ScaLAPACK 2.1  2.1 ScaLAPACK: Scalable Linear Algebra PACKage
psqrt16.f
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1  SUBROUTINE psqrt16( TRANS, M, N, NRHS, A, IA, JA, DESCA, X, IX,
2  \$ JX, DESCX, B, IB, JB, DESCB, RWORK, RESID )
3 *
4 * -- ScaLAPACK routine (version 1.7) --
5 * University of Tennessee, Knoxville, Oak Ridge National Laboratory,
6 * and University of California, Berkeley.
7 * May 1, 1997
8 *
9 * .. Scalar Arguments ..
10  CHARACTER TRANS
11  INTEGER IA, IB, IX, JA, JB, JX, M, N, NRHS
12  REAL RESID
13 * ..
14 * .. Array Arguments ..
15  INTEGER DESCA( * ), DESCB( * ), DESCX( * )
16  REAL A( * ), B( * ), RWORK( * ), X( * )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * PSQRT16 computes the residual for a solution of a system of linear
23 * equations sub( A )*sub( X ) = B or sub( A' )*sub( X ) = B:
24 * RESID = norm(B - sub( A )*sub( X ) ) /
25 * ( max(m,n) * norm(sub( A ) ) * norm(sub( X ) ) * EPS ),
26 * where EPS is the machine epsilon, sub( A ) denotes
27 * A(IA:IA+N-1,JA,JA+N-1), and sub( X ) denotes
28 * X(IX:IX+N-1, JX:JX+NRHS-1).
29 *
30 * Notes
31 * =====
32 *
33 * Each global data object is described by an associated description
34 * vector. This vector stores the information required to establish
35 * the mapping between an object element and its corresponding process
36 * and memory location.
37 *
38 * Let A be a generic term for any 2D block cyclicly distributed array.
39 * Such a global array has an associated description vector DESCA.
40 * In the following comments, the character _ should be read as
41 * "of the global array".
42 *
43 * NOTATION STORED IN EXPLANATION
44 * --------------- -------------- --------------------------------------
45 * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
46 * DTYPE_A = 1.
47 * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
48 * the BLACS process grid A is distribu-
49 * ted over. The context itself is glo-
50 * bal, but the handle (the integer
51 * value) may vary.
52 * M_A (global) DESCA( M_ ) The number of rows in the global
53 * array A.
54 * N_A (global) DESCA( N_ ) The number of columns in the global
55 * array A.
56 * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
57 * the rows of the array.
58 * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
59 * the columns of the array.
60 * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
61 * row of the array A is distributed.
62 * CSRC_A (global) DESCA( CSRC_ ) The process column over which the
63 * first column of the array A is
64 * distributed.
65 * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
66 * array. LLD_A >= MAX(1,LOCr(M_A)).
67 *
68 * Let K be the number of rows or columns of a distributed matrix,
69 * and assume that its process grid has dimension p x q.
70 * LOCr( K ) denotes the number of elements of K that a process
71 * would receive if K were distributed over the p processes of its
72 * process column.
73 * Similarly, LOCc( K ) denotes the number of elements of K that a
74 * process would receive if K were distributed over the q processes of
75 * its process row.
76 * The values of LOCr() and LOCc() may be determined via a call to the
77 * ScaLAPACK tool function, NUMROC:
78 * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
79 * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
80 * An upper bound for these quantities may be computed by:
81 * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
82 * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
83 *
84 * Arguments
85 * =========
86 *
87 * TRANS (global input) CHARACTER*1
88 * Specifies the form of the system of equations:
89 * = 'N': sub( A )*sub( X ) = sub( B )
90 * = 'T': sub( A' )*sub( X )= sub( B ), where A' is the
91 * transpose of sub( A ).
92 * = 'C': sub( A' )*sub( X )= B, where A' is the transpose
93 * of sub( A ).
94 *
95 * M (global input) INTEGER
96 * The number of rows to be operated on, i.e. the number of rows
97 * of the distributed submatrix sub( A ). M >= 0.
98 *
99 * N (global input) INTEGER
100 * The number of columns to be operated on, i.e. the number of
101 * columns of the distributed submatrix sub( A ). N >= 0.
102 *
103 * NRHS (global input) INTEGER
104 * The number of right hand sides, i.e., the number of columns
105 * of the distributed submatrix sub( B ). NRHS >= 0.
106 *
107 * A (local input) REAL pointer into the local
108 * memory to an array of dimension (LLD_A,LOCc(JA+N-1)).
109 * The original M x N matrix A.
110 *
111 * IA (global input) INTEGER
112 * The row index in the global array A indicating the first
113 * row of sub( A ).
114 *
115 * JA (global input) INTEGER
116 * The column index in the global array A indicating the
117 * first column of sub( A ).
118 *
119 * DESCA (global and local input) INTEGER array of dimension DLEN_.
120 * The array descriptor for the distributed matrix A.
121 *
122 * X (local input) REAL pointer into the local
123 * memory to an array of dimension (LLD_X,LOCc(JX+NRHS-1)). This
124 * array contains the local pieces of the computed solution
125 * distributed vectors for the system of linear equations.
126 *
127 * IX (global input) INTEGER
128 * The row index in the global array X indicating the first
129 * row of sub( X ).
130 *
131 * JX (global input) INTEGER
132 * The column index in the global array X indicating the
133 * first column of sub( X ).
134 *
135 * DESCX (global and local input) INTEGER array of dimension DLEN_.
136 * The array descriptor for the distributed matrix X.
137 *
138 * B (local input/local output) REAL pointer into
139 * the local memory to an array of dimension
140 * (LLD_B,LOCc(JB+NRHS-1)). On entry, this array contains the
141 * local pieces of the distributes right hand side vectors for
142 * the system of linear equations. On exit, sub( B ) is over-
143 * written with the difference sub( B ) - sub( A )*sub( X ) or
144 * sub( B ) - sub( A )'*sub( X ).
145 *
146 * IB (global input) INTEGER
147 * The row index in the global array B indicating the first
148 * row of sub( B ).
149 *
150 * JB (global input) INTEGER
151 * The column index in the global array B indicating the
152 * first column of sub( B ).
153 *
154 * DESCB (global and local input) INTEGER array of dimension DLEN_.
155 * The array descriptor for the distributed matrix B.
156 *
157 * RWORK (local workspace) REAL array, dimension (LRWORK)
158 * LWORK >= Nq0 if TRANS = 'N', and LRWORK >= Mp0 otherwise.
159 *
160 * where
161 *
162 * IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ),
163 * IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ),
164 * IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
165 * Mp0 = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ),
166 * Nq0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),
167 *
168 * INDXG2P and NUMROC are ScaLAPACK tool functions; MYROW,
169 * MYCOL, NPROW and NPCOL can be determined by calling the
170 * subroutine BLACS_GRIDINFO.
171 *
172 * RESID (global output) REAL
173 * The maximum over the number of right hand sides of
174 * norm( sub( B )- sub( A )*sub( X ) ) /
175 * ( max(m,n) * norm( sub( A ) ) * norm( sub( X ) ) * EPS ).
176 *
177 * =====================================================================
178 *
179 * .. Parameters ..
180  INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
181  \$ lld_, mb_, m_, nb_, n_, rsrc_
182  parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
183  \$ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
184  \$ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
185  REAL ZERO, ONE
186  parameter( zero = 0.0e+0, one = 1.0e+0 )
187 * ..
188 * .. Local Scalars ..
189  INTEGER ICTXT, IDUMM, J, MYCOL, MYROW, N1, N2, NPCOL,
190  \$ nprow
191  REAL ANORM, BNORM, EPS, XNORM
192 * ..
193 * .. Local Arrays ..
194  REAL TEMP( 2 )
195 * ..
196 * .. External Functions ..
197  LOGICAL LSAME
198  REAL PSLAMCH, PSLANGE
199  EXTERNAL lsame, pslamch, pslange
200 * ..
201 * .. External Subroutines ..
202  EXTERNAL blacs_gridinfo, psasum, psgemm, sgamx2d
203 * ..
204 * .. Intrinsic Functions ..
205  INTRINSIC max
206 * ..
207 * .. Executable Statements ..
208 *
209 * Get grid parameters
210 *
211  ictxt = desca( ctxt_ )
212  CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
213 *
214 * Quick exit if M = 0 or N = 0 or NRHS = 0
215 *
216  IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.EQ.0 ) THEN
217  resid = zero
218  RETURN
219  END IF
220 *
221  IF( lsame( trans, 'T' ) .OR. lsame( trans, 'C' ) ) THEN
222  anorm = pslange( 'I', m, n, a, ia, ja, desca, rwork )
223  n1 = n
224  n2 = m
225  ELSE
226  anorm = pslange( '1', m, n, a, ia, ja, desca, rwork )
227  n1 = m
228  n2 = n
229  END IF
230 *
231  eps = pslamch( ictxt, 'Epsilon' )
232 *
233 * Compute B - sub( A )*sub( X ) (or B - sub( A' )*sub( X ) ) and
234 * store in B.
235 *
236  CALL psgemm( trans, 'No transpose', n1, nrhs, n2, -one, a, ia,
237  \$ ja, desca, x, ix, jx, descx, one, b, ib, jb, descb )
238 *
239 * Compute the maximum over the number of right hand sides of
240 * norm( sub( B ) - sub( A )*sub( X ) ) /
241 * ( max(m,n) * norm( sub( A ) ) * norm( sub( X ) ) * EPS ).
242 *
243  resid = zero
244  DO 10 j = 1, nrhs
245 *
246  CALL psasum( n1, bnorm, b, ib, jb+j-1, descb, 1 )
247  CALL psasum( n2, xnorm, x, ix, jx+j-1, descx, 1 )
248 *
249 * Only the process columns owning the vector operands will have
250 * the correct result, the other will have zero.
251 *
252  temp( 1 ) = bnorm
253  temp( 2 ) = xnorm
254  idumm = 0
255  CALL sgamx2d( ictxt, 'All', ' ', 2, 1, temp, 2, idumm, idumm,
256  \$ -1, -1, idumm )
257  bnorm = temp( 1 )
258  xnorm = temp( 2 )
259 *
260 * Every processes have ANORM, BNORM and XNORM now.
261 *
262  IF( anorm.EQ.zero .AND. bnorm.EQ.zero ) THEN
263  resid = zero
264  ELSE IF( anorm.LE.zero .OR. xnorm.LE.zero ) THEN
265  resid = one / eps
266  ELSE
267  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) /
268  \$ ( max( m, n )*eps ) )
269  END IF
270 *
271  10 CONTINUE
272 *
273  RETURN
274 *
275 * End of PSQRT16
276 *
277  END
max
#define max(A, B)
Definition: pcgemr.c:180
psqrt16
subroutine psqrt16(TRANS, M, N, NRHS, A, IA, JA, DESCA, X, IX, JX, DESCX, B, IB, JB, DESCB, RWORK, RESID)
Definition: psqrt16.f:3