SCALAPACK 2.2.2
LAPACK: Linear Algebra PACKage
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◆ pdlauu2()

subroutine pdlauu2 ( character  uplo,
integer  n,
double precision, dimension( * )  a,
integer  ia,
integer  ja,
integer, dimension( * )  desca 
)

Definition at line 1 of file pdlauu2.f.

2*
3* -- ScaLAPACK auxiliary 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 UPLO
10 INTEGER IA, JA, N
11* ..
12* .. Array Arguments ..
13 INTEGER DESCA( * )
14 DOUBLE PRECISION A( * )
15* ..
16*
17* Purpose
18* =======
19*
20* PDLAUU2 computes the product U * U' or L' * L, where the triangular
21* factor U or L is stored in the upper or lower triangular part of
22* the matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1).
23*
24* If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
25* overwriting the factor U in sub( A ).
26* If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
27* overwriting the factor L in sub( A ).
28*
29* This is the unblocked form of the algorithm, calling Level 2 BLAS.
30* No communication is performed by this routine, the matrix to operate
31* on should be strictly local to one process.
32*
33* Notes
34* =====
35*
36* Each global data object is described by an associated description
37* vector. This vector stores the information required to establish
38* the mapping between an object element and its corresponding process
39* and memory location.
40*
41* Let A be a generic term for any 2D block cyclicly distributed array.
42* Such a global array has an associated description vector DESCA.
43* In the following comments, the character _ should be read as
44* "of the global array".
45*
46* NOTATION STORED IN EXPLANATION
47* --------------- -------------- --------------------------------------
48* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
49* DTYPE_A = 1.
50* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
51* the BLACS process grid A is distribu-
52* ted over. The context itself is glo-
53* bal, but the handle (the integer
54* value) may vary.
55* M_A (global) DESCA( M_ ) The number of rows in the global
56* array A.
57* N_A (global) DESCA( N_ ) The number of columns in the global
58* array A.
59* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
60* the rows of the array.
61* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
62* the columns of the array.
63* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
64* row of the array A is distributed.
65* CSRC_A (global) DESCA( CSRC_ ) The process column over which the
66* first column of the array A is
67* distributed.
68* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
69* array. LLD_A >= MAX(1,LOCr(M_A)).
70*
71* Let K be the number of rows or columns of a distributed matrix,
72* and assume that its process grid has dimension p x q.
73* LOCr( K ) denotes the number of elements of K that a process
74* would receive if K were distributed over the p processes of its
75* process column.
76* Similarly, LOCc( K ) denotes the number of elements of K that a
77* process would receive if K were distributed over the q processes of
78* its process row.
79* The values of LOCr() and LOCc() may be determined via a call to the
80* ScaLAPACK tool function, NUMROC:
81* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
82* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
83* An upper bound for these quantities may be computed by:
84* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
85* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
86*
87* Arguments
88* =========
89*
90* UPLO (global input) CHARACTER*1
91* Specifies whether the triangular factor stored in the matrix
92* sub( A ) is upper or lower triangular:
93* = 'U': Upper triangular,
94* = 'L': Lower triangular.
95*
96* N (global input) INTEGER
97* The number of rows and columns to be operated on, i.e. the
98* order of the order of the triangular factor U or L. N >= 0.
99*
100* A (local input/local output) DOUBLE PRECISION pointer into the
101* local memory to an array of dimension (LLD_A, LOCc(JA+N-1)).
102* On entry, the local pieces of the triangular factor L or U.
103* On exit, if UPLO = 'U', the upper triangle of the distributed
104* matrix sub( A ) is overwritten with the upper triangle of the
105* product U * U'; if UPLO = 'L', the lower triangle of sub( A )
106* is overwritten with the lower triangle of the product L' * L.
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* =====================================================================
120*
121* .. Parameters ..
122 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
123 $ LLD_, MB_, M_, NB_, N_, RSRC_
124 parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
125 $ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
126 $ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
127 DOUBLE PRECISION ONE
128 parameter( one = 1.0d+0 )
129* ..
130* .. Local Scalars ..
131 INTEGER IACOL, IAROW, ICURR, IDIAG, IIA, IOFFA, JJA,
132 $ LDA, MYCOL, MYROW, NA, NPCOL, NPROW
133 DOUBLE PRECISION AII
134* ..
135* .. External Subroutines ..
136 EXTERNAL blacs_gridinfo, infog2l, dgemv, dscal
137* ..
138* .. External Functions ..
139 LOGICAL LSAME
140 DOUBLE PRECISION DDOT
141 EXTERNAL ddot, lsame
142* ..
143* .. Executable Statements ..
144*
145* Quick return if possible
146*
147 IF( n.EQ.0 )
148 $ RETURN
149*
150* Get grid parameters and compute local indexes
151*
152 CALL blacs_gridinfo( desca( ctxt_ ), nprow, npcol, myrow, mycol )
153 CALL infog2l( ia, ja, desca, nprow, npcol, myrow, mycol, iia, jja,
154 $ iarow, iacol )
155*
156 IF( myrow.EQ.iarow .AND. mycol.EQ.iacol ) THEN
157*
158 lda = desca( lld_ )
159 idiag = iia + ( jja - 1 ) * lda
160 ioffa = idiag
161*
162 IF( lsame( uplo, 'U' ) ) THEN
163*
164* Compute the product U * U'.
165*
166 DO 10 na = n-1, 1, -1
167 aii = a( idiag )
168 icurr = idiag + lda
169 a( idiag ) = aii*aii + ddot( na, a( icurr ), lda,
170 $ a( icurr ), lda )
171 CALL dgemv( 'No transpose', n-na-1, na, one,
172 $ a( ioffa+lda ), lda, a( icurr ), lda, aii,
173 $ a( ioffa ), 1 )
174 idiag = idiag + lda + 1
175 ioffa = ioffa + lda
176 10 CONTINUE
177 aii = a( idiag )
178 CALL dscal( n, aii, a( ioffa ), 1 )
179*
180 ELSE
181*
182* Compute the product L' * L.
183*
184 DO 20 na = 1, n-1
185 aii = a( idiag )
186 icurr = idiag + 1
187 a(idiag) = aii*aii + ddot( n-na, a( icurr ), 1,
188 $ a( icurr ), 1 )
189 CALL dgemv( 'Transpose', n-na, na-1, one, a( ioffa+1 ),
190 $ lda, a( icurr ), 1, aii, a( ioffa ), lda )
191 idiag = idiag + lda + 1
192 ioffa = ioffa + 1
193 20 CONTINUE
194 aii = a( idiag )
195 CALL dscal( n, aii, a( ioffa ), lda )
196*
197 END IF
198*
199 END IF
200*
201 RETURN
202*
203* End of PDLAUU2
204*
infog2l
subroutine infog2l(grindx, gcindx, desc, nprow, npcol, myrow, mycol, lrindx, lcindx, rsrc, csrc)
Definition infog2l.f:3
lsame
logical function lsame(ca, cb)
Definition tools.f:1724
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