LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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clatm3.f
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1*> \brief \b CLATM3
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8* Definition:
9* ===========
10*
11* COMPLEX FUNCTION CLATM3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST,
12* ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
13* SPARSE )
14*
15* .. Scalar Arguments ..
16*
17* INTEGER I, IDIST, IGRADE, IPVTNG, ISUB, J, JSUB, KL,
18* $ KU, M, N
19* REAL SPARSE
20* ..
21*
22* .. Array Arguments ..
23*
24* INTEGER ISEED( 4 ), IWORK( * )
25* COMPLEX D( * ), DL( * ), DR( * )
26* ..
27*
28*
29*> \par Purpose:
30* =============
31*>
32*> \verbatim
33*>
34*> CLATM3 returns the (ISUB,JSUB) entry of a random matrix of
35*> dimension (M, N) described by the other parameters. (ISUB,JSUB)
36*> is the final position of the (I,J) entry after pivoting
37*> according to IPVTNG and IWORK. CLATM3 is called by the
38*> CLATMR routine in order to build random test matrices. No error
39*> checking on parameters is done, because this routine is called in
40*> a tight loop by CLATMR which has already checked the parameters.
41*>
42*> Use of CLATM3 differs from CLATM2 in the order in which the random
43*> number generator is called to fill in random matrix entries.
44*> With CLATM2, the generator is called to fill in the pivoted matrix
45*> columnwise. With CLATM3, the generator is called to fill in the
46*> matrix columnwise, after which it is pivoted. Thus, CLATM3 can
47*> be used to construct random matrices which differ only in their
48*> order of rows and/or columns. CLATM2 is used to construct band
49*> matrices while avoiding calling the random number generator for
50*> entries outside the band (and therefore generating random numbers
51*> in different orders for different pivot orders).
52*>
53*> The matrix whose (ISUB,JSUB) entry is returned is constructed as
54*> follows (this routine only computes one entry):
55*>
56*> If ISUB is outside (1..M) or JSUB is outside (1..N), return zero
57*> (this is convenient for generating matrices in band format).
58*>
59*> Generate a matrix A with random entries of distribution IDIST.
60*>
61*> Set the diagonal to D.
62*>
63*> Grade the matrix, if desired, from the left (by DL) and/or
64*> from the right (by DR or DL) as specified by IGRADE.
65*>
66*> Permute, if desired, the rows and/or columns as specified by
67*> IPVTNG and IWORK.
68*>
69*> Band the matrix to have lower bandwidth KL and upper
70*> bandwidth KU.
71*>
72*> Set random entries to zero as specified by SPARSE.
73*> \endverbatim
74*
75* Arguments:
76* ==========
77*
78*> \param[in] M
79*> \verbatim
80*> M is INTEGER
81*> Number of rows of matrix. Not modified.
82*> \endverbatim
83*>
84*> \param[in] N
85*> \verbatim
86*> N is INTEGER
87*> Number of columns of matrix. Not modified.
88*> \endverbatim
89*>
90*> \param[in] I
91*> \verbatim
92*> I is INTEGER
93*> Row of unpivoted entry to be returned. Not modified.
94*> \endverbatim
95*>
96*> \param[in] J
97*> \verbatim
98*> J is INTEGER
99*> Column of unpivoted entry to be returned. Not modified.
100*> \endverbatim
101*>
102*> \param[in,out] ISUB
103*> \verbatim
104*> ISUB is INTEGER
105*> Row of pivoted entry to be returned. Changed on exit.
106*> \endverbatim
107*>
108*> \param[in,out] JSUB
109*> \verbatim
110*> JSUB is INTEGER
111*> Column of pivoted entry to be returned. Changed on exit.
112*> \endverbatim
113*>
114*> \param[in] KL
115*> \verbatim
116*> KL is INTEGER
117*> Lower bandwidth. Not modified.
118*> \endverbatim
119*>
120*> \param[in] KU
121*> \verbatim
122*> KU is INTEGER
123*> Upper bandwidth. Not modified.
124*> \endverbatim
125*>
126*> \param[in] IDIST
127*> \verbatim
128*> IDIST is INTEGER
129*> On entry, IDIST specifies the type of distribution to be
130*> used to generate a random matrix .
131*> 1 => real and imaginary parts each UNIFORM( 0, 1 )
132*> 2 => real and imaginary parts each UNIFORM( -1, 1 )
133*> 3 => real and imaginary parts each NORMAL( 0, 1 )
134*> 4 => complex number uniform in DISK( 0 , 1 )
135*> Not modified.
136*> \endverbatim
137*>
138*> \param[in,out] ISEED
139*> \verbatim
140*> ISEED is INTEGER array of dimension ( 4 )
141*> Seed for random number generator.
142*> Changed on exit.
143*> \endverbatim
144*>
145*> \param[in] D
146*> \verbatim
147*> D is COMPLEX array of dimension ( MIN( I , J ) )
148*> Diagonal entries of matrix. Not modified.
149*> \endverbatim
150*>
151*> \param[in] IGRADE
152*> \verbatim
153*> IGRADE is INTEGER
154*> Specifies grading of matrix as follows:
155*> 0 => no grading
156*> 1 => matrix premultiplied by diag( DL )
157*> 2 => matrix postmultiplied by diag( DR )
158*> 3 => matrix premultiplied by diag( DL ) and
159*> postmultiplied by diag( DR )
160*> 4 => matrix premultiplied by diag( DL ) and
161*> postmultiplied by inv( diag( DL ) )
162*> 5 => matrix premultiplied by diag( DL ) and
163*> postmultiplied by diag( CONJG(DL) )
164*> 6 => matrix premultiplied by diag( DL ) and
165*> postmultiplied by diag( DL )
166*> Not modified.
167*> \endverbatim
168*>
169*> \param[in] DL
170*> \verbatim
171*> DL is COMPLEX array ( I or J, as appropriate )
172*> Left scale factors for grading matrix. Not modified.
173*> \endverbatim
174*>
175*> \param[in] DR
176*> \verbatim
177*> DR is COMPLEX array ( I or J, as appropriate )
178*> Right scale factors for grading matrix. Not modified.
179*> \endverbatim
180*>
181*> \param[in] IPVTNG
182*> \verbatim
183*> IPVTNG is INTEGER
184*> On entry specifies pivoting permutations as follows:
185*> 0 => none.
186*> 1 => row pivoting.
187*> 2 => column pivoting.
188*> 3 => full pivoting, i.e., on both sides.
189*> Not modified.
190*> \endverbatim
191*>
192*> \param[in] IWORK
193*> \verbatim
194*> IWORK is INTEGER array ( I or J, as appropriate )
195*> This array specifies the permutation used. The
196*> row (or column) originally in position K is in
197*> position IWORK( K ) after pivoting.
198*> This differs from IWORK for CLATM2. Not modified.
199*> \endverbatim
200*>
201*> \param[in] SPARSE
202*> \verbatim
203*> SPARSE is REAL between 0. and 1.
204*> On entry specifies the sparsity of the matrix
205*> if sparse matrix is to be generated.
206*> SPARSE should lie between 0 and 1.
207*> A uniform ( 0, 1 ) random number x is generated and
208*> compared to SPARSE; if x is larger the matrix entry
209*> is unchanged and if x is smaller the entry is set
210*> to zero. Thus on the average a fraction SPARSE of the
211*> entries will be set to zero.
212*> Not modified.
213*> \endverbatim
214*
215* Authors:
216* ========
217*
218*> \author Univ. of Tennessee
219*> \author Univ. of California Berkeley
220*> \author Univ. of Colorado Denver
221*> \author NAG Ltd.
222*
223*> \ingroup complex_matgen
224*
225* =====================================================================
226 COMPLEX FUNCTION clatm3( M, N, I, J, ISUB, JSUB, KL, KU, IDIST,
227 $ ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK,
228 $ SPARSE )
229*
230* -- LAPACK auxiliary routine --
231* -- LAPACK is a software package provided by Univ. of Tennessee, --
232* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
233*
234* .. Scalar Arguments ..
235*
236 INTEGER i, idist, igrade, ipvtng, isub, j, jsub, kl,
237 $ ku, m, n
238 REAL sparse
239* ..
240*
241* .. Array Arguments ..
242*
243 INTEGER iseed( 4 ), iwork( * )
244 COMPLEX d( * ), dl( * ), dr( * )
245* ..
246*
247* =====================================================================
248*
249* .. Parameters ..
250*
251 REAL zero
252 PARAMETER ( zero = 0.0e0 )
253 COMPLEX czero
254 parameter( czero = ( 0.0e0, 0.0e0 ) )
255* ..
256*
257* .. Local Scalars ..
258*
259 COMPLEX ctemp
260* ..
261*
262* .. External Functions ..
263*
264 REAL slaran
265 COMPLEX clarnd
266 EXTERNAL slaran, clarnd
267* ..
268*
269* .. Intrinsic Functions ..
270*
271 INTRINSIC conjg
272* ..
273*
274*-----------------------------------------------------------------------
275*
276* .. Executable Statements ..
277*
278*
279* Check for I and J in range
280*
281 IF( i.LT.1 .OR. i.GT.m .OR. j.LT.1 .OR. j.GT.n ) THEN
282 isub = i
283 jsub = j
284 clatm3 = czero
285 RETURN
286 END IF
287*
288* Compute subscripts depending on IPVTNG
289*
290 IF( ipvtng.EQ.0 ) THEN
291 isub = i
292 jsub = j
293 ELSE IF( ipvtng.EQ.1 ) THEN
294 isub = iwork( i )
295 jsub = j
296 ELSE IF( ipvtng.EQ.2 ) THEN
297 isub = i
298 jsub = iwork( j )
299 ELSE IF( ipvtng.EQ.3 ) THEN
300 isub = iwork( i )
301 jsub = iwork( j )
302 END IF
303*
304* Check for banding
305*
306 IF( jsub.GT.isub+ku .OR. jsub.LT.isub-kl ) THEN
307 clatm3 = czero
308 RETURN
309 END IF
310*
311* Check for sparsity
312*
313 IF( sparse.GT.zero ) THEN
314 IF( slaran( iseed ).LT.sparse ) THEN
315 clatm3 = czero
316 RETURN
317 END IF
318 END IF
319*
320* Compute entry and grade it according to IGRADE
321*
322 IF( i.EQ.j ) THEN
323 ctemp = d( i )
324 ELSE
325 ctemp = clarnd( idist, iseed )
326 END IF
327 IF( igrade.EQ.1 ) THEN
328 ctemp = ctemp*dl( i )
329 ELSE IF( igrade.EQ.2 ) THEN
330 ctemp = ctemp*dr( j )
331 ELSE IF( igrade.EQ.3 ) THEN
332 ctemp = ctemp*dl( i )*dr( j )
333 ELSE IF( igrade.EQ.4 .AND. i.NE.j ) THEN
334 ctemp = ctemp*dl( i ) / dl( j )
335 ELSE IF( igrade.EQ.5 ) THEN
336 ctemp = ctemp*dl( i )*conjg( dl( j ) )
337 ELSE IF( igrade.EQ.6 ) THEN
338 ctemp = ctemp*dl( i )*dl( j )
339 END IF
340 clatm3 = ctemp
341 RETURN
342*
343* End of CLATM3
344*
345 END
complex function clatm3(M, N, I, J, ISUB, JSUB, KL, KU, IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE)
CLATM3
Definition: clatm3.f:229
complex function clarnd(IDIST, ISEED)
CLARND
Definition: clarnd.f:75
real function slaran(ISEED)
SLARAN
Definition: slaran.f:67