1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
|
/* -- translated by f2c (version 19940927).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
#include "f2c.h"
/* Double Complex */ VOID zlatm2_(doublecomplex * ret_val, integer *m,
integer *n, integer *i, integer *j, integer *kl, integer *ku, integer
*idist, integer *iseed, doublecomplex *d, integer *igrade,
doublecomplex *dl, doublecomplex *dr, integer *ipvtng, integer *iwork,
doublereal *sparse)
{
/* System generated locals */
integer i__1, i__2;
doublecomplex z__1, z__2, z__3;
/* Builtin functions */
void z_div(doublecomplex *, doublecomplex *, doublecomplex *), d_cnjg(
doublecomplex *, doublecomplex *);
/* Local variables */
static integer isub, jsub;
static doublecomplex ctemp;
extern doublereal dlaran_(integer *);
extern /* Double Complex */ VOID zlarnd_(doublecomplex *, integer *,
integer *);
/* -- LAPACK auxiliary test routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
ZLATM2 returns the (I,J) entry of a random matrix of dimension
(M, N) described by the other paramters. It is called by the
ZLATMR routine in order to build random test matrices. No error
checking on parameters is done, because this routine is called in
a tight loop by ZLATMR which has already checked the parameters.
Use of ZLATM2 differs from CLATM3 in the order in which the random
number generator is called to fill in random matrix entries.
With ZLATM2, the generator is called to fill in the pivoted matrix
columnwise. With ZLATM3, the generator is called to fill in the
matrix columnwise, after which it is pivoted. Thus, ZLATM3 can
be used to construct random matrices which differ only in their
order of rows and/or columns. ZLATM2 is used to construct band
matrices while avoiding calling the random number generator for
entries outside the band (and therefore generating random numbers
The matrix whose (I,J) entry is returned is constructed as
follows (this routine only computes one entry):
If I is outside (1..M) or J is outside (1..N), return zero
(this is convenient for generating matrices in band format).
Generate a matrix A with random entries of distribution IDIST.
Set the diagonal to D.
Grade the matrix, if desired, from the left (by DL) and/or
from the right (by DR or DL) as specified by IGRADE.
Permute, if desired, the rows and/or columns as specified by
IPVTNG and IWORK.
Band the matrix to have lower bandwidth KL and upper
bandwidth KU.
Set random entries to zero as specified by SPARSE.
Arguments
=========
M - INTEGER
Number of rows of matrix. Not modified.
N - INTEGER
Number of columns of matrix. Not modified.
I - INTEGER
Row of entry to be returned. Not modified.
J - INTEGER
Column of entry to be returned. Not modified.
KL - INTEGER
Lower bandwidth. Not modified.
KU - INTEGER
Upper bandwidth. Not modified.
IDIST - INTEGER
On entry, IDIST specifies the type of distribution to be
used to generate a random matrix .
1 => real and imaginary parts each UNIFORM( 0, 1 )
2 => real and imaginary parts each UNIFORM( -1, 1 )
3 => real and imaginary parts each NORMAL( 0, 1 )
4 => complex number uniform in DISK( 0 , 1 )
Not modified.
ISEED - INTEGER array of dimension ( 4 )
Seed for random number generator.
Changed on exit.
D - COMPLEX*16 array of dimension ( MIN( I , J ) )
Diagonal entries of matrix. Not modified.
IGRADE - INTEGER
Specifies grading of matrix as follows:
0 => no grading
1 => matrix premultiplied by diag( DL )
2 => matrix postmultiplied by diag( DR )
3 => matrix premultiplied by diag( DL ) and
postmultiplied by diag( DR )
4 => matrix premultiplied by diag( DL ) and
postmultiplied by inv( diag( DL ) )
5 => matrix premultiplied by diag( DL ) and
postmultiplied by diag( CONJG(DL) )
6 => matrix premultiplied by diag( DL ) and
postmultiplied by diag( DL )
Not modified.
DL - COMPLEX*16 array ( I or J, as appropriate )
Left scale factors for grading matrix. Not modified.
DR - COMPLEX*16 array ( I or J, as appropriate )
Right scale factors for grading matrix. Not modified.
IPVTNG - INTEGER
On entry specifies pivoting permutations as follows:
0 => none.
1 => row pivoting.
2 => column pivoting.
3 => full pivoting, i.e., on both sides.
Not modified.
IWORK - INTEGER array ( I or J, as appropriate )
This array specifies the permutation used. The
row (or column) in position K was originally in
position IWORK( K ).
This differs from IWORK for ZLATM3. Not modified.
SPARSE - DOUBLE PRECISION between 0. and 1.
On entry specifies the sparsity of the matrix
if sparse matix is to be generated.
SPARSE should lie between 0 and 1.
A uniform ( 0, 1 ) random number x is generated and
compared to SPARSE; if x is larger the matrix entry
is unchanged and if x is smaller the entry is set
to zero. Thus on the average a fraction SPARSE of the
entries will be set to zero.
Not modified.
=====================================================================
-----------------------------------------------------------------------
Check for I and J in range
Parameter adjustments */
--iwork;
--dr;
--dl;
--d;
--iseed;
/* Function Body */
if (*i < 1 || *i > *m || *j < 1 || *j > *n) {
ret_val->r = 0., ret_val->i = 0.;
return ;
}
/* Check for banding */
if (*j > *i + *ku || *j < *i - *kl) {
ret_val->r = 0., ret_val->i = 0.;
return ;
}
/* Check for sparsity */
if (*sparse > 0.) {
if (dlaran_(&iseed[1]) < *sparse) {
ret_val->r = 0., ret_val->i = 0.;
return ;
}
}
/* Compute subscripts depending on IPVTNG */
if (*ipvtng == 0) {
isub = *i;
jsub = *j;
} else if (*ipvtng == 1) {
isub = iwork[*i];
jsub = *j;
} else if (*ipvtng == 2) {
isub = *i;
jsub = iwork[*j];
} else if (*ipvtng == 3) {
isub = iwork[*i];
jsub = iwork[*j];
}
/* Compute entry and grade it according to IGRADE */
if (isub == jsub) {
i__1 = isub;
ctemp.r = d[i__1].r, ctemp.i = d[i__1].i;
} else {
zlarnd_(&z__1, idist, &iseed[1]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
}
if (*igrade == 1) {
i__1 = isub;
z__1.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__1.i =
ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r;
ctemp.r = z__1.r, ctemp.i = z__1.i;
} else if (*igrade == 2) {
i__1 = jsub;
z__1.r = ctemp.r * dr[i__1].r - ctemp.i * dr[i__1].i, z__1.i =
ctemp.r * dr[i__1].i + ctemp.i * dr[i__1].r;
ctemp.r = z__1.r, ctemp.i = z__1.i;
} else if (*igrade == 3) {
i__1 = isub;
z__2.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__2.i =
ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r;
i__2 = jsub;
z__1.r = z__2.r * dr[i__2].r - z__2.i * dr[i__2].i, z__1.i = z__2.r *
dr[i__2].i + z__2.i * dr[i__2].r;
ctemp.r = z__1.r, ctemp.i = z__1.i;
} else if (*igrade == 4 && isub != jsub) {
i__1 = isub;
z__2.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__2.i =
ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r;
z_div(&z__1, &z__2, &dl[jsub]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
} else if (*igrade == 5) {
i__1 = isub;
z__2.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__2.i =
ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r;
d_cnjg(&z__3, &dl[jsub]);
z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = z__2.r * z__3.i
+ z__2.i * z__3.r;
ctemp.r = z__1.r, ctemp.i = z__1.i;
} else if (*igrade == 6) {
i__1 = isub;
z__2.r = ctemp.r * dl[i__1].r - ctemp.i * dl[i__1].i, z__2.i =
ctemp.r * dl[i__1].i + ctemp.i * dl[i__1].r;
i__2 = jsub;
z__1.r = z__2.r * dl[i__2].r - z__2.i * dl[i__2].i, z__1.i = z__2.r *
dl[i__2].i + z__2.i * dl[i__2].r;
ctemp.r = z__1.r, ctemp.i = z__1.i;
}
ret_val->r = ctemp.r, ret_val->i = ctemp.i;
return ;
/* End of ZLATM2 */
} /* zlatm2_ */
|
