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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DORGTR 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DORGTR + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorgtr.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorgtr.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgtr.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER UPLO 00025 * INTEGER INFO, LDA, LWORK, N 00026 * .. 00027 * .. Array Arguments .. 00028 * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> DORGTR generates a real orthogonal matrix Q which is defined as the 00038 *> product of n-1 elementary reflectors of order N, as returned by 00039 *> DSYTRD: 00040 *> 00041 *> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), 00042 *> 00043 *> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). 00044 *> \endverbatim 00045 * 00046 * Arguments: 00047 * ========== 00048 * 00049 *> \param[in] UPLO 00050 *> \verbatim 00051 *> UPLO is CHARACTER*1 00052 *> = 'U': Upper triangle of A contains elementary reflectors 00053 *> from DSYTRD; 00054 *> = 'L': Lower triangle of A contains elementary reflectors 00055 *> from DSYTRD. 00056 *> \endverbatim 00057 *> 00058 *> \param[in] N 00059 *> \verbatim 00060 *> N is INTEGER 00061 *> The order of the matrix Q. N >= 0. 00062 *> \endverbatim 00063 *> 00064 *> \param[in,out] A 00065 *> \verbatim 00066 *> A is DOUBLE PRECISION array, dimension (LDA,N) 00067 *> On entry, the vectors which define the elementary reflectors, 00068 *> as returned by DSYTRD. 00069 *> On exit, the N-by-N orthogonal matrix Q. 00070 *> \endverbatim 00071 *> 00072 *> \param[in] LDA 00073 *> \verbatim 00074 *> LDA is INTEGER 00075 *> The leading dimension of the array A. LDA >= max(1,N). 00076 *> \endverbatim 00077 *> 00078 *> \param[in] TAU 00079 *> \verbatim 00080 *> TAU is DOUBLE PRECISION array, dimension (N-1) 00081 *> TAU(i) must contain the scalar factor of the elementary 00082 *> reflector H(i), as returned by DSYTRD. 00083 *> \endverbatim 00084 *> 00085 *> \param[out] WORK 00086 *> \verbatim 00087 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 00088 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00089 *> \endverbatim 00090 *> 00091 *> \param[in] LWORK 00092 *> \verbatim 00093 *> LWORK is INTEGER 00094 *> The dimension of the array WORK. LWORK >= max(1,N-1). 00095 *> For optimum performance LWORK >= (N-1)*NB, where NB is 00096 *> the optimal blocksize. 00097 *> 00098 *> If LWORK = -1, then a workspace query is assumed; the routine 00099 *> only calculates the optimal size of the WORK array, returns 00100 *> this value as the first entry of the WORK array, and no error 00101 *> message related to LWORK is issued by XERBLA. 00102 *> \endverbatim 00103 *> 00104 *> \param[out] INFO 00105 *> \verbatim 00106 *> INFO is INTEGER 00107 *> = 0: successful exit 00108 *> < 0: if INFO = -i, the i-th argument had an illegal value 00109 *> \endverbatim 00110 * 00111 * Authors: 00112 * ======== 00113 * 00114 *> \author Univ. of Tennessee 00115 *> \author Univ. of California Berkeley 00116 *> \author Univ. of Colorado Denver 00117 *> \author NAG Ltd. 00118 * 00119 *> \date November 2011 00120 * 00121 *> \ingroup doubleOTHERcomputational 00122 * 00123 * ===================================================================== 00124 SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO ) 00125 * 00126 * -- LAPACK computational routine (version 3.4.0) -- 00127 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00129 * November 2011 00130 * 00131 * .. Scalar Arguments .. 00132 CHARACTER UPLO 00133 INTEGER INFO, LDA, LWORK, N 00134 * .. 00135 * .. Array Arguments .. 00136 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) 00137 * .. 00138 * 00139 * ===================================================================== 00140 * 00141 * .. Parameters .. 00142 DOUBLE PRECISION ZERO, ONE 00143 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00144 * .. 00145 * .. Local Scalars .. 00146 LOGICAL LQUERY, UPPER 00147 INTEGER I, IINFO, J, LWKOPT, NB 00148 * .. 00149 * .. External Functions .. 00150 LOGICAL LSAME 00151 INTEGER ILAENV 00152 EXTERNAL LSAME, ILAENV 00153 * .. 00154 * .. External Subroutines .. 00155 EXTERNAL DORGQL, DORGQR, XERBLA 00156 * .. 00157 * .. Intrinsic Functions .. 00158 INTRINSIC MAX 00159 * .. 00160 * .. Executable Statements .. 00161 * 00162 * Test the input arguments 00163 * 00164 INFO = 0 00165 LQUERY = ( LWORK.EQ.-1 ) 00166 UPPER = LSAME( UPLO, 'U' ) 00167 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00168 INFO = -1 00169 ELSE IF( N.LT.0 ) THEN 00170 INFO = -2 00171 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00172 INFO = -4 00173 ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN 00174 INFO = -7 00175 END IF 00176 * 00177 IF( INFO.EQ.0 ) THEN 00178 IF( UPPER ) THEN 00179 NB = ILAENV( 1, 'DORGQL', ' ', N-1, N-1, N-1, -1 ) 00180 ELSE 00181 NB = ILAENV( 1, 'DORGQR', ' ', N-1, N-1, N-1, -1 ) 00182 END IF 00183 LWKOPT = MAX( 1, N-1 )*NB 00184 WORK( 1 ) = LWKOPT 00185 END IF 00186 * 00187 IF( INFO.NE.0 ) THEN 00188 CALL XERBLA( 'DORGTR', -INFO ) 00189 RETURN 00190 ELSE IF( LQUERY ) THEN 00191 RETURN 00192 END IF 00193 * 00194 * Quick return if possible 00195 * 00196 IF( N.EQ.0 ) THEN 00197 WORK( 1 ) = 1 00198 RETURN 00199 END IF 00200 * 00201 IF( UPPER ) THEN 00202 * 00203 * Q was determined by a call to DSYTRD with UPLO = 'U' 00204 * 00205 * Shift the vectors which define the elementary reflectors one 00206 * column to the left, and set the last row and column of Q to 00207 * those of the unit matrix 00208 * 00209 DO 20 J = 1, N - 1 00210 DO 10 I = 1, J - 1 00211 A( I, J ) = A( I, J+1 ) 00212 10 CONTINUE 00213 A( N, J ) = ZERO 00214 20 CONTINUE 00215 DO 30 I = 1, N - 1 00216 A( I, N ) = ZERO 00217 30 CONTINUE 00218 A( N, N ) = ONE 00219 * 00220 * Generate Q(1:n-1,1:n-1) 00221 * 00222 CALL DORGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO ) 00223 * 00224 ELSE 00225 * 00226 * Q was determined by a call to DSYTRD with UPLO = 'L'. 00227 * 00228 * Shift the vectors which define the elementary reflectors one 00229 * column to the right, and set the first row and column of Q to 00230 * those of the unit matrix 00231 * 00232 DO 50 J = N, 2, -1 00233 A( 1, J ) = ZERO 00234 DO 40 I = J + 1, N 00235 A( I, J ) = A( I, J-1 ) 00236 40 CONTINUE 00237 50 CONTINUE 00238 A( 1, 1 ) = ONE 00239 DO 60 I = 2, N 00240 A( I, 1 ) = ZERO 00241 60 CONTINUE 00242 IF( N.GT.1 ) THEN 00243 * 00244 * Generate Q(2:n,2:n) 00245 * 00246 CALL DORGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK, 00247 $ LWORK, IINFO ) 00248 END IF 00249 END IF 00250 WORK( 1 ) = LWKOPT 00251 RETURN 00252 * 00253 * End of DORGTR 00254 * 00255 END