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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 PDDBLASCHK( SYMM, UPLO, TRANS, N, BWL, BWU, NRHS, X, 00002 $ IX, JX, DESCX, IASEED, A, IA, JA, DESCA, 00003 $ IBSEED, ANORM, RESID, WORK, WORKSIZ ) 00004 * 00005 * 00006 * -- ScaLAPACK routine (version 1.7) -- 00007 * University of Tennessee, Knoxville, Oak Ridge National Laboratory, 00008 * and University of California, Berkeley. 00009 * November 15, 1997 00010 * 00011 * .. Scalar Arguments .. 00012 CHARACTER SYMM, TRANS, UPLO 00013 INTEGER BWL, BWU, IA, IASEED, IBSEED, 00014 $ IX, JA, JX, N, NRHS, WORKSIZ 00015 DOUBLE PRECISION ANORM, RESID 00016 * .. 00017 * .. Array Arguments .. 00018 INTEGER DESCA( * ), DESCX( * ) 00019 DOUBLE PRECISION A( * ), WORK( * ), X( * ) 00020 * .. External Functions .. 00021 LOGICAL LSAME 00022 * .. 00023 * 00024 * Purpose 00025 * ======= 00026 * 00027 * PDDBLASCHK computes the residual 00028 * || sub( A )*sub( X ) - B || / (|| sub( A ) ||*|| sub( X ) ||*eps*N) 00029 * to check the accuracy of the factorization and solve steps in the 00030 * LU and Cholesky decompositions, where sub( A ) denotes 00031 * A(IA:IA+N-1,JA,JA+N-1), sub( X ) denotes X(IX:IX+N-1, JX:JX+NRHS-1). 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 * SYMM (global input) CHARACTER 00091 * if SYMM = 'S', sub( A ) is a symmetric distributed band 00092 * matrix, otherwise sub( A ) is a general distributed matrix. 00093 * 00094 * UPLO (global input) CHARACTER 00095 * if SYMM = 'S', then 00096 * if UPLO = 'L', the lower half of the matrix is stored 00097 * if UPLO = 'U', the upper half of the matrix is stored 00098 * if SYMM != 'S' or 'H', then 00099 * if UPLO = 'D', the matrix is stable during factorization 00100 * without interchanges 00101 * if UPLO != 'D', the matrix is general 00102 * 00103 * TRANS if TRANS= 'T', A 'Transpose' is used as the 00104 * coefficient matrix in the solve. 00105 * 00106 * N (global input) INTEGER 00107 * The number of columns to be operated on, i.e. the number of 00108 * columns of the distributed submatrix sub( A ). N >= 0. 00109 * 00110 * NRHS (global input) INTEGER 00111 * The number of right-hand-sides, i.e the number of columns 00112 * of the distributed matrix sub( X ). NRHS >= 1. 00113 * 00114 * X (local input) DOUBLE PRECISION pointer into the local memory 00115 * to an array of dimension (LLD_X,LOCq(JX+NRHS-1). This array 00116 * contains the local pieces of the answer vector(s) sub( X ) of 00117 * sub( A ) sub( X ) - B, split up over a column of processes. 00118 * 00119 * IX (global input) INTEGER 00120 * The row index in the global array X indicating the first 00121 * row of sub( X ). 00122 * 00123 * DESCX (global and local input) INTEGER array of dimension DLEN_. 00124 * The array descriptor for the distributed matrix X. 00125 * 00126 * IASEED (global input) INTEGER 00127 * The seed number to generate the original matrix Ao. 00128 * 00129 * JA (global input) INTEGER 00130 * The column index in the global array A indicating the 00131 * first column of sub( A ). 00132 * 00133 * DESCA (global and local input) INTEGER array of dimension DLEN_. 00134 * The array descriptor for the distributed matrix A. 00135 * 00136 * IBSEED (global input) INTEGER 00137 * The seed number to generate the original matrix B. 00138 * 00139 * ANORM (global input) DOUBLE PRECISION 00140 * The 1-norm or infinity norm of the distributed matrix 00141 * sub( A ). 00142 * 00143 * RESID (global output) DOUBLE PRECISION 00144 * The residual error: 00145 * ||sub( A )*sub( X )-B|| / (||sub( A )||*||sub( X )||*eps*N). 00146 * 00147 * WORK (local workspace) DOUBLE PRECISION array, dimension (LWORK) 00148 * IF SYMM='S' 00149 * LWORK >= max(5,max(max(bwl,bwu)*(max(bwl,bwu)+2),NB))+2*NB 00150 * IF SYMM!='S' or 'H' 00151 * LWORK >= max(5,max(max(bwl,bwu)*(max(bwl,bwu)+2),NB))+2*NB 00152 * 00153 * WORKSIZ (local input) size of WORK. 00154 * 00155 * ===================================================================== 00156 * 00157 * Code Developer: Andrew J. Cleary, University of Tennessee. 00158 * Current address: Lawrence Livermore National Labs. 00159 * This version released: August, 2001. 00160 * 00161 * ===================================================================== 00162 * 00163 * .. Parameters .. 00164 DOUBLE PRECISION ZERO, ONE 00165 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00166 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, 00167 $ LLD_, MB_, M_, NB_, N_, RSRC_ 00168 PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, 00169 $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, 00170 $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) 00171 INTEGER INT_ONE 00172 PARAMETER ( INT_ONE = 1 ) 00173 * .. 00174 * .. Local Scalars .. 00175 INTEGER IACOL, IAROW, ICTXT, 00176 $ IIA, IIX, IPB, IPW, 00177 $ IXCOL, IXROW, J, JJA, JJX, LDA, 00178 $ MYCOL, MYROW, NB, NP, NPCOL, NPROW, NQ 00179 INTEGER BW, INFO, IPPRODUCT, WORK_MIN 00180 DOUBLE PRECISION DIVISOR, EPS, RESID1, NORMX 00181 * .. 00182 * .. Local Arrays .. 00183 * .. 00184 * .. External Subroutines .. 00185 EXTERNAL BLACS_GRIDINFO, DGAMX2D, DGEBR2D, 00186 $ DGEBS2D, DGEMM, DGERV2D, DGESD2D, 00187 $ DGSUM2D, DLASET, PBDTRAN, PDMATGEN 00188 * .. 00189 * .. External Functions .. 00190 INTEGER IDAMAX, NUMROC 00191 DOUBLE PRECISION PDLAMCH 00192 EXTERNAL IDAMAX, NUMROC, PDLAMCH 00193 * .. 00194 * .. Intrinsic Functions .. 00195 INTRINSIC ABS, DBLE, MAX, MIN, MOD 00196 * .. 00197 * .. Executable Statements .. 00198 * 00199 * Get needed initial parameters 00200 * 00201 ICTXT = DESCA( CTXT_ ) 00202 NB = DESCA( NB_ ) 00203 * 00204 IF( LSAME( SYMM, 'S' ) ) THEN 00205 BW = BWL 00206 WORK_MIN = MAX(5,MAX(MAX(BWL,BWU)*(MAX(BWL,BWU)+2),NB))+2*NB 00207 ELSE 00208 BW = MAX(BWL, BWU) 00209 WORK_MIN = MAX(5,MAX(MAX(BWL,BWU)*(MAX(BWL,BWU)+2),NB))+2*NB 00210 ENDIF 00211 * 00212 IF ( WORKSIZ .LT. WORK_MIN ) THEN 00213 CALL PXERBLA( ICTXT, 'PDBLASCHK', -18 ) 00214 RETURN 00215 END IF 00216 * 00217 CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) 00218 * 00219 EPS = PDLAMCH( ICTXT, 'eps' ) 00220 RESID = 0.0D+0 00221 DIVISOR = ANORM * EPS * DBLE( N ) 00222 * 00223 CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA, 00224 $ IAROW, IACOL ) 00225 CALL INFOG2L( IX, JX, DESCX, NPROW, NPCOL, MYROW, MYCOL, IIX, JJX, 00226 $ IXROW, IXCOL ) 00227 NP = NUMROC( (BWL+BWU+1), DESCA( MB_ ), MYROW, 0, NPROW ) 00228 NQ = NUMROC( N, DESCA( NB_ ), MYCOL, 0, NPCOL ) 00229 * 00230 IPB = 1 00231 IPPRODUCT = 1 + DESCA( NB_ ) 00232 IPW = 1 + 2*DESCA( NB_ ) 00233 * 00234 LDA = DESCA( LLD_ ) 00235 * 00236 * Regenerate A 00237 * 00238 IF( LSAME( SYMM, 'S' )) THEN 00239 CALL PDBMATGEN( ICTXT, UPLO, 'D', BW, BW, N, BW+1, 00240 $ DESCA( NB_ ), A, DESCA( LLD_ ), 0, 0, 00241 $ IASEED, MYROW, MYCOL, NPROW, NPCOL ) 00242 ELSE 00243 * 00244 CALL PDBMATGEN( ICTXT, 'N', UPLO, BWL, BWU, N, 00245 $ DESCA( MB_ ), DESCA( NB_ ), A, 00246 $ DESCA( LLD_ ), 0, 0, IASEED, MYROW, 00247 $ MYCOL, NPROW, NPCOL ) 00248 ENDIF 00249 * 00250 * Loop over the rhs 00251 * 00252 RESID = 0.0 00253 * 00254 DO 40 J = 1, NRHS 00255 * 00256 * Multiply A * current column of X 00257 * 00258 * 00259 CALL PDGBDCMV( BWL+BWU+1, BWL, BWU, TRANS, N, A, 1, DESCA, 00260 $ 1, X( 1 + (J-1)*DESCX( LLD_ )), 1, DESCX, 00261 $ WORK( IPPRODUCT ), WORK( IPW ), 00262 $ (MAX(BWL,BWU)+2)*MAX(BWL,BWU), INFO ) 00263 * 00264 * 00265 * Regenerate column of B 00266 * 00267 CALL PDMATGEN( DESCX( CTXT_ ), 'No', 'No', DESCX( M_ ), 00268 $ DESCX( N_ ), DESCX( MB_ ), DESCX( NB_ ), 00269 $ WORK( IPB ), DESCX( LLD_ ), DESCX( RSRC_ ), 00270 $ DESCX( CSRC_ ), IBSEED, 0, NQ, J-1, 1, MYCOL, 00271 $ MYROW, NPCOL, NPROW ) 00272 * 00273 * Figure || A * X - B || & || X || 00274 * 00275 CALL PDAXPY( N, -ONE, WORK( IPPRODUCT ), 1, 1, DESCX, 1, 00276 $ WORK( IPB ), 1, 1, DESCX, 1 ) 00277 * 00278 CALL PDNRM2( N, NORMX, 00279 $ X, 1, J, DESCX, 1 ) 00280 * 00281 CALL PDNRM2( N, RESID1, 00282 $ WORK( IPB ), 1, 1, DESCX, 1 ) 00283 * 00284 * 00285 * Calculate residual = ||Ax-b|| / (||x||*||A||*eps*N) 00286 * 00287 RESID1 = RESID1 / ( NORMX*DIVISOR ) 00288 * 00289 RESID = MAX( RESID, RESID1 ) 00290 * 00291 40 CONTINUE 00292 * 00293 RETURN 00294 * 00295 * End of PDBLASCHK 00296 * 00297 END
