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
|
COMPLEX FUNCTION CLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST,
$ ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
$ SPARSE )
*
* -- LAPACK auxiliary test routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
*
INTEGER I, IDIST, IGRADE, IPVTNG, ISUB, J, JSUB, KL,
$ KU, M, N
REAL SPARSE
* ..
*
* .. Array Arguments ..
*
INTEGER ISEED( 4 ), IWORK( * )
COMPLEX D( * ), DL( * ), DR( * )
* ..
*
* Purpose
* =======
*
* CLATM3 returns the (ISUB,JSUB) entry of a random matrix of
* dimension (M, N) described by the other paramters. (ISUB,JSUB)
* is the final position of the (I,J) entry after pivoting
* according to IPVTNG and IWORK. CLATM3 is called by the
* CLATMR 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 CLATMR which has already checked the parameters.
*
* Use of CLATM3 differs from CLATM2 in the order in which the random
* number generator is called to fill in random matrix entries.
* With CLATM2, the generator is called to fill in the pivoted matrix
* columnwise. With CLATM3, the generator is called to fill in the
* matrix columnwise, after which it is pivoted. Thus, CLATM3 can
* be used to construct random matrices which differ only in their
* order of rows and/or columns. CLATM2 is used to construct band
* matrices while avoiding calling the random number generator for
* entries outside the band (and therefore generating random numbers
* in different orders for different pivot orders).
*
* The matrix whose (ISUB,JSUB) entry is returned is constructed as
* follows (this routine only computes one entry):
*
* If ISUB is outside (1..M) or JSUB 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 unpivoted entry to be returned. Not modified.
*
* J - INTEGER
* Column of unpivoted entry to be returned. Not modified.
*
* ISUB - INTEGER
* Row of pivoted entry to be returned. Changed on exit.
*
* JSUB - INTEGER
* Column of pivoted entry to be returned. Changed on exit.
*
* 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 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 array ( I or J, as appropriate )
* Left scale factors for grading matrix. Not modified.
*
* DR - COMPLEX 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) originally in position K is in
* position IWORK( K ) after pivoting.
* This differs from IWORK for CLATM2. Not modified.
*
* SPARSE - REAL 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.
*
* =====================================================================
*
* .. Parameters ..
*
REAL ZERO
PARAMETER ( ZERO = 0.0E0 )
COMPLEX CZERO
PARAMETER ( CZERO = ( 0.0E0, 0.0E0 ) )
* ..
*
* .. Local Scalars ..
*
COMPLEX CTEMP
* ..
*
* .. External Functions ..
*
REAL SLARAN
COMPLEX CLARND
EXTERNAL SLARAN, CLARND
* ..
*
* .. Intrinsic Functions ..
*
INTRINSIC CONJG
* ..
*
*-----------------------------------------------------------------------
*
* .. Executable Statements ..
*
*
* Check for I and J in range
*
IF( I.LT.1 .OR. I.GT.M .OR. J.LT.1 .OR. J.GT.N ) THEN
ISUB = I
JSUB = J
CLATM3 = CZERO
RETURN
END IF
*
* Compute subscripts depending on IPVTNG
*
IF( IPVTNG.EQ.0 ) THEN
ISUB = I
JSUB = J
ELSE IF( IPVTNG.EQ.1 ) THEN
ISUB = IWORK( I )
JSUB = J
ELSE IF( IPVTNG.EQ.2 ) THEN
ISUB = I
JSUB = IWORK( J )
ELSE IF( IPVTNG.EQ.3 ) THEN
ISUB = IWORK( I )
JSUB = IWORK( J )
END IF
*
* Check for banding
*
IF( JSUB.GT.ISUB+KU .OR. JSUB.LT.ISUB-KL ) THEN
CLATM3 = CZERO
RETURN
END IF
*
* Check for sparsity
*
IF( SPARSE.GT.ZERO ) THEN
IF( SLARAN( ISEED ).LT.SPARSE ) THEN
CLATM3 = CZERO
RETURN
END IF
END IF
*
* Compute entry and grade it according to IGRADE
*
IF( I.EQ.J ) THEN
CTEMP = D( I )
ELSE
CTEMP = CLARND( IDIST, ISEED )
END IF
IF( IGRADE.EQ.1 ) THEN
CTEMP = CTEMP*DL( I )
ELSE IF( IGRADE.EQ.2 ) THEN
CTEMP = CTEMP*DR( J )
ELSE IF( IGRADE.EQ.3 ) THEN
CTEMP = CTEMP*DL( I )*DR( J )
ELSE IF( IGRADE.EQ.4 .AND. I.NE.J ) THEN
CTEMP = CTEMP*DL( I ) / DL( J )
ELSE IF( IGRADE.EQ.5 ) THEN
CTEMP = CTEMP*DL( I )*CONJG( DL( J ) )
ELSE IF( IGRADE.EQ.6 ) THEN
CTEMP = CTEMP*DL( I )*DL( J )
END IF
CLATM3 = CTEMP
RETURN
*
* End of CLATM3
*
END
|
