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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b STPQRT 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download STPQRT + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/stpqrt.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/stpqrt.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/stpqrt.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE STPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, 00022 * INFO ) 00023 * 00024 * .. Scalar Arguments .. 00025 * INTEGER INFO, LDA, LDB, LDT, N, M, L, NB 00026 * .. 00027 * .. Array Arguments .. 00028 * REAL A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> STPQRT computes a blocked QR factorization of a real 00038 *> "triangular-pentagonal" matrix C, which is composed of a 00039 *> triangular block A and pentagonal block B, using the compact 00040 *> WY representation for Q. 00041 *> \endverbatim 00042 * 00043 * Arguments: 00044 * ========== 00045 * 00046 *> \param[in] M 00047 *> \verbatim 00048 *> M is INTEGER 00049 *> The number of rows of the matrix B. 00050 *> M >= 0. 00051 *> \endverbatim 00052 *> 00053 *> \param[in] N 00054 *> \verbatim 00055 *> N is INTEGER 00056 *> The number of columns of the matrix B, and the order of the 00057 *> triangular matrix A. 00058 *> N >= 0. 00059 *> \endverbatim 00060 *> 00061 *> \param[in] L 00062 *> \verbatim 00063 *> L is INTEGER 00064 *> The number of rows of the upper trapezoidal part of B. 00065 *> MIN(M,N) >= L >= 0. See Further Details. 00066 *> \endverbatim 00067 *> 00068 *> \param[in] NB 00069 *> \verbatim 00070 *> NB is INTEGER 00071 *> The block size to be used in the blocked QR. N >= NB >= 1. 00072 *> \endverbatim 00073 *> 00074 *> \param[in,out] A 00075 *> \verbatim 00076 *> A is REAL array, dimension (LDA,N) 00077 *> On entry, the upper triangular N-by-N matrix A. 00078 *> On exit, the elements on and above the diagonal of the array 00079 *> contain the upper triangular matrix R. 00080 *> \endverbatim 00081 *> 00082 *> \param[in] LDA 00083 *> \verbatim 00084 *> LDA is INTEGER 00085 *> The leading dimension of the array A. LDA >= max(1,N). 00086 *> \endverbatim 00087 *> 00088 *> \param[in,out] B 00089 *> \verbatim 00090 *> B is REAL array, dimension (LDB,N) 00091 *> On entry, the pentagonal M-by-N matrix B. The first M-L rows 00092 *> are rectangular, and the last L rows are upper trapezoidal. 00093 *> On exit, B contains the pentagonal matrix V. See Further Details. 00094 *> \endverbatim 00095 *> 00096 *> \param[in] LDB 00097 *> \verbatim 00098 *> LDB is INTEGER 00099 *> The leading dimension of the array B. LDB >= max(1,M). 00100 *> \endverbatim 00101 *> 00102 *> \param[out] T 00103 *> \verbatim 00104 *> T is REAL array, dimension (LDT,N) 00105 *> The upper triangular block reflectors stored in compact form 00106 *> as a sequence of upper triangular blocks. See Further Details. 00107 *> \endverbatim 00108 *> 00109 *> \param[in] LDT 00110 *> \verbatim 00111 *> LDT is INTEGER 00112 *> The leading dimension of the array T. LDT >= NB. 00113 *> \endverbatim 00114 *> 00115 *> \param[out] WORK 00116 *> \verbatim 00117 *> WORK is REAL array, dimension (NB*N) 00118 *> \endverbatim 00119 *> 00120 *> \param[out] INFO 00121 *> \verbatim 00122 *> INFO is INTEGER 00123 *> = 0: successful exit 00124 *> < 0: if INFO = -i, the i-th argument had an illegal value 00125 *> \endverbatim 00126 * 00127 * Authors: 00128 * ======== 00129 * 00130 *> \author Univ. of Tennessee 00131 *> \author Univ. of California Berkeley 00132 *> \author Univ. of Colorado Denver 00133 *> \author NAG Ltd. 00134 * 00135 *> \date April 2012 00136 * 00137 *> \ingroup realOTHERcomputational 00138 * 00139 *> \par Further Details: 00140 * ===================== 00141 *> 00142 *> \verbatim 00143 *> 00144 *> The input matrix C is a (N+M)-by-N matrix 00145 *> 00146 *> C = [ A ] 00147 *> [ B ] 00148 *> 00149 *> where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal 00150 *> matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N 00151 *> upper trapezoidal matrix B2: 00152 *> 00153 *> B = [ B1 ] <- (M-L)-by-N rectangular 00154 *> [ B2 ] <- L-by-N upper trapezoidal. 00155 *> 00156 *> The upper trapezoidal matrix B2 consists of the first L rows of a 00157 *> N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N). If L=0, 00158 *> B is rectangular M-by-N; if M=L=N, B is upper triangular. 00159 *> 00160 *> The matrix W stores the elementary reflectors H(i) in the i-th column 00161 *> below the diagonal (of A) in the (N+M)-by-N input matrix C 00162 *> 00163 *> C = [ A ] <- upper triangular N-by-N 00164 *> [ B ] <- M-by-N pentagonal 00165 *> 00166 *> so that W can be represented as 00167 *> 00168 *> W = [ I ] <- identity, N-by-N 00169 *> [ V ] <- M-by-N, same form as B. 00170 *> 00171 *> Thus, all of information needed for W is contained on exit in B, which 00172 *> we call V above. Note that V has the same form as B; that is, 00173 *> 00174 *> V = [ V1 ] <- (M-L)-by-N rectangular 00175 *> [ V2 ] <- L-by-N upper trapezoidal. 00176 *> 00177 *> The columns of V represent the vectors which define the H(i)'s. 00178 *> 00179 *> The number of blocks is B = ceiling(N/NB), where each 00180 *> block is of order NB except for the last block, which is of order 00181 *> IB = N - (B-1)*NB. For each of the B blocks, a upper triangular block 00182 *> reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB 00183 *> for the last block) T's are stored in the NB-by-N matrix T as 00184 *> 00185 *> T = [T1 T2 ... TB]. 00186 *> \endverbatim 00187 *> 00188 * ===================================================================== 00189 SUBROUTINE STPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, 00190 $ INFO ) 00191 * 00192 * -- LAPACK computational routine (version 3.4.1) -- 00193 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00194 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00195 * April 2012 00196 * 00197 * .. Scalar Arguments .. 00198 INTEGER INFO, LDA, LDB, LDT, N, M, L, NB 00199 * .. 00200 * .. Array Arguments .. 00201 REAL A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * ) 00202 * .. 00203 * 00204 * ===================================================================== 00205 * 00206 * .. 00207 * .. Local Scalars .. 00208 INTEGER I, IB, LB, MB, IINFO 00209 * .. 00210 * .. External Subroutines .. 00211 EXTERNAL STPQRT2, STPRFB, XERBLA 00212 * .. 00213 * .. Executable Statements .. 00214 * 00215 * Test the input arguments 00216 * 00217 INFO = 0 00218 IF( M.LT.0 ) THEN 00219 INFO = -1 00220 ELSE IF( N.LT.0 ) THEN 00221 INFO = -2 00222 ELSE IF( L.LT.0 .OR. L.GT.MIN(M,N) ) THEN 00223 INFO = -3 00224 ELSE IF( NB.LT.1 .OR. NB.GT.N ) THEN 00225 INFO = -4 00226 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00227 INFO = -6 00228 ELSE IF( LDB.LT.MAX( 1, M ) ) THEN 00229 INFO = -8 00230 ELSE IF( LDT.LT.NB ) THEN 00231 INFO = -10 00232 END IF 00233 IF( INFO.NE.0 ) THEN 00234 CALL XERBLA( 'STPQRT', -INFO ) 00235 RETURN 00236 END IF 00237 * 00238 * Quick return if possible 00239 * 00240 IF( M.EQ.0 .OR. N.EQ.0 ) RETURN 00241 * 00242 DO I = 1, N, NB 00243 * 00244 * Compute the QR factorization of the current block 00245 * 00246 IB = MIN( N-I+1, NB ) 00247 MB = MIN( M-L+I+IB-1, M ) 00248 IF( I.GE.L ) THEN 00249 LB = 0 00250 ELSE 00251 LB = MB-M+L-I+1 00252 END IF 00253 * 00254 CALL STPQRT2( MB, IB, LB, A(I,I), LDA, B( 1, I ), LDB, 00255 $ T(1, I ), LDT, IINFO ) 00256 * 00257 * Update by applying H^H to B(:,I+IB:N) from the left 00258 * 00259 IF( I+IB.LE.N ) THEN 00260 CALL STPRFB( 'L', 'T', 'F', 'C', MB, N-I-IB+1, IB, LB, 00261 $ B( 1, I ), LDB, T( 1, I ), LDT, 00262 $ A( I, I+IB ), LDA, B( 1, I+IB ), LDB, 00263 $ WORK, IB ) 00264 END IF 00265 END DO 00266 RETURN 00267 * 00268 * End of STPQRT 00269 * 00270 END