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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DORGHR 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DORGHR + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorghr.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorghr.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorghr.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * INTEGER IHI, ILO, INFO, LDA, LWORK, N 00025 * .. 00026 * .. Array Arguments .. 00027 * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) 00028 * .. 00029 * 00030 * 00031 *> \par Purpose: 00032 * ============= 00033 *> 00034 *> \verbatim 00035 *> 00036 *> DORGHR generates a real orthogonal matrix Q which is defined as the 00037 *> product of IHI-ILO elementary reflectors of order N, as returned by 00038 *> DGEHRD: 00039 *> 00040 *> Q = H(ilo) H(ilo+1) . . . H(ihi-1). 00041 *> \endverbatim 00042 * 00043 * Arguments: 00044 * ========== 00045 * 00046 *> \param[in] N 00047 *> \verbatim 00048 *> N is INTEGER 00049 *> The order of the matrix Q. N >= 0. 00050 *> \endverbatim 00051 *> 00052 *> \param[in] ILO 00053 *> \verbatim 00054 *> ILO is INTEGER 00055 *> \endverbatim 00056 *> 00057 *> \param[in] IHI 00058 *> \verbatim 00059 *> IHI is INTEGER 00060 *> 00061 *> ILO and IHI must have the same values as in the previous call 00062 *> of DGEHRD. Q is equal to the unit matrix except in the 00063 *> submatrix Q(ilo+1:ihi,ilo+1:ihi). 00064 *> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. 00065 *> \endverbatim 00066 *> 00067 *> \param[in,out] A 00068 *> \verbatim 00069 *> A is DOUBLE PRECISION array, dimension (LDA,N) 00070 *> On entry, the vectors which define the elementary reflectors, 00071 *> as returned by DGEHRD. 00072 *> On exit, the N-by-N orthogonal matrix Q. 00073 *> \endverbatim 00074 *> 00075 *> \param[in] LDA 00076 *> \verbatim 00077 *> LDA is INTEGER 00078 *> The leading dimension of the array A. LDA >= max(1,N). 00079 *> \endverbatim 00080 *> 00081 *> \param[in] TAU 00082 *> \verbatim 00083 *> TAU is DOUBLE PRECISION array, dimension (N-1) 00084 *> TAU(i) must contain the scalar factor of the elementary 00085 *> reflector H(i), as returned by DGEHRD. 00086 *> \endverbatim 00087 *> 00088 *> \param[out] WORK 00089 *> \verbatim 00090 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 00091 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00092 *> \endverbatim 00093 *> 00094 *> \param[in] LWORK 00095 *> \verbatim 00096 *> LWORK is INTEGER 00097 *> The dimension of the array WORK. LWORK >= IHI-ILO. 00098 *> For optimum performance LWORK >= (IHI-ILO)*NB, where NB is 00099 *> the optimal blocksize. 00100 *> 00101 *> If LWORK = -1, then a workspace query is assumed; the routine 00102 *> only calculates the optimal size of the WORK array, returns 00103 *> this value as the first entry of the WORK array, and no error 00104 *> message related to LWORK is issued by XERBLA. 00105 *> \endverbatim 00106 *> 00107 *> \param[out] INFO 00108 *> \verbatim 00109 *> INFO is INTEGER 00110 *> = 0: successful exit 00111 *> < 0: if INFO = -i, the i-th argument had an illegal value 00112 *> \endverbatim 00113 * 00114 * Authors: 00115 * ======== 00116 * 00117 *> \author Univ. of Tennessee 00118 *> \author Univ. of California Berkeley 00119 *> \author Univ. of Colorado Denver 00120 *> \author NAG Ltd. 00121 * 00122 *> \date November 2011 00123 * 00124 *> \ingroup doubleOTHERcomputational 00125 * 00126 * ===================================================================== 00127 SUBROUTINE DORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) 00128 * 00129 * -- LAPACK computational routine (version 3.4.0) -- 00130 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00132 * November 2011 00133 * 00134 * .. Scalar Arguments .. 00135 INTEGER IHI, ILO, INFO, LDA, LWORK, N 00136 * .. 00137 * .. Array Arguments .. 00138 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) 00139 * .. 00140 * 00141 * ===================================================================== 00142 * 00143 * .. Parameters .. 00144 DOUBLE PRECISION ZERO, ONE 00145 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00146 * .. 00147 * .. Local Scalars .. 00148 LOGICAL LQUERY 00149 INTEGER I, IINFO, J, LWKOPT, NB, NH 00150 * .. 00151 * .. External Subroutines .. 00152 EXTERNAL DORGQR, XERBLA 00153 * .. 00154 * .. External Functions .. 00155 INTEGER ILAENV 00156 EXTERNAL ILAENV 00157 * .. 00158 * .. Intrinsic Functions .. 00159 INTRINSIC MAX, MIN 00160 * .. 00161 * .. Executable Statements .. 00162 * 00163 * Test the input arguments 00164 * 00165 INFO = 0 00166 NH = IHI - ILO 00167 LQUERY = ( LWORK.EQ.-1 ) 00168 IF( N.LT.0 ) THEN 00169 INFO = -1 00170 ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN 00171 INFO = -2 00172 ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN 00173 INFO = -3 00174 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00175 INFO = -5 00176 ELSE IF( LWORK.LT.MAX( 1, NH ) .AND. .NOT.LQUERY ) THEN 00177 INFO = -8 00178 END IF 00179 * 00180 IF( INFO.EQ.0 ) THEN 00181 NB = ILAENV( 1, 'DORGQR', ' ', NH, NH, NH, -1 ) 00182 LWKOPT = MAX( 1, NH )*NB 00183 WORK( 1 ) = LWKOPT 00184 END IF 00185 * 00186 IF( INFO.NE.0 ) THEN 00187 CALL XERBLA( 'DORGHR', -INFO ) 00188 RETURN 00189 ELSE IF( LQUERY ) THEN 00190 RETURN 00191 END IF 00192 * 00193 * Quick return if possible 00194 * 00195 IF( N.EQ.0 ) THEN 00196 WORK( 1 ) = 1 00197 RETURN 00198 END IF 00199 * 00200 * Shift the vectors which define the elementary reflectors one 00201 * column to the right, and set the first ilo and the last n-ihi 00202 * rows and columns to those of the unit matrix 00203 * 00204 DO 40 J = IHI, ILO + 1, -1 00205 DO 10 I = 1, J - 1 00206 A( I, J ) = ZERO 00207 10 CONTINUE 00208 DO 20 I = J + 1, IHI 00209 A( I, J ) = A( I, J-1 ) 00210 20 CONTINUE 00211 DO 30 I = IHI + 1, N 00212 A( I, J ) = ZERO 00213 30 CONTINUE 00214 40 CONTINUE 00215 DO 60 J = 1, ILO 00216 DO 50 I = 1, N 00217 A( I, J ) = ZERO 00218 50 CONTINUE 00219 A( J, J ) = ONE 00220 60 CONTINUE 00221 DO 80 J = IHI + 1, N 00222 DO 70 I = 1, N 00223 A( I, J ) = ZERO 00224 70 CONTINUE 00225 A( J, J ) = ONE 00226 80 CONTINUE 00227 * 00228 IF( NH.GT.0 ) THEN 00229 * 00230 * Generate Q(ilo+1:ihi,ilo+1:ihi) 00231 * 00232 CALL DORGQR( NH, NH, NH, A( ILO+1, ILO+1 ), LDA, TAU( ILO ), 00233 $ WORK, LWORK, IINFO ) 00234 END IF 00235 WORK( 1 ) = LWKOPT 00236 RETURN 00237 * 00238 * End of DORGHR 00239 * 00240 END