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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 PDGEEQU( M, N, A, IA, JA, DESCA, R, C, ROWCND, COLCND, 00002 $ AMAX, INFO ) 00003 * 00004 * -- ScaLAPACK routine (version 1.7) -- 00005 * University of Tennessee, Knoxville, Oak Ridge National Laboratory, 00006 * and University of California, Berkeley. 00007 * May 1, 1997 00008 * 00009 * .. Scalar Arguments .. 00010 INTEGER IA, INFO, JA, M, N 00011 DOUBLE PRECISION AMAX, COLCND, ROWCND 00012 * .. 00013 * .. Array Arguments .. 00014 INTEGER DESCA( * ) 00015 DOUBLE PRECISION A( * ), C( * ), R( * ) 00016 * .. 00017 * 00018 * Purpose 00019 * ======= 00020 * 00021 * PDGEEQU computes row and column scalings intended to equilibrate an 00022 * M-by-N distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA:JA+N-1) and 00023 * reduce its condition number. R returns the row scale factors and C 00024 * the column scale factors, chosen to try to make the largest entry in 00025 * each row and column of the distributed matrix B with elements 00026 * B(i,j) = R(i) * A(i,j) * C(j) have absolute value 1. 00027 * 00028 * R(i) and C(j) are restricted to be between SMLNUM = smallest safe 00029 * number and BIGNUM = largest safe number. Use of these scaling 00030 * factors is not guaranteed to reduce the condition number of 00031 * sub( A ) but works well in practice. 00032 * 00033 * Notes 00034 * ===== 00035 * 00036 * Each global data object is described by an associated description 00037 * vector. This vector stores the information required to establish 00038 * the mapping between an object element and its corresponding process 00039 * and memory location. 00040 * 00041 * Let A be a generic term for any 2D block cyclicly distributed array. 00042 * Such a global array has an associated description vector DESCA. 00043 * In the following comments, the character _ should be read as 00044 * "of the global array". 00045 * 00046 * NOTATION STORED IN EXPLANATION 00047 * --------------- -------------- -------------------------------------- 00048 * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, 00049 * DTYPE_A = 1. 00050 * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating 00051 * the BLACS process grid A is distribu- 00052 * ted over. The context itself is glo- 00053 * bal, but the handle (the integer 00054 * value) may vary. 00055 * M_A (global) DESCA( M_ ) The number of rows in the global 00056 * array A. 00057 * N_A (global) DESCA( N_ ) The number of columns in the global 00058 * array A. 00059 * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute 00060 * the rows of the array. 00061 * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute 00062 * the columns of the array. 00063 * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first 00064 * row of the array A is distributed. 00065 * CSRC_A (global) DESCA( CSRC_ ) The process column over which the 00066 * first column of the array A is 00067 * distributed. 00068 * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local 00069 * array. LLD_A >= MAX(1,LOCr(M_A)). 00070 * 00071 * Let K be the number of rows or columns of a distributed matrix, 00072 * and assume that its process grid has dimension p x q. 00073 * LOCr( K ) denotes the number of elements of K that a process 00074 * would receive if K were distributed over the p processes of its 00075 * process column. 00076 * Similarly, LOCc( K ) denotes the number of elements of K that a 00077 * process would receive if K were distributed over the q processes of 00078 * its process row. 00079 * The values of LOCr() and LOCc() may be determined via a call to the 00080 * ScaLAPACK tool function, NUMROC: 00081 * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ), 00082 * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). 00083 * An upper bound for these quantities may be computed by: 00084 * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A 00085 * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A 00086 * 00087 * Arguments 00088 * ========= 00089 * 00090 * M (global input) INTEGER 00091 * The number of rows to be operated on i.e the number of rows 00092 * of the distributed submatrix sub( A ). M >= 0. 00093 * 00094 * N (global input) INTEGER 00095 * The number of columns to be operated on i.e the number of 00096 * columns of the distributed submatrix sub( A ). N >= 0. 00097 * 00098 * A (local input) DOUBLE PRECISION pointer into the local memory 00099 * to an array of dimension ( LLD_A, LOCc(JA+N-1) ), the 00100 * local pieces of the M-by-N distributed matrix whose 00101 * equilibration factors are to be computed. 00102 * 00103 * IA (global input) INTEGER 00104 * The row index in the global array A indicating the first 00105 * row of sub( A ). 00106 * 00107 * JA (global input) INTEGER 00108 * The column index in the global array A indicating the 00109 * first column of sub( A ). 00110 * 00111 * DESCA (global and local input) INTEGER array of dimension DLEN_. 00112 * The array descriptor for the distributed matrix A. 00113 * 00114 * R (local output) DOUBLE PRECISION array, dimension LOCr(M_A) 00115 * If INFO = 0 or INFO > IA+M-1, R(IA:IA+M-1) contains the row 00116 * scale factors for sub( A ). R is aligned with the distributed 00117 * matrix A, and replicated across every process column. R is 00118 * tied to the distributed matrix A. 00119 * 00120 * C (local output) DOUBLE PRECISION array, dimension LOCc(N_A) 00121 * If INFO = 0, C(JA:JA+N-1) contains the column scale factors 00122 * for sub( A ). C is aligned with the distributed matrix A, and 00123 * replicated down every process row. C is tied to the distri- 00124 * buted matrix A. 00125 * 00126 * ROWCND (global output) DOUBLE PRECISION 00127 * If INFO = 0 or INFO > IA+M-1, ROWCND contains the ratio of 00128 * the smallest R(i) to the largest R(i) (IA <= i <= IA+M-1). 00129 * If ROWCND >= 0.1 and AMAX is neither too large nor too small, 00130 * it is not worth scaling by R(IA:IA+M-1). 00131 * 00132 * COLCND (global output) DOUBLE PRECISION 00133 * If INFO = 0, COLCND contains the ratio of the smallest C(j) 00134 * to the largest C(j) (JA <= j <= JA+N-1). If COLCND >= 0.1, it 00135 * is not worth scaling by C(JA:JA+N-1). 00136 * 00137 * AMAX (global output) DOUBLE PRECISION 00138 * Absolute value of largest distributed matrix element. If 00139 * AMAX is very close to overflow or very close to underflow, 00140 * the matrix should be scaled. 00141 * 00142 * INFO (global output) INTEGER 00143 * = 0: successful exit 00144 * < 0: If the i-th argument is an array and the j-entry had 00145 * an illegal value, then INFO = -(i*100+j), if the i-th 00146 * argument is a scalar and had an illegal value, then 00147 * INFO = -i. 00148 * > 0: If INFO = i, and i is 00149 * <= M: the i-th row of the distributed matrix sub( A ) 00150 * is exactly zero, 00151 * > M: the (i-M)-th column of the distributed 00152 * matrix sub( A ) is exactly zero. 00153 * 00154 * ===================================================================== 00155 * 00156 * .. Parameters .. 00157 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, 00158 $ LLD_, MB_, M_, NB_, N_, RSRC_ 00159 PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, 00160 $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, 00161 $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) 00162 DOUBLE PRECISION ONE, ZERO 00163 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00164 * .. 00165 * .. Local Scalars .. 00166 CHARACTER COLCTOP, ROWCTOP 00167 INTEGER I, IACOL, IAROW, ICOFF, ICTXT, IDUMM, IIA, 00168 $ IOFFA, IROFF, J, JJA, LDA, MP, MYCOL, MYROW, 00169 $ NPCOL, NPROW, NQ 00170 DOUBLE PRECISION BIGNUM, RCMAX, RCMIN, SMLNUM 00171 * .. 00172 * .. Local Arrays .. 00173 INTEGER DESCC( DLEN_ ), DESCR( DLEN_ ) 00174 * .. 00175 * .. External Subroutines .. 00176 EXTERNAL BLACS_GRIDINFO, CHK1MAT, DESCSET, DGAMN2D, 00177 $ DGAMX2D, IGAMX2D, INFOG2L, PCHK1MAT, PB_TOPGET, 00178 $ PXERBLA 00179 * .. 00180 * .. External Functions .. 00181 INTEGER INDXL2G, NUMROC 00182 DOUBLE PRECISION PDLAMCH 00183 EXTERNAL INDXL2G, NUMROC, PDLAMCH 00184 * .. 00185 * .. Intrinsic Functions .. 00186 INTRINSIC ABS, MAX, MIN, MOD 00187 * .. 00188 * .. Executable Statements .. 00189 * 00190 * Get grid parameters 00191 * 00192 ICTXT = DESCA( CTXT_ ) 00193 CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) 00194 * 00195 * Test the input parameters. 00196 * 00197 INFO = 0 00198 IF( NPROW.EQ.-1 ) THEN 00199 INFO = -(600+CTXT_) 00200 ELSE 00201 CALL CHK1MAT( M, 1, N, 2, IA, JA, DESCA, 6, INFO ) 00202 CALL PCHK1MAT( M, 1, N, 2, IA, JA, DESCA, 6, 0, IDUMM, IDUMM, 00203 $ INFO ) 00204 END IF 00205 * 00206 IF( INFO.NE.0 ) THEN 00207 CALL PXERBLA( ICTXT, 'PDGEEQU', -INFO ) 00208 RETURN 00209 END IF 00210 * 00211 * Quick return if possible 00212 * 00213 IF( M.EQ.0 .OR. N.EQ.0 ) THEN 00214 ROWCND = ONE 00215 COLCND = ONE 00216 AMAX = ZERO 00217 RETURN 00218 END IF 00219 * 00220 CALL PB_TOPGET( ICTXT, 'Combine', 'Rowwise', ROWCTOP ) 00221 CALL PB_TOPGET( ICTXT, 'Combine', 'Columnwise', COLCTOP ) 00222 * 00223 * Get machine constants and local indexes. 00224 * 00225 SMLNUM = PDLAMCH( ICTXT, 'S' ) 00226 BIGNUM = ONE / SMLNUM 00227 CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA, 00228 $ IAROW, IACOL ) 00229 IROFF = MOD( IA-1, DESCA( MB_ ) ) 00230 ICOFF = MOD( JA-1, DESCA( NB_ ) ) 00231 MP = NUMROC( M+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW ) 00232 NQ = NUMROC( N+ICOFF, DESCA( NB_ ), MYCOL, IACOL, NPCOL ) 00233 IF( MYROW.EQ.IAROW ) 00234 $ MP = MP - IROFF 00235 IF( MYCOL.EQ.IACOL ) 00236 $ NQ = NQ - ICOFF 00237 LDA = DESCA( LLD_ ) 00238 * 00239 * Assign descriptors for R and C arrays 00240 * 00241 CALL DESCSET( DESCR, M, 1, DESCA( MB_ ), 1, 0, 0, ICTXT, 00242 $ MAX( 1, MP ) ) 00243 CALL DESCSET( DESCC, 1, N, 1, DESCA( NB_ ), 0, 0, ICTXT, 1 ) 00244 * 00245 * Compute row scale factors. 00246 * 00247 DO 10 I = IIA, IIA+MP-1 00248 R( I ) = ZERO 00249 10 CONTINUE 00250 * 00251 * Find the maximum element in each row. 00252 * 00253 IOFFA = (JJA-1)*LDA 00254 DO 30 J = JJA, JJA+NQ-1 00255 DO 20 I = IIA, IIA+MP-1 00256 R( I ) = MAX( R( I ), ABS( A( IOFFA + I ) ) ) 00257 20 CONTINUE 00258 IOFFA = IOFFA + LDA 00259 30 CONTINUE 00260 CALL DGAMX2D( ICTXT, 'Rowwise', ROWCTOP, MP, 1, R( IIA ), 00261 $ MAX( 1, MP ), IDUMM, IDUMM, -1, -1, MYCOL ) 00262 * 00263 * Find the maximum and minimum scale factors. 00264 * 00265 RCMIN = BIGNUM 00266 RCMAX = ZERO 00267 DO 40 I = IIA, IIA+MP-1 00268 RCMAX = MAX( RCMAX, R( I ) ) 00269 RCMIN = MIN( RCMIN, R( I ) ) 00270 40 CONTINUE 00271 CALL DGAMX2D( ICTXT, 'Columnwise', COLCTOP, 1, 1, RCMAX, 1, IDUMM, 00272 $ IDUMM, -1, -1, MYCOL ) 00273 CALL DGAMN2D( ICTXT, 'Columnwise', COLCTOP, 1, 1, RCMIN, 1, IDUMM, 00274 $ IDUMM, -1, -1, MYCOL ) 00275 AMAX = RCMAX 00276 * 00277 IF( RCMIN.EQ.ZERO ) THEN 00278 * 00279 * Find the first zero scale factor and return an error code. 00280 * 00281 DO 50 I = IIA, IIA+MP-1 00282 IF( R( I ).EQ.ZERO .AND. INFO.EQ.0 ) 00283 $ INFO = INDXL2G( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), 00284 $ NPROW ) - IA + 1 00285 50 CONTINUE 00286 CALL IGAMX2D( ICTXT, 'Columnwise', COLCTOP, 1, 1, INFO, 1, 00287 $ IDUMM, IDUMM, -1, -1, MYCOL ) 00288 IF( INFO.NE.0 ) 00289 $ RETURN 00290 ELSE 00291 * 00292 * Invert the scale factors. 00293 * 00294 DO 60 I = IIA, IIA+MP-1 00295 R( I ) = ONE / MIN( MAX( R( I ), SMLNUM ), BIGNUM ) 00296 60 CONTINUE 00297 * 00298 * Compute ROWCND = min(R(I)) / max(R(I)) 00299 * 00300 ROWCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM ) 00301 * 00302 END IF 00303 * 00304 * Compute column scale factors 00305 * 00306 DO 70 J = JJA, JJA+NQ-1 00307 C( J ) = ZERO 00308 70 CONTINUE 00309 * 00310 * Find the maximum element in each column, 00311 * assuming the row scaling computed above. 00312 * 00313 IOFFA = (JJA-1)*LDA 00314 DO 90 J = JJA, JJA+NQ-1 00315 DO 80 I = IIA, IIA+MP-1 00316 C( J ) = MAX( C( J ), ABS( A( IOFFA + I ) )*R( I ) ) 00317 80 CONTINUE 00318 IOFFA = IOFFA + LDA 00319 90 CONTINUE 00320 CALL DGAMX2D( ICTXT, 'Columnwise', COLCTOP, 1, NQ, C( JJA ), 00321 $ 1, IDUMM, IDUMM, -1, -1, MYCOL ) 00322 * 00323 * Find the maximum and minimum scale factors. 00324 * 00325 RCMIN = BIGNUM 00326 RCMAX = ZERO 00327 DO 100 J = JJA, JJA+NQ-1 00328 RCMIN = MIN( RCMIN, C( J ) ) 00329 RCMAX = MAX( RCMAX, C( J ) ) 00330 100 CONTINUE 00331 CALL DGAMX2D( ICTXT, 'Columnwise', COLCTOP, 1, 1, RCMAX, 1, IDUMM, 00332 $ IDUMM, -1, -1, MYCOL ) 00333 CALL DGAMN2D( ICTXT, 'Columnwise', COLCTOP, 1, 1, RCMIN, 1, IDUMM, 00334 $ IDUMM, -1, -1, MYCOL ) 00335 * 00336 IF( RCMIN.EQ.ZERO ) THEN 00337 * 00338 * Find the first zero scale factor and return an error code. 00339 * 00340 DO 110 J = JJA, JJA+NQ-1 00341 IF( C( J ).EQ.ZERO .AND. INFO.EQ.0 ) 00342 $ INFO = M + INDXL2G( J, DESCA( NB_ ), MYCOL, 00343 $ DESCA( CSRC_ ), NPCOL ) - JA + 1 00344 110 CONTINUE 00345 CALL IGAMX2D( ICTXT, 'Columnwise', COLCTOP, 1, 1, INFO, 1, 00346 $ IDUMM, IDUMM, -1, -1, MYCOL ) 00347 IF( INFO.NE.0 ) 00348 $ RETURN 00349 ELSE 00350 * 00351 * Invert the scale factors. 00352 * 00353 DO 120 J = JJA, JJA+NQ-1 00354 C( J ) = ONE / MIN( MAX( C( J ), SMLNUM ), BIGNUM ) 00355 120 CONTINUE 00356 * 00357 * Compute COLCND = min(C(J)) / max(C(J)) 00358 * 00359 COLCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM ) 00360 * 00361 END IF 00362 * 00363 RETURN 00364 * 00365 * End of PDGEEQU 00366 * 00367 END
