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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 * 00002 * 00003 SUBROUTINE PZLAGHE( N, K, D, A, IA, JA, DESCA, ISEED, ORDER, WORK, 00004 $ LWORK, INFO ) 00005 * 00006 * 00007 * -- ScaLAPACK routine (version 1.7) -- 00008 * University of Tennessee, Knoxville, Oak Ridge National Laboratory, 00009 * and University of California, Berkeley. 00010 * May 1, 1997 00011 * 00012 * .. Scalar Arguments .. 00013 INTEGER IA, INFO, JA, K, LWORK, N, ORDER 00014 * .. 00015 * .. Array Arguments .. 00016 INTEGER DESCA( * ), ISEED( 4 ) 00017 DOUBLE PRECISION D( * ) 00018 COMPLEX*16 A( * ), WORK( * ) 00019 * .. 00020 * 00021 * Notes 00022 * ===== 00023 * 00024 * Each global data object is described by an associated description 00025 * vector. This vector stores the information required to establish 00026 * the mapping between an object element and its corresponding process 00027 * and memory location. 00028 * 00029 * Let A be a generic term for any 2D block cyclicly distributed array. 00030 * Such a global array has an associated description vector DESCA. 00031 * In the following comments, the character _ should be read as 00032 * "of the global array". 00033 * 00034 * NOTATION STORED IN EXPLANATION 00035 * --------------- -------------- -------------------------------------- 00036 * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, 00037 * DTYPE_A = 1. 00038 * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating 00039 * the BLACS process grid A is distribu- 00040 * ted over. The context itself is glo- 00041 * bal, but the handle (the integer 00042 * value) may vary. 00043 * M_A (global) DESCA( M_ ) The number of rows in the global 00044 * array A. 00045 * N_A (global) DESCA( N_ ) The number of columns in the global 00046 * array A. 00047 * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute 00048 * the rows of the array. 00049 * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute 00050 * the columns of the array. 00051 * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first 00052 * row of the array A is distributed. 00053 * CSRC_A (global) DESCA( CSRC_ ) The process column over which the 00054 * first column of the array A is 00055 * distributed. 00056 * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local 00057 * array. LLD_A >= MAX(1,LOCr(M_A)). 00058 * 00059 * Let K be the number of rows or columns of a distributed matrix, 00060 * and assume that its process grid has dimension p x q. 00061 * LOCr( K ) denotes the number of elements of K that a process 00062 * would receive if K were distributed over the p processes of its 00063 * process column. 00064 * Similarly, LOCc( K ) denotes the number of elements of K that a 00065 * process would receive if K were distributed over the q processes of 00066 * its process row. 00067 * The values of LOCr() and LOCc() may be determined via a call to the 00068 * ScaLAPACK tool function, NUMROC: 00069 * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ), 00070 * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). 00071 * An upper bound for these quantities may be computed by: 00072 * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A 00073 * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A 00074 * 00075 * Purpose 00076 * ======= 00077 * 00078 * PZLAGHE generates a real Hermitian matrix A, by pre- and post- 00079 * multiplying a real diagonal matrix D with a random orthogonal matrix: 00080 * A = U*D*U'. 00081 * 00082 * This is just a quick implementation which will be replaced in the 00083 * future. The random orthogonal matrix is computed by creating a 00084 * random matrix and running QR on it. This requires vastly more 00085 * computation than necessary, but not significantly more communication 00086 * than is used in the rest of this rouinte, and hence is not that much 00087 * slower than an efficient solution. 00088 * 00089 * Arguments 00090 * ========= 00091 * 00092 * N (global input) INTEGER 00093 * The size of the matrix A. N >= 0. 00094 * 00095 * K (global input) INTEGER 00096 * The number of nonzero subdiagonals within the band of A. 00097 * 0 <= K <= N-1. 00098 * ### K must be 0 or N-1, 0 < K < N-1 is not supported yet. 00099 * 00100 * D (global input) COMPLEX*16 array, dimension (N) 00101 * The diagonal elements of the diagonal matrix D. 00102 * 00103 * A (local output) COMPLEX*16 array 00104 * Global dimension (N, N), local dimension (NP, NQ) 00105 * The generated n by n Hermitian matrix A (the full matrix is 00106 * stored). 00107 * 00108 * IA (global input) INTEGER 00109 * A's global row index, which points to the beginning of the 00110 * submatrix which is to be operated on. 00111 * 00112 * JA (global input) INTEGER 00113 * A's global column index, which points to the beginning of 00114 * the submatrix which is to be operated on. 00115 * 00116 * DESCA (global and local input) INTEGER array of dimension DLEN_. 00117 * The array descriptor for the distributed matrix A. 00118 * 00119 * ISEED (global input/output) INTEGER array, dimension (4) 00120 * On entry, the seed of the random number generator; the array 00121 * elements must be between 0 and 4095, and ISEED(4) must be 00122 * odd. 00123 * On exit, the seed is updated and will remain identical on 00124 * all processes in the context. 00125 * 00126 * ORDER (global input) INTEGER 00127 * Number of reflectors in the matrix Q 00128 * At present, ORDER .NE. N is not supported 00129 * 00130 * WORK (local workspace) COMPLEX*16 array, dimension (LWORK) 00131 * 00132 * LWORK (local input) INTEGER dimension of WORK 00133 * LWORK >= SIZETMS as returned by PZLASIZESEP 00134 * 00135 * 00136 * INFO (local output) INTEGER 00137 * = 0: successful exit 00138 * < 0: If the i-th argument is an array and the j-entry had 00139 * an illegal value, then INFO = -(i*100+j), if the i-th 00140 * argument is a scalar and had an illegal value, then 00141 * INFO = -i. 00142 * 00143 * 00144 * .. Parameters .. 00145 INTEGER BLOCK_CYCLIC_2D, DLEN_, DTYPE_, CTXT_, M_, N_, 00146 $ MB_, NB_, RSRC_, CSRC_, LLD_ 00147 PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, 00148 $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, 00149 $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) 00150 COMPLEX*16 ZZERO 00151 PARAMETER ( ZZERO = 0.0D+0 ) 00152 * .. 00153 * .. Local Scalars .. 00154 INTEGER CSRC_A, I, IACOL, IAROW, ICOFFA, II, IIROW, 00155 $ INDAA, INDTAU, INDWORK, IPOSTPAD, IPREPAD, 00156 $ IROFFA, ISIZEHEEVX, ISIZESUBTST, ISIZETST, 00157 $ JJCOL, LDAA, LII, LIII, LJJ, LJJJ, LWMIN, MAXI, 00158 $ MB_A, MYCOL, MYROW, NB_A, NP, NPCOL, NPROW, NQ, 00159 $ RSIZECHK, RSIZEHEEVX, RSIZEQTQ, RSIZESUBTST, 00160 $ RSIZETST, RSRC_A, SIZEHEEVX, SIZEMQRLEFT, 00161 $ SIZEMQRRIGHT, SIZEQRF, SIZESUBTST, SIZETMS, 00162 $ SIZETST,SIZEHEEVD, RSIZEHEEVD, ISIZEHEEVD 00163 * .. 00164 * .. External Subroutines .. 00165 EXTERNAL BLACS_GRIDINFO, CHK1MAT, PXERBLA, PZGEQRF, 00166 $ PZLASIZESEP, PZMATGEN, PZUNMQR, ZLASET 00167 * .. 00168 * .. External Functions .. 00169 INTEGER INDXG2P, NUMROC 00170 EXTERNAL INDXG2P, NUMROC 00171 * .. 00172 * .. Intrinsic Functions .. 00173 * 00174 INTRINSIC MAX, MIN, MOD 00175 * .. 00176 * .. Executable Statements .. 00177 * This is just to keep ftnchek happy 00178 IF( BLOCK_CYCLIC_2D*CSRC_*CTXT_*DLEN_*DTYPE_*LLD_*MB_*M_*NB_*N_* 00179 $ RSRC_.LT.0 )RETURN 00180 * 00181 * Initialize grid information 00182 * 00183 CALL BLACS_GRIDINFO( DESCA( CTXT_ ), NPROW, NPCOL, MYROW, MYCOL ) 00184 * 00185 * Check LWORK 00186 * 00187 INFO = 0 00188 IF( NPROW.EQ.-1 ) THEN 00189 INFO = -( 700+CTXT_ ) 00190 ELSE 00191 CALL CHK1MAT( N, 1, N, 1, IA, JA, DESCA, 7, INFO ) 00192 END IF 00193 * 00194 LDAA = DESCA( LLD_ ) 00195 MB_A = DESCA( MB_ ) 00196 NB_A = DESCA( NB_ ) 00197 RSRC_A = DESCA( RSRC_ ) 00198 CSRC_A = DESCA( CSRC_ ) 00199 IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ) 00200 IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ) 00201 IROFFA = MOD( IA-1, MB_A ) 00202 ICOFFA = MOD( JA-1, NB_A ) 00203 NP = NUMROC( N+IROFFA, MB_A, MYROW, IAROW, NPROW ) 00204 NQ = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ) 00205 IPREPAD = 0 00206 IPOSTPAD = 0 00207 CALL PZLASIZESEP( DESCA, IPREPAD, IPOSTPAD, SIZEMQRLEFT, 00208 $ SIZEMQRRIGHT, SIZEQRF, SIZETMS, RSIZEQTQ, 00209 $ RSIZECHK, SIZEHEEVX, RSIZEHEEVX, ISIZEHEEVX, 00210 $ SIZEHEEVD, RSIZEHEEVD, ISIZEHEEVD, 00211 $ SIZESUBTST, RSIZESUBTST, ISIZESUBTST, SIZETST, 00212 $ RSIZETST, ISIZETST ) 00213 LWMIN = SIZETMS 00214 * 00215 * Test the input arguments 00216 * 00217 IF( INFO.EQ.0 ) THEN 00218 IF( K.LT.0 .OR. K.GT.N-1 ) THEN 00219 INFO = -2 00220 ELSE IF( N.NE.ORDER ) THEN 00221 INFO = -9 00222 ELSE IF( LWORK.LT.LWMIN ) THEN 00223 INFO = -11 00224 END IF 00225 END IF 00226 IF( INFO.LT.0 ) THEN 00227 CALL PXERBLA( DESCA( CTXT_ ), 'PZLAGHE', -INFO ) 00228 RETURN 00229 END IF 00230 * 00231 INDAA = 1 00232 INDTAU = INDAA + LDAA*MAX( 1, NQ ) 00233 INDWORK = INDTAU + MAX( 1, NQ ) 00234 * 00235 IF( K.NE.0 ) THEN 00236 CALL ZLASET( 'A', LDAA, NQ, ZZERO, ZZERO, WORK( INDAA ), LDAA ) 00237 * 00238 * 00239 * Build a random matrix 00240 * 00241 * 00242 CALL PZMATGEN( DESCA( CTXT_ ), 'N', 'N', N, ORDER, 00243 $ DESCA( MB_ ), DESCA( NB_ ), WORK( INDAA ), 00244 $ DESCA( LLD_ ), DESCA( RSRC_ ), DESCA( CSRC_ ), 00245 $ ISEED( 1 ), 0, NP, 0, NQ, MYROW, MYCOL, NPROW, 00246 $ NPCOL ) 00247 CALL PZGEQRF( N, ORDER, WORK( INDAA ), IA, JA, DESCA, 00248 $ WORK( INDTAU ), WORK( INDWORK ), SIZEQRF, INFO ) 00249 * 00250 END IF 00251 * 00252 * Build a diagonal matrix A with the eigenvalues specified in D 00253 * 00254 CALL ZLASET( 'A', NP, NQ, ZZERO, ZZERO, A, DESCA( LLD_ ) ) 00255 * 00256 IIROW = 0 00257 JJCOL = 0 00258 LII = 1 00259 LJJ = 1 00260 * 00261 DO 20 II = 1, N, DESCA( MB_ ) 00262 MAXI = MIN( N, II+DESCA( MB_ )-1 ) 00263 IF( ( MYROW.EQ.IIROW ) .AND. ( MYCOL.EQ.JJCOL ) ) THEN 00264 LIII = LII 00265 LJJJ = LJJ 00266 DO 10 I = II, MAXI 00267 A( LIII+( LJJJ-1 )*DESCA( LLD_ ) ) = D( I ) 00268 LIII = LIII + 1 00269 LJJJ = LJJJ + 1 00270 10 CONTINUE 00271 END IF 00272 IF( MYROW.EQ.IIROW ) 00273 $ LII = LII + DESCA( MB_ ) 00274 IF( MYCOL.EQ.JJCOL ) 00275 $ LJJ = LJJ + DESCA( MB_ ) 00276 IIROW = MOD( IIROW+1, NPROW ) 00277 JJCOL = MOD( JJCOL+1, NPCOL ) 00278 20 CONTINUE 00279 * 00280 * A = Q * A 00281 * 00282 IF( K.NE.0 ) THEN 00283 * 00284 CALL PZUNMQR( 'L', 'Conjugate transpose', N, N, ORDER, 00285 $ WORK( INDAA ), IA, JA, DESCA, WORK( INDTAU ), A, 00286 $ IA, JA, DESCA, WORK( INDWORK ), SIZEMQRLEFT, 00287 $ INFO ) 00288 * 00289 * 00290 * A = A * Q' 00291 * 00292 * 00293 CALL PZUNMQR( 'R', 'N', N, N, ORDER, WORK( INDAA ), IA, JA, 00294 $ DESCA, WORK( INDTAU ), A, IA, JA, DESCA, 00295 $ WORK( INDWORK ), SIZEMQRRIGHT, INFO ) 00296 * 00297 END IF 00298 * 00299 * End of PZLAGHE 00300 * 00301 END
