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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZGELQF 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZGELQF + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgelqf.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgelqf.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgelqf.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * INTEGER INFO, LDA, LWORK, M, N 00025 * .. 00026 * .. Array Arguments .. 00027 * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) 00028 * .. 00029 * 00030 * 00031 *> \par Purpose: 00032 * ============= 00033 *> 00034 *> \verbatim 00035 *> 00036 *> ZGELQF computes an LQ factorization of a complex M-by-N matrix A: 00037 *> A = L * Q. 00038 *> \endverbatim 00039 * 00040 * Arguments: 00041 * ========== 00042 * 00043 *> \param[in] M 00044 *> \verbatim 00045 *> M is INTEGER 00046 *> The number of rows of the matrix A. M >= 0. 00047 *> \endverbatim 00048 *> 00049 *> \param[in] N 00050 *> \verbatim 00051 *> N is INTEGER 00052 *> The number of columns of the matrix A. N >= 0. 00053 *> \endverbatim 00054 *> 00055 *> \param[in,out] A 00056 *> \verbatim 00057 *> A is COMPLEX*16 array, dimension (LDA,N) 00058 *> On entry, the M-by-N matrix A. 00059 *> On exit, the elements on and below the diagonal of the array 00060 *> contain the m-by-min(m,n) lower trapezoidal matrix L (L is 00061 *> lower triangular if m <= n); the elements above the diagonal, 00062 *> with the array TAU, represent the unitary matrix Q as a 00063 *> product of elementary reflectors (see Further Details). 00064 *> \endverbatim 00065 *> 00066 *> \param[in] LDA 00067 *> \verbatim 00068 *> LDA is INTEGER 00069 *> The leading dimension of the array A. LDA >= max(1,M). 00070 *> \endverbatim 00071 *> 00072 *> \param[out] TAU 00073 *> \verbatim 00074 *> TAU is COMPLEX*16 array, dimension (min(M,N)) 00075 *> The scalar factors of the elementary reflectors (see Further 00076 *> Details). 00077 *> \endverbatim 00078 *> 00079 *> \param[out] WORK 00080 *> \verbatim 00081 *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) 00082 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00083 *> \endverbatim 00084 *> 00085 *> \param[in] LWORK 00086 *> \verbatim 00087 *> LWORK is INTEGER 00088 *> The dimension of the array WORK. LWORK >= max(1,M). 00089 *> For optimum performance LWORK >= M*NB, where NB is the 00090 *> optimal blocksize. 00091 *> 00092 *> If LWORK = -1, then a workspace query is assumed; the routine 00093 *> only calculates the optimal size of the WORK array, returns 00094 *> this value as the first entry of the WORK array, and no error 00095 *> message related to LWORK is issued by XERBLA. 00096 *> \endverbatim 00097 *> 00098 *> \param[out] INFO 00099 *> \verbatim 00100 *> INFO is INTEGER 00101 *> = 0: successful exit 00102 *> < 0: if INFO = -i, the i-th argument had an illegal value 00103 *> \endverbatim 00104 * 00105 * Authors: 00106 * ======== 00107 * 00108 *> \author Univ. of Tennessee 00109 *> \author Univ. of California Berkeley 00110 *> \author Univ. of Colorado Denver 00111 *> \author NAG Ltd. 00112 * 00113 *> \date November 2011 00114 * 00115 *> \ingroup complex16GEcomputational 00116 * 00117 *> \par Further Details: 00118 * ===================== 00119 *> 00120 *> \verbatim 00121 *> 00122 *> The matrix Q is represented as a product of elementary reflectors 00123 *> 00124 *> Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n). 00125 *> 00126 *> Each H(i) has the form 00127 *> 00128 *> H(i) = I - tau * v * v**H 00129 *> 00130 *> where tau is a complex scalar, and v is a complex vector with 00131 *> v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in 00132 *> A(i,i+1:n), and tau in TAU(i). 00133 *> \endverbatim 00134 *> 00135 * ===================================================================== 00136 SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) 00137 * 00138 * -- LAPACK computational routine (version 3.4.0) -- 00139 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00140 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00141 * November 2011 00142 * 00143 * .. Scalar Arguments .. 00144 INTEGER INFO, LDA, LWORK, M, N 00145 * .. 00146 * .. Array Arguments .. 00147 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) 00148 * .. 00149 * 00150 * ===================================================================== 00151 * 00152 * .. Local Scalars .. 00153 LOGICAL LQUERY 00154 INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB, 00155 $ NBMIN, NX 00156 * .. 00157 * .. External Subroutines .. 00158 EXTERNAL XERBLA, ZGELQ2, ZLARFB, ZLARFT 00159 * .. 00160 * .. Intrinsic Functions .. 00161 INTRINSIC MAX, MIN 00162 * .. 00163 * .. External Functions .. 00164 INTEGER ILAENV 00165 EXTERNAL ILAENV 00166 * .. 00167 * .. Executable Statements .. 00168 * 00169 * Test the input arguments 00170 * 00171 INFO = 0 00172 NB = ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 ) 00173 LWKOPT = M*NB 00174 WORK( 1 ) = LWKOPT 00175 LQUERY = ( LWORK.EQ.-1 ) 00176 IF( M.LT.0 ) THEN 00177 INFO = -1 00178 ELSE IF( N.LT.0 ) THEN 00179 INFO = -2 00180 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00181 INFO = -4 00182 ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN 00183 INFO = -7 00184 END IF 00185 IF( INFO.NE.0 ) THEN 00186 CALL XERBLA( 'ZGELQF', -INFO ) 00187 RETURN 00188 ELSE IF( LQUERY ) THEN 00189 RETURN 00190 END IF 00191 * 00192 * Quick return if possible 00193 * 00194 K = MIN( M, N ) 00195 IF( K.EQ.0 ) THEN 00196 WORK( 1 ) = 1 00197 RETURN 00198 END IF 00199 * 00200 NBMIN = 2 00201 NX = 0 00202 IWS = M 00203 IF( NB.GT.1 .AND. NB.LT.K ) THEN 00204 * 00205 * Determine when to cross over from blocked to unblocked code. 00206 * 00207 NX = MAX( 0, ILAENV( 3, 'ZGELQF', ' ', M, N, -1, -1 ) ) 00208 IF( NX.LT.K ) THEN 00209 * 00210 * Determine if workspace is large enough for blocked code. 00211 * 00212 LDWORK = M 00213 IWS = LDWORK*NB 00214 IF( LWORK.LT.IWS ) THEN 00215 * 00216 * Not enough workspace to use optimal NB: reduce NB and 00217 * determine the minimum value of NB. 00218 * 00219 NB = LWORK / LDWORK 00220 NBMIN = MAX( 2, ILAENV( 2, 'ZGELQF', ' ', M, N, -1, 00221 $ -1 ) ) 00222 END IF 00223 END IF 00224 END IF 00225 * 00226 IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN 00227 * 00228 * Use blocked code initially 00229 * 00230 DO 10 I = 1, K - NX, NB 00231 IB = MIN( K-I+1, NB ) 00232 * 00233 * Compute the LQ factorization of the current block 00234 * A(i:i+ib-1,i:n) 00235 * 00236 CALL ZGELQ2( IB, N-I+1, A( I, I ), LDA, TAU( I ), WORK, 00237 $ IINFO ) 00238 IF( I+IB.LE.M ) THEN 00239 * 00240 * Form the triangular factor of the block reflector 00241 * H = H(i) H(i+1) . . . H(i+ib-1) 00242 * 00243 CALL ZLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ), 00244 $ LDA, TAU( I ), WORK, LDWORK ) 00245 * 00246 * Apply H to A(i+ib:m,i:n) from the right 00247 * 00248 CALL ZLARFB( 'Right', 'No transpose', 'Forward', 00249 $ 'Rowwise', M-I-IB+1, N-I+1, IB, A( I, I ), 00250 $ LDA, WORK, LDWORK, A( I+IB, I ), LDA, 00251 $ WORK( IB+1 ), LDWORK ) 00252 END IF 00253 10 CONTINUE 00254 ELSE 00255 I = 1 00256 END IF 00257 * 00258 * Use unblocked code to factor the last or only block. 00259 * 00260 IF( I.LE.K ) 00261 $ CALL ZGELQ2( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK, 00262 $ IINFO ) 00263 * 00264 WORK( 1 ) = IWS 00265 RETURN 00266 * 00267 * End of ZGELQF 00268 * 00269 END