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ScaLAPACK
2.0.2
ScaLAPACK: Scalable Linear Algebra PACKage
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ScaLAPACK
2.0.2
ScaLAPACK: Scalable Linear Algebra PACKage
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00001 SUBROUTINE PDGERQRV( M, N, A, IA, JA, DESCA, TAU, WORK ) 00002 * 00003 * -- ScaLAPACK routine (version 1.7) -- 00004 * University of Tennessee, Knoxville, Oak Ridge National Laboratory, 00005 * and University of California, Berkeley. 00006 * May 28, 2001 00007 * 00008 * .. Scalar Arguments .. 00009 INTEGER IA, JA, M, N 00010 * .. 00011 * .. Array Arguments .. 00012 INTEGER DESCA( * ) 00013 DOUBLE PRECISION A( * ), TAU( * ), WORK( * ) 00014 * .. 00015 * 00016 * Purpose 00017 * ======= 00018 * 00019 * PDGERQRV computes sub( A ) = A(IA:IA+M-1,JA:JA+N-1) from R, Q 00020 * computed by PDGERQF. 00021 * 00022 * Notes 00023 * ===== 00024 * 00025 * Each global data object is described by an associated description 00026 * vector. This vector stores the information required to establish 00027 * the mapping between an object element and its corresponding process 00028 * and memory location. 00029 * 00030 * Let A be a generic term for any 2D block cyclicly distributed array. 00031 * Such a global array has an associated description vector DESCA. 00032 * In the following comments, the character _ should be read as 00033 * "of the global array". 00034 * 00035 * NOTATION STORED IN EXPLANATION 00036 * --------------- -------------- -------------------------------------- 00037 * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, 00038 * DTYPE_A = 1. 00039 * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating 00040 * the BLACS process grid A is distribu- 00041 * ted over. The context itself is glo- 00042 * bal, but the handle (the integer 00043 * value) may vary. 00044 * M_A (global) DESCA( M_ ) The number of rows in the global 00045 * array A. 00046 * N_A (global) DESCA( N_ ) The number of columns in the global 00047 * array A. 00048 * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute 00049 * the rows of the array. 00050 * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute 00051 * the columns of the array. 00052 * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first 00053 * row of the array A is distributed. 00054 * CSRC_A (global) DESCA( CSRC_ ) The process column over which the 00055 * first column of the array A is 00056 * distributed. 00057 * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local 00058 * array. LLD_A >= MAX(1,LOCr(M_A)). 00059 * 00060 * Let K be the number of rows or columns of a distributed matrix, 00061 * and assume that its process grid has dimension p x q. 00062 * LOCr( K ) denotes the number of elements of K that a process 00063 * would receive if K were distributed over the p processes of its 00064 * process column. 00065 * Similarly, LOCc( K ) denotes the number of elements of K that a 00066 * process would receive if K were distributed over the q processes of 00067 * its process row. 00068 * The values of LOCr() and LOCc() may be determined via a call to the 00069 * ScaLAPACK tool function, NUMROC: 00070 * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ), 00071 * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). 00072 * An upper bound for these quantities may be computed by: 00073 * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A 00074 * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A 00075 * 00076 * Arguments 00077 * ========= 00078 * 00079 * M (global input) INTEGER 00080 * The number of rows to be operated on, i.e. the number of rows 00081 * of the distributed submatrix sub( A ). M >= 0. 00082 * 00083 * N (global input) INTEGER 00084 * The number of columns to be operated on, i.e. the number of 00085 * columns of the distributed submatrix sub( A ). N >= 0. 00086 * 00087 * A (local input/local output) DOUBLE PRECISION pointer into the 00088 * local memory to an array of dimension (LLD_A, LOCc(JA+N-1)). 00089 * On entry, sub( A ) contains the the factors R and Q computed 00090 * by PDGERQF. On exit, the original matrix is restored. 00091 * 00092 * IA (global input) INTEGER 00093 * The row index in the global array A indicating the first 00094 * row of sub( A ). 00095 * 00096 * JA (global input) INTEGER 00097 * The column index in the global array A indicating the 00098 * first column of sub( A ). 00099 * 00100 * DESCA (global and local input) INTEGER array of dimension DLEN_. 00101 * The array descriptor for the distributed matrix A. 00102 * 00103 * TAU (local input) DOUBLE PRECISION, array, dimension LOCr(M_A). 00104 * This array contains the scalar factors TAU of the elementary 00105 * reflectors computed by PDGERQF. TAU is tied to the dis- 00106 * tributed matrix A. 00107 * 00108 * WORK (local workspace) DOUBLE PRECISION array, dimension (LWORK) 00109 * LWORK = MB_A * ( Mp0 + 2*Nq0 + MB_A ), where 00110 * Mp0 = NUMROC( M+IROFF, MB_A, MYROW, IAROW, NPROW ) * NB_A, 00111 * Nq0 = NUMROC( N+ICOFF, NB_A, MYCOL, IACOL, NPCOL ) * MB_A, 00112 * IROFF = MOD( IA-1, MB_A ), ICOFF = MOD( JA-1, NB_A ), 00113 * IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), 00114 * NPROW ), 00115 * IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), 00116 * NPCOL ), 00117 * and NUMROC, INDXG2P are ScaLAPACK tool functions. 00118 * 00119 * ===================================================================== 00120 * 00121 * .. Parameters .. 00122 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, 00123 $ LLD_, MB_, M_, NB_, N_, RSRC_ 00124 PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, 00125 $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, 00126 $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) 00127 DOUBLE PRECISION ONE, ZERO 00128 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00129 * .. 00130 * .. Local Scalars .. 00131 CHARACTER COLBTOP, ROWBTOP 00132 INTEGER I, IACOL, IAROW, IB, ICOFF, ICTXT, IIA, IN, 00133 $ IPT, IPV, IPW, JJA, JV, K, MYCOL, MYROW, NPCOL, 00134 $ NPROW, NQ 00135 * .. 00136 * .. Local Arrays .. 00137 INTEGER DESCV( DLEN_ ) 00138 * .. 00139 * .. External Subroutines .. 00140 EXTERNAL BLACS_GRIDINFO, DESCSET, INFOG2L, PDLACPY, 00141 $ PDLARFB, PDLARFT, PDLASET, PB_TOPGET, 00142 $ PB_TOPSET 00143 * .. 00144 * .. External Functions .. 00145 INTEGER ICEIL, NUMROC 00146 EXTERNAL ICEIL, NUMROC 00147 * .. 00148 * .. Intrinsic Functions .. 00149 INTRINSIC MAX, MIN, MOD 00150 * .. 00151 * .. Executable Statements .. 00152 * 00153 * Get grid parameters 00154 * 00155 ICTXT = DESCA( CTXT_ ) 00156 CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) 00157 * 00158 K = MIN( M, N ) 00159 IN = MIN( ICEIL( IA+M-K, DESCA( MB_ ) ) * DESCA( MB_ ), IA+M-1 ) 00160 * 00161 ICOFF = MOD( JA-1, DESCA( NB_ ) ) 00162 CALL INFOG2L( IA+M-K, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, 00163 $ IIA, JJA, IAROW, IACOL ) 00164 NQ = NUMROC( N+ICOFF, DESCA( NB_ ), MYCOL, IACOL, NPCOL ) 00165 IPV = 1 00166 IPT = IPV + NQ * DESCA( MB_ ) 00167 IPW = IPT + DESCA( MB_ ) * DESCA( MB_ ) 00168 CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) 00169 CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) 00170 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ' ' ) 00171 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', 'I-ring' ) 00172 * 00173 CALL DESCSET( DESCV, DESCA( MB_), N + ICOFF, DESCA( MB_ ), 00174 $ DESCA( NB_ ), IAROW, IACOL, ICTXT, DESCA( MB_ ) ) 00175 * 00176 * Handle first block separately 00177 * 00178 IB = IN - IA - M + K + 1 00179 JV = 1 + N - K + ICOFF 00180 * 00181 * Compute upper triangular matrix T 00182 * 00183 CALL PDLARFT( 'Backward', 'Rowwise', N-M+IN-IA+1, IB, A, IA+M-K, 00184 $ JA, DESCA, TAU, WORK( IPT ), WORK( IPW ) ) 00185 * 00186 * Copy Householder vectors into workspace 00187 * 00188 CALL PDLACPY( 'All', IB, N-M+IN-IA+1, A, IA+M-K, JA, DESCA, 00189 $ WORK( IPV ), 1, ICOFF+1, DESCV ) 00190 CALL PDLASET( 'Upper', IB, IB, ZERO, ONE, WORK( IPV ), 1, JV, 00191 $ DESCV ) 00192 * 00193 * Zeoes the strict lower triangular part of sub( A ) to get block 00194 * column of R 00195 * 00196 CALL PDLASET( 'All', IB, N-K, ZERO, ZERO, A, IA+M-K, JA, 00197 $ DESCA ) 00198 CALL PDLASET( 'Lower', IB-1, IB, ZERO, ZERO, A, IA+M-K+1, 00199 $ JA+N-K, DESCA ) 00200 * 00201 * Apply block Householder transformation 00202 * 00203 CALL PDLARFB( 'Right', 'Transpose', 'Backward', 'Rowwise', 00204 $ IN-IA+1, N-M+IN-IA+1, IB, WORK( IPV ), 1, ICOFF+1, 00205 $ DESCV, WORK( IPT ), A, IA, JA, DESCA, WORK( IPW ) ) 00206 * 00207 DESCV( RSRC_ ) = MOD( DESCV( RSRC_ ) + 1, NPROW ) 00208 * 00209 * Loop over the remaining row blocks 00210 * 00211 DO 10 I = IN+1, IA+M-1, DESCA( MB_ ) 00212 IB = MIN( IA+M-I, DESCA( MB_ ) ) 00213 JV = 1 + N - M + I - IA + ICOFF 00214 * 00215 * Compute upper triangular matrix T 00216 * 00217 CALL PDLARFT( 'Backward', 'Rowwise', N-M+I+IB-IA, IB, A, I, JA, 00218 $ DESCA, TAU, WORK( IPT ), WORK( IPW ) ) 00219 * 00220 * Copy Householder vectors into workspace 00221 * 00222 CALL PDLACPY( 'All', IB, N-M+I+IB-IA, A, I, JA, DESCA, 00223 $ WORK( IPV ), 1, ICOFF+1, DESCV ) 00224 CALL PDLASET( 'Upper', IB, IB, ZERO, ONE, WORK( IPV ), 1, JV, 00225 $ DESCV ) 00226 * 00227 * Zeoes the strict Lower triangular part of sub( A ) to get 00228 * block column of R 00229 * 00230 CALL PDLASET( 'All', IB, N-M+I-IA, ZERO, ZERO, A, I, JA, 00231 $ DESCA ) 00232 CALL PDLASET( 'Lower', IB-1, IB, ZERO, ZERO, A, I+1, 00233 $ JA+N-M+I-IA, DESCA ) 00234 * 00235 * Apply block Householder transformation 00236 * 00237 CALL PDLARFB( 'Right', 'Transpose', 'Backward', 'Rowwise', 00238 $ I+IB-IA, N-M+I+IB-IA, IB, WORK( IPV ), 1, 00239 $ ICOFF+1, DESCV, WORK( IPT ), A, IA, JA, DESCA, 00240 $ WORK( IPW ) ) 00241 * 00242 DESCV( RSRC_ ) = MOD( DESCV( RSRC_ ) + 1, NPROW ) 00243 * 00244 10 CONTINUE 00245 * 00246 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) 00247 CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) 00248 * 00249 RETURN 00250 * 00251 * End of PDGERQRV 00252 * 00253 END
