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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZUNG2R 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZUNG2R + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zung2r.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zung2r.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zung2r.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZUNG2R( M, N, K, A, LDA, TAU, WORK, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * INTEGER INFO, K, LDA, 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 *> ZUNG2R generates an m by n complex matrix Q with orthonormal columns, 00037 *> which is defined as the first n columns of a product of k elementary 00038 *> reflectors of order m 00039 *> 00040 *> Q = H(1) H(2) . . . H(k) 00041 *> 00042 *> as returned by ZGEQRF. 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 COMPLEX*16 array, dimension (LDA,N) 00070 *> On entry, the i-th column must contain the vector which 00071 *> defines the elementary reflector H(i), for i = 1,2,...,k, as 00072 *> returned by ZGEQRF in the first 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 COMPLEX*16 array, dimension (K) 00086 *> TAU(i) must contain the scalar factor of the elementary 00087 *> reflector H(i), as returned by ZGEQRF. 00088 *> \endverbatim 00089 *> 00090 *> \param[out] WORK 00091 *> \verbatim 00092 *> WORK is COMPLEX*16 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 complex16OTHERcomputational 00113 * 00114 * ===================================================================== 00115 SUBROUTINE ZUNG2R( 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 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) 00127 * .. 00128 * 00129 * ===================================================================== 00130 * 00131 * .. Parameters .. 00132 COMPLEX*16 ONE, ZERO 00133 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), 00134 $ ZERO = ( 0.0D+0, 0.0D+0 ) ) 00135 * .. 00136 * .. Local Scalars .. 00137 INTEGER I, J, L 00138 * .. 00139 * .. External Subroutines .. 00140 EXTERNAL XERBLA, ZLARF, ZSCAL 00141 * .. 00142 * .. Intrinsic Functions .. 00143 INTRINSIC MAX 00144 * .. 00145 * .. Executable Statements .. 00146 * 00147 * Test the input arguments 00148 * 00149 INFO = 0 00150 IF( M.LT.0 ) THEN 00151 INFO = -1 00152 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN 00153 INFO = -2 00154 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN 00155 INFO = -3 00156 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00157 INFO = -5 00158 END IF 00159 IF( INFO.NE.0 ) THEN 00160 CALL XERBLA( 'ZUNG2R', -INFO ) 00161 RETURN 00162 END IF 00163 * 00164 * Quick return if possible 00165 * 00166 IF( N.LE.0 ) 00167 $ RETURN 00168 * 00169 * Initialise columns k+1:n to columns of the unit matrix 00170 * 00171 DO 20 J = K + 1, N 00172 DO 10 L = 1, M 00173 A( L, J ) = ZERO 00174 10 CONTINUE 00175 A( J, J ) = ONE 00176 20 CONTINUE 00177 * 00178 DO 40 I = K, 1, -1 00179 * 00180 * Apply H(i) to A(i:m,i:n) from the left 00181 * 00182 IF( I.LT.N ) THEN 00183 A( I, I ) = ONE 00184 CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ), 00185 $ A( I, I+1 ), LDA, WORK ) 00186 END IF 00187 IF( I.LT.M ) 00188 $ CALL ZSCAL( M-I, -TAU( I ), A( I+1, I ), 1 ) 00189 A( I, I ) = ONE - TAU( I ) 00190 * 00191 * Set A(1:i-1,i) to zero 00192 * 00193 DO 30 L = 1, I - 1 00194 A( L, I ) = ZERO 00195 30 CONTINUE 00196 40 CONTINUE 00197 RETURN 00198 * 00199 * End of ZUNG2R 00200 * 00201 END