 * 00110 *> \date November 2011 00111 * 00112 *> \ingroup doubleOTHERcomputational 00113 * 00114 * ===================================================================== 00115 SUBROUTINE DORG2L( M, N, K, A, LDA, TAU, WORK, INFO ) 00116 * 00117 * -- LAPACK computational routine (version 3.4.0) -- 00118 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00119 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00120 * November 2011 00121 * 00122 * .. Scalar Arguments .. 00123 INTEGER INFO, K, LDA, M, N 00124 * .. 00125 * .. Array Arguments .. 00126 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) 00127 * .. 00128 * 00129 * ===================================================================== 00130 * 00131 * .. Parameters .. 00132 DOUBLE PRECISION ONE, ZERO 00133 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00134 * .. 00135 * .. Local Scalars .. 00136 INTEGER I, II, J, L 00137 * .. 00138 * .. External Subroutines .. 00139 EXTERNAL DLARF, DSCAL, XERBLA 00140 * .. 00141 * .. Intrinsic Functions .. 00142 INTRINSIC MAX 00143 * .. 00144 * .. Executable Statements .. 00145 * 00146 * Test the input arguments 00147 * 00148 INFO = 0 00149 IF( M.LT.0 ) THEN 00150 INFO = -1 00151 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN 00152 INFO = -2 00153 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN 00154 INFO = -3 00155 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00156 INFO = -5 00157 END IF 00158 IF( INFO.NE.0 ) THEN 00159 CALL XERBLA( 'DORG2L', -INFO ) 00160 RETURN 00161 END IF 00162 * 00163 * Quick return if possible 00164 * 00165 IF( N.LE.0 ) 00166 $ RETURN 00167 * 00168 * Initialise columns 1:n-k to columns of the unit matrix 00169 * 00170 DO 20 J = 1, N - K 00171 DO 10 L = 1, M 00172 A( L, J ) = ZERO 00173 10 CONTINUE 00174 A( M-N+J, J ) = ONE 00175 20 CONTINUE 00176 * 00177 DO 40 I = 1, K 00178 II = N - K + I 00179 * 00180 * Apply H(i) to A(1:m-k+i,1:n-k+i) from the left 00181 * 00182 A( M-N+II, II ) = ONE 00183 CALL DLARF( 'Left', M-N+II, II-1, A( 1, II ), 1, TAU( I ), A, 00184 $ LDA, WORK ) 00185 CALL DSCAL( M-N+II-1, -TAU( I ), A( 1, II ), 1 ) 00186 A( M-N+II, II ) = ONE - TAU( I ) 00187 * 00188 * Set A(m-k+i+1:m,n-k+i) to zero 00189 * 00190 DO 30 L = M - N + II + 1, M 00191 A( L, II ) = ZERO 00192 30 CONTINUE 00193 40 CONTINUE 00194 RETURN 00195 * 00196 * End of DORG2L 00197 * 00198 END