ScaLAPACK 2.1  2.1 ScaLAPACK: Scalable Linear Algebra PACKage
pdlatrz.f
Go to the documentation of this file.
1  SUBROUTINE pdlatrz( M, N, L, A, IA, JA, DESCA, TAU, WORK )
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  INTEGER IA, JA, L, M, N
10 * ..
11 * .. Array Arguments ..
12  INTEGER DESCA( * )
13  DOUBLE PRECISION A( * ), TAU( * ), WORK( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * PDLATRZ reduces the M-by-N ( M<=N ) real upper trapezoidal matrix
20 * sub( A ) = [ A(IA:IA+M-1,JA:JA+M-1) A(IA:IA+M-1,JA+N-L:JA+N-1) ] to
21 * upper triangular form by means of orthogonal transformations.
22 *
23 * The upper trapezoidal matrix sub( A ) is factored as
24 *
25 * sub( A ) = ( R 0 ) * Z,
26 *
27 * where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
28 * triangular matrix.
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 * M (global input) INTEGER
88 * The number of rows to be operated on, i.e. the number of rows
89 * of the distributed submatrix sub( A ). M >= 0.
90 *
91 * N (global input) INTEGER
92 * The number of columns to be operated on, i.e. the number of
93 * columns of the distributed submatrix sub( A ). N >= 0.
94 *
95 * L (global input) INTEGER
96 * The columns of the distributed submatrix sub( A ) containing
97 * the meaningful part of the Householder reflectors. L > 0.
98 *
99 * A (local input/local output) DOUBLE PRECISION pointer into the
100 * local memory to an array of dimension (LLD_A, LOCc(JA+N-1)).
101 * On entry, the local pieces of the M-by-N distributed matrix
102 * sub( A ) which is to be factored. On exit, the leading M-by-M
103 * upper triangular part of sub( A ) contains the upper trian-
104 * gular matrix R, and elements N-L+1 to N of the first M rows
105 * of sub( A ), with the array TAU, represent the orthogonal
106 * matrix Z as a product of M elementary reflectors.
107 *
108 * IA (global input) INTEGER
109 * The row index in the global array A indicating the first
110 * row of sub( A ).
111 *
112 * JA (global input) INTEGER
113 * The column index in the global array A indicating the
114 * first column of sub( A ).
115 *
116 * DESCA (global and local input) INTEGER array of dimension DLEN_.
117 * The array descriptor for the distributed matrix A.
118 *
119 * TAU (local output) DOUBLE PRECISION array, dimension LOCr(IA+M-1)
120 * This array contains the scalar factors of the elementary
121 * reflectors. TAU is tied to the distributed matrix A.
122 *
123 * WORK (local workspace) DOUBLE PRECISION array, dimension (LWORK)
124 * LWORK >= Nq0 + MAX( 1, Mp0 ), where
125 *
126 * IROFF = MOD( IA-1, MB_A ), ICOFF = MOD( JA-1, NB_A ),
127 * IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ),
128 * IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
129 * Mp0 = NUMROC( M+IROFF, MB_A, MYROW, IAROW, NPROW ),
130 * Nq0 = NUMROC( N+ICOFF, NB_A, MYCOL, IACOL, NPCOL ),
131 *
132 * and NUMROC, INDXG2P are ScaLAPACK tool functions;
133 * MYROW, MYCOL, NPROW and NPCOL can be determined by calling
134 * the subroutine BLACS_GRIDINFO.
135 *
136 * Further Details
137 * ===============
138 *
139 * The factorization is obtained by Householder's method. The kth
140 * transformation matrix, Z( k ), which is used to introduce zeros into
141 * the (m - k + 1)th row of sub( A ), is given in the form
142 *
143 * Z( k ) = ( I 0 ),
144 * ( 0 T( k ) )
145 *
146 * where
147 *
148 * T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ),
149 * ( 0 )
150 * ( z( k ) )
151 *
152 * tau is a scalar and z( k ) is an ( n - m ) element vector.
153 * tau and z( k ) are chosen to annihilate the elements of the kth row
154 * of sub( A ).
155 *
156 * The scalar tau is returned in the kth element of TAU and the vector
157 * u( k ) in the kth row of sub( A ), such that the elements of z( k )
158 * are in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned
159 * in the upper triangular part of sub( A ).
160 *
161 * Z is given by
162 *
163 * Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
164 *
165 * =====================================================================
166 *
167 * .. Parameters ..
168  INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
169  \$ LLD_, MB_, M_, NB_, N_, RSRC_
170  parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
171  \$ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
172  \$ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
173  DOUBLE PRECISION ONE, ZERO
174  parameter( one = 1.0d+0, zero = 0.0d+0 )
175 * ..
176 * .. Local Scalars ..
177  INTEGER I, IAROW, ICTXT, II, J, J1, MP, MYCOL, MYROW,
178  \$ NPCOL, NPROW
179  DOUBLE PRECISION AII
180 * ..
181 * .. External Subroutines ..
182  EXTERNAL infog1l, pdelset, pdlarfg, pdlarz
183 * ..
184 * .. External Functions ..
185  INTEGER NUMROC
186  EXTERNAL numroc
187 * ..
188 * .. Executable Statements ..
189 *
190 * Quick return if possible
191 *
192  IF( m.EQ.0 .OR. n.EQ.0 )
193  \$ RETURN
194 *
195 * Get grid parameters
196 *
197  ictxt = desca( ctxt_ )
198  CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
199 *
200  mp = numroc( ia+m-1, desca( mb_ ), myrow, desca( rsrc_ ),
201  \$ nprow )
202 *
203  IF( m.EQ.n ) THEN
204 *
205  CALL infog1l( ia, desca( mb_ ), nprow, myrow, desca( rsrc_ ),
206  \$ ii, iarow )
207  DO 10 i = ii, mp
208  tau( i ) = zero
209  10 CONTINUE
210 *
211  ELSE
212 *
213  j1 = ja + n - l
214  DO 20 i = ia+m-1, ia, -1
215  j = ja + i - ia
216 *
217 * Generate elementary reflector H(i) to annihilate
218 * [ A(i, j) A(i,j1:ja+n-1) ]
219 *
220  CALL pdlarfg( l+1, aii, i, j, a, i, j1, desca, desca( m_ ),
221  \$ tau )
222 *
223 * Apply H(i) to A(ia:i-1,j:ja+n-1) from the right
224 *
225  CALL pdlarz( 'Right', i-ia, ja+n-j, l, a, i, j1, desca,
226  \$ desca( m_ ), tau, a, ia, j, desca, work )
227  CALL pdelset( a, i, j, desca, aii )
228 *
229  20 CONTINUE
230 *
231  END IF
232 *
233  RETURN
234 *
235 * End of PDLATRZ
236 *
237  END
infog1l
subroutine infog1l(GINDX, NB, NPROCS, MYROC, ISRCPROC, LINDX, ROCSRC)
Definition: infog1l.f:3
pdlarz
subroutine pdlarz(SIDE, M, N, L, V, IV, JV, DESCV, INCV, TAU, C, IC, JC, DESCC, WORK)
Definition: pdlarz.f:3
pdlatrz
subroutine pdlatrz(M, N, L, A, IA, JA, DESCA, TAU, WORK)
Definition: pdlatrz.f:2
pdlarfg
subroutine pdlarfg(N, ALPHA, IAX, JAX, X, IX, JX, DESCX, INCX, TAU)
Definition: pdlarfg.f:3
pdelset
subroutine pdelset(A, IA, JA, DESCA, ALPHA)
Definition: pdelset.f:2