ScaLAPACK 2.1  2.1
ScaLAPACK: Scalable Linear Algebra PACKage
pdtrtri.f
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1  SUBROUTINE pdtrtri( UPLO, DIAG, N, A, IA, JA, DESCA, INFO )
2 *
3 * -- ScaLAPACK routine (version 1.7) --
4 * University of Tennessee, Knoxville, Oak Ridge National Laboratory,
5 * and University of California, Berkeley.
6 * May 1, 1997
7 *
8 * .. Scalar Arguments ..
9  CHARACTER DIAG, UPLO
10  INTEGER IA, INFO, JA, N
11 * ..
12 * .. Array Arguments ..
13  INTEGER DESCA( * )
14  DOUBLE PRECISION A( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * PDTRTRI computes the inverse of a upper or lower triangular
21 * distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1).
22 *
23 * Notes
24 * =====
25 *
26 * Each global data object is described by an associated description
27 * vector. This vector stores the information required to establish
28 * the mapping between an object element and its corresponding process
29 * and memory location.
30 *
31 * Let A be a generic term for any 2D block cyclicly distributed array.
32 * Such a global array has an associated description vector DESCA.
33 * In the following comments, the character _ should be read as
34 * "of the global array".
35 *
36 * NOTATION STORED IN EXPLANATION
37 * --------------- -------------- --------------------------------------
38 * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
39 * DTYPE_A = 1.
40 * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
41 * the BLACS process grid A is distribu-
42 * ted over. The context itself is glo-
43 * bal, but the handle (the integer
44 * value) may vary.
45 * M_A (global) DESCA( M_ ) The number of rows in the global
46 * array A.
47 * N_A (global) DESCA( N_ ) The number of columns in the global
48 * array A.
49 * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
50 * the rows of the array.
51 * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
52 * the columns of the array.
53 * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
54 * row of the array A is distributed.
55 * CSRC_A (global) DESCA( CSRC_ ) The process column over which the
56 * first column of the array A is
57 * distributed.
58 * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
59 * array. LLD_A >= MAX(1,LOCr(M_A)).
60 *
61 * Let K be the number of rows or columns of a distributed matrix,
62 * and assume that its process grid has dimension p x q.
63 * LOCr( K ) denotes the number of elements of K that a process
64 * would receive if K were distributed over the p processes of its
65 * process column.
66 * Similarly, LOCc( K ) denotes the number of elements of K that a
67 * process would receive if K were distributed over the q processes of
68 * its process row.
69 * The values of LOCr() and LOCc() may be determined via a call to the
70 * ScaLAPACK tool function, NUMROC:
71 * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
72 * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
73 * An upper bound for these quantities may be computed by:
74 * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
75 * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
76 *
77 * Arguments
78 * =========
79 *
80 * UPLO (global input) CHARACTER
81 * Specifies whether the distributed matrix sub( A ) is upper
82 * or lower triangular:
83 * = 'U': Upper triangular,
84 * = 'L': Lower triangular.
85 *
86 * DIAG (global input) CHARACTER
87 * Specifies whether or not the distributed matrix sub( A )
88 * is unit triangular:
89 * = 'N': Non-unit triangular,
90 * = 'U': Unit triangular.
91 *
92 * N (global input) INTEGER
93 * The number of rows and columns to be operated on, i.e. the
94 * order of the distributed submatrix sub( A ). N >= 0.
95 *
96 * A (local input/local output) DOUBLE PRECISION pointer into the
97 * local memory to an array of dimension (LLD_A,LOCc(JA+N-1)).
98 * On entry, this array contains the local pieces of the
99 * triangular matrix sub( A ). If UPLO = 'U', the leading
100 * N-by-N upper triangular part of the matrix sub( A ) contains
101 * the upper triangular matrix to be inverted, and the strictly
102 * lower triangular part of sub( A ) is not referenced.
103 * If UPLO = 'L', the leading N-by-N lower triangular part of
104 * the matrix sub( A ) contains the lower triangular matrix,
105 * and the strictly upper triangular part of sub( A ) is not
106 * referenced.
107 * On exit, the (triangular) inverse of the original matrix.
108 *
109 * IA (global input) INTEGER
110 * The row index in the global array A indicating the first
111 * row of sub( A ).
112 *
113 * JA (global input) INTEGER
114 * The column index in the global array A indicating the
115 * first column of sub( A ).
116 *
117 * DESCA (global and local input) INTEGER array of dimension DLEN_.
118 * The array descriptor for the distributed matrix A.
119 *
120 * INFO (global output) INTEGER
121 * = 0: successful exit
122 * < 0: If the i-th argument is an array and the j-entry had
123 * an illegal value, then INFO = -(i*100+j), if the i-th
124 * argument is a scalar and had an illegal value, then
125 * INFO = -i.
126 * > 0: If INFO = K, A(IA+K-1,JA+K-1) is exactly zero. The
127 * triangular matrix sub( A ) is singular and its
128 * inverse can not be computed.
129 *
130 * ====================================================================
131 *
132 * .. Parameters ..
133  INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
134  $ LLD_, MB_, M_, NB_, N_, RSRC_
135  parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
136  $ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
137  $ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
138  DOUBLE PRECISION ZERO, ONE
139  parameter( zero = 0.0d+0, one = 1.0d+0 )
140 * ..
141 * .. Local Scalars ..
142  LOGICAL NOUNIT, UPPER
143  INTEGER I, ICOFF, ICTXT, IROFF, ICURCOL, ICURROW,
144  $ IDUMMY, II, IOFFA, J, JB, JJ, JN, LDA, MYCOL,
145  $ MYROW, NN, NPCOL, NPROW
146 * ..
147 * .. Local Arrays ..
148  INTEGER IDUM1( 2 ), IDUM2( 2 )
149 * ..
150 * .. External Subroutines ..
151  EXTERNAL blacs_gridinfo, chk1mat, igamx2d, infog2l,
152  $ pchk1mat, pdtrti2, pdtrmm, pdtrsm,
153  $ pxerbla
154 * ..
155 * .. External Functions ..
156  LOGICAL LSAME
157  INTEGER ICEIL
158  EXTERNAL iceil, lsame
159 * ..
160 * .. Intrinsic Functions ..
161  INTRINSIC ichar, min, mod
162 * ..
163 * .. Executable Statements ..
164 *
165 * Get grid parameters
166 *
167  ictxt = desca( ctxt_ )
168  CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
169 *
170 * Test input parameters
171 *
172  info = 0
173  IF( nprow.EQ.-1 ) THEN
174  info = -(700+ctxt_)
175  ELSE
176  upper = lsame( uplo, 'U' )
177  nounit = lsame( diag, 'N' )
178 *
179  CALL chk1mat( n, 3, n, 3, ia, ja, desca, 7, info )
180  IF( info.EQ.0 ) THEN
181  iroff = mod( ia-1, desca( mb_ ) )
182  icoff = mod( ja-1, desca( nb_ ) )
183  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
184  info = -1
185  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
186  info = -2
187  ELSE IF( iroff.NE.icoff .OR. iroff.NE.0 ) THEN
188  info = -6
189  ELSE IF( desca( mb_ ).NE.desca( nb_ ) ) THEN
190  info = -(700+nb_)
191  END IF
192  END IF
193 *
194  IF( upper ) THEN
195  idum1( 1 ) = ichar( 'U' )
196  ELSE
197  idum1( 1 ) = ichar( 'L' )
198  END IF
199  idum2( 1 ) = 1
200  IF( nounit ) THEN
201  idum1( 2 ) = ichar( 'N' )
202  ELSE
203  idum1( 2 ) = ichar( 'U' )
204  END IF
205  idum2( 2 ) = 2
206 *
207  CALL pchk1mat( n, 3, n, 3, ia, ja, desca, 7, 2, idum1, idum2,
208  $ info )
209  END IF
210 *
211  IF( info.NE.0 ) THEN
212  CALL pxerbla( ictxt, 'PDTRTRI', -info )
213  RETURN
214  END IF
215 *
216 * Quick return if possible
217 *
218  IF( n.EQ.0 )
219  $ RETURN
220 *
221 * Check for singularity if non-unit.
222 *
223  jn = min( iceil( ja, desca( nb_ ) ) * desca( nb_ ), ja+n-1 )
224  IF( nounit ) THEN
225  CALL infog2l( ia, ja, desca, nprow, npcol, myrow, mycol,
226  $ ii, jj, icurrow, icurcol )
227 *
228 * Handle first block separately
229 *
230  jb = jn-ja+1
231  lda = desca( lld_ )
232  IF( myrow.EQ.icurrow .AND. mycol.EQ.icurcol ) THEN
233  ioffa = ii+(jj-1)*lda
234  DO 10 i = 0, jb-1
235  IF( a( ioffa ).EQ.zero .AND. info.EQ.0 )
236  $ info = i + 1
237  ioffa = ioffa + lda + 1
238  10 CONTINUE
239  END IF
240  IF( myrow.EQ.icurrow )
241  $ ii = ii + jb
242  IF( mycol.EQ.icurcol )
243  $ jj = jj + jb
244  icurrow = mod( icurrow+1, nprow )
245  icurcol = mod( icurcol+1, npcol )
246 *
247 * Loop over remaining blocks of columns
248 *
249  DO 30 j = jn+1, ja+n-1, desca( nb_ )
250  jb = min( ja+n-j, desca( nb_ ) )
251  IF( myrow.EQ.icurrow .AND. mycol.EQ.icurcol ) THEN
252  ioffa = ii+(jj-1)*lda
253  DO 20 i = 0, jb-1
254  IF( a( ioffa ).EQ.zero .AND. info.EQ.0 )
255  $ info = j + i - ja + 1
256  ioffa = ioffa + lda + 1
257  20 CONTINUE
258  END IF
259  IF( myrow.EQ.icurrow )
260  $ ii = ii + jb
261  IF( mycol.EQ.icurcol )
262  $ jj = jj + jb
263  icurrow = mod( icurrow+1, nprow )
264  icurcol = mod( icurcol+1, npcol )
265  30 CONTINUE
266  CALL igamx2d( ictxt, 'All', ' ', 1, 1, info, 1, idummy,
267  $ idummy, -1, -1, mycol )
268  IF( info.NE.0 )
269  $ RETURN
270  END IF
271 *
272 * Use blocked code
273 *
274  IF( upper ) THEN
275 *
276 * Compute inverse of upper triangular matrix
277 *
278  jb = jn-ja+1
279 *
280 * Handle first block of column separately
281 *
282  CALL pdtrti2( uplo, diag, jb, a, ia, ja, desca, info )
283 *
284 * Loop over remaining block of columns
285 *
286  DO 40 j = jn+1, ja+n-1, desca( nb_ )
287  jb = min( desca( nb_ ), ja+n-j )
288  i = ia + j - ja
289 *
290 * Compute rows 1:j-1 of current block column
291 *
292  CALL pdtrmm( 'Left', uplo, 'No transpose', diag, j-ja, jb,
293  $ one, a, ia, ja, desca, a, ia, j, desca )
294  CALL pdtrsm( 'Right', uplo, 'No transpose', diag, j-ja,
295  $ jb, -one, a, i, j, desca, a, ia, j, desca )
296 *
297 * Compute inverse of current diagonal block
298 *
299  CALL pdtrti2( uplo, diag, jb, a, i, j, desca, info )
300 *
301  40 CONTINUE
302 *
303  ELSE
304 *
305 * Compute inverse of lower triangular matrix
306 *
307  nn = ( ( ja+n-2 ) / desca( nb_ ) )*desca( nb_ ) + 1
308  DO 50 j = nn, jn+1, -desca( nb_ )
309  jb = min( desca( nb_ ), ja+n-j )
310  i = ia + j - ja
311  IF( j+jb.LE.ja+n-1 ) THEN
312 *
313 * Compute rows j+jb:ja+n-1 of current block column
314 *
315  CALL pdtrmm( 'Left', uplo, 'No transpose', diag,
316  $ ja+n-j-jb, jb, one, a, i+jb, j+jb, desca,
317  $ a, i+jb, j, desca )
318  CALL pdtrsm( 'Right', uplo, 'No transpose', diag,
319  $ ja+n-j-jb, jb, -one, a, i, j, desca,
320  $ a, i+jb, j, desca )
321  END IF
322 *
323 * Compute inverse of current diagonal block
324 *
325  CALL pdtrti2( uplo, diag, jb, a, i, j, desca, info )
326 *
327  50 CONTINUE
328 *
329 * Handle the last block of columns separately
330 *
331  jb = jn-ja+1
332  IF( ja+jb.LE.ja+n-1 ) THEN
333 *
334 * Compute rows ja+jb:ja+n-1 of current block column
335 *
336  CALL pdtrmm( 'Left', uplo, 'No transpose', diag, n-jb, jb,
337  $ one, a, ia+jb, ja+jb, desca, a, ia+jb, ja,
338  $ desca )
339  CALL pdtrsm( 'Right', uplo, 'No transpose', diag, n-jb, jb,
340  $ -one, a, ia, ja, desca, a, ia+jb, ja, desca )
341  END IF
342 *
343 * Compute inverse of current diagonal block
344 *
345  CALL pdtrti2( uplo, diag, jb, a, ia, ja, desca, info )
346 *
347  END IF
348 *
349  RETURN
350 *
351 * End PDTRTRI
352 *
353  END
infog2l
subroutine infog2l(GRINDX, GCINDX, DESC, NPROW, NPCOL, MYROW, MYCOL, LRINDX, LCINDX, RSRC, CSRC)
Definition: infog2l.f:3
pdtrti2
subroutine pdtrti2(UPLO, DIAG, N, A, IA, JA, DESCA, INFO)
Definition: pdtrti2.f:2
pchk1mat
subroutine pchk1mat(MA, MAPOS0, NA, NAPOS0, IA, JA, DESCA, DESCAPOS0, NEXTRA, EX, EXPOS, INFO)
Definition: pchkxmat.f:3
chk1mat
subroutine chk1mat(MA, MAPOS0, NA, NAPOS0, IA, JA, DESCA, DESCAPOS0, INFO)
Definition: chk1mat.f:3
pxerbla
subroutine pxerbla(ICTXT, SRNAME, INFO)
Definition: pxerbla.f:2
min
#define min(A, B)
Definition: pcgemr.c:181
pdtrtri
subroutine pdtrtri(UPLO, DIAG, N, A, IA, JA, DESCA, INFO)
Definition: pdtrtri.f:2