LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches
slatm2.f
Go to the documentation of this file.
1*> \brief \b SLATM2
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8* Definition:
9* ===========
10*
11* REAL FUNCTION SLATM2( M, N, I, J, KL, KU, IDIST,
12* ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE )
13*
14* .. Scalar Arguments ..
15*
16* INTEGER I, IDIST, IGRADE, IPVTNG, J, KL, KU, M, N
17* REAL SPARSE
18* ..
19*
20* .. Array Arguments ..
21*
22* INTEGER ISEED( 4 ), IWORK( * )
23* REAL D( * ), DL( * ), DR( * )
24* ..
25*
26*
27*> \par Purpose:
28* =============
29*>
30*> \verbatim
31*>
32*> SLATM2 returns the (I,J) entry of a random matrix of dimension
33*> (M, N) described by the other parameters. It is called by the
34*> SLATMR routine in order to build random test matrices. No error
35*> checking on parameters is done, because this routine is called in
36*> a tight loop by SLATMR which has already checked the parameters.
37*>
38*> Use of SLATM2 differs from SLATM3 in the order in which the random
39*> number generator is called to fill in random matrix entries.
40*> With SLATM2, the generator is called to fill in the pivoted matrix
41*> columnwise. With SLATM3, the generator is called to fill in the
42*> matrix columnwise, after which it is pivoted. Thus, SLATM3 can
43*> be used to construct random matrices which differ only in their
44*> order of rows and/or columns. SLATM2 is used to construct band
45*> matrices while avoiding calling the random number generator for
46*> entries outside the band (and therefore generating random numbers
47*>
48*> The matrix whose (I,J) entry is returned is constructed as
49*> follows (this routine only computes one entry):
50*>
51*> If I is outside (1..M) or J is outside (1..N), return zero
52*> (this is convenient for generating matrices in band format).
53*>
54*> Generate a matrix A with random entries of distribution IDIST.
55*>
56*> Set the diagonal to D.
57*>
58*> Grade the matrix, if desired, from the left (by DL) and/or
59*> from the right (by DR or DL) as specified by IGRADE.
60*>
61*> Permute, if desired, the rows and/or columns as specified by
62*> IPVTNG and IWORK.
63*>
64*> Band the matrix to have lower bandwidth KL and upper
65*> bandwidth KU.
66*>
67*> Set random entries to zero as specified by SPARSE.
68*> \endverbatim
69*
70* Arguments:
71* ==========
72*
73*> \param[in] M
74*> \verbatim
75*> M is INTEGER
76*> Number of rows of matrix. Not modified.
77*> \endverbatim
78*>
79*> \param[in] N
80*> \verbatim
81*> N is INTEGER
82*> Number of columns of matrix. Not modified.
83*> \endverbatim
84*>
85*> \param[in] I
86*> \verbatim
87*> I is INTEGER
88*> Row of entry to be returned. Not modified.
89*> \endverbatim
90*>
91*> \param[in] J
92*> \verbatim
93*> J is INTEGER
94*> Column of entry to be returned. Not modified.
95*> \endverbatim
96*>
97*> \param[in] KL
98*> \verbatim
99*> KL is INTEGER
100*> Lower bandwidth. Not modified.
101*> \endverbatim
102*>
103*> \param[in] KU
104*> \verbatim
105*> KU is INTEGER
106*> Upper bandwidth. Not modified.
107*> \endverbatim
108*>
109*> \param[in] IDIST
110*> \verbatim
111*> IDIST is INTEGER
112*> On entry, IDIST specifies the type of distribution to be
113*> used to generate a random matrix .
114*> 1 => UNIFORM( 0, 1 )
115*> 2 => UNIFORM( -1, 1 )
116*> 3 => NORMAL( 0, 1 )
117*> Not modified.
118*> \endverbatim
119*>
120*> \param[in,out] ISEED
121*> \verbatim
122*> ISEED is INTEGER array of dimension ( 4 )
123*> Seed for random number generator.
124*> Changed on exit.
125*> \endverbatim
126*>
127*> \param[in] D
128*> \verbatim
129*> D is REAL array of dimension ( MIN( I , J ) )
130*> Diagonal entries of matrix. Not modified.
131*> \endverbatim
132*>
133*> \param[in] IGRADE
134*> \verbatim
135*> IGRADE is INTEGER
136*> Specifies grading of matrix as follows:
137*> 0 => no grading
138*> 1 => matrix premultiplied by diag( DL )
139*> 2 => matrix postmultiplied by diag( DR )
140*> 3 => matrix premultiplied by diag( DL ) and
141*> postmultiplied by diag( DR )
142*> 4 => matrix premultiplied by diag( DL ) and
143*> postmultiplied by inv( diag( DL ) )
144*> 5 => matrix premultiplied by diag( DL ) and
145*> postmultiplied by diag( DL )
146*> Not modified.
147*> \endverbatim
148*>
149*> \param[in] DL
150*> \verbatim
151*> DL is REAL array ( I or J, as appropriate )
152*> Left scale factors for grading matrix. Not modified.
153*> \endverbatim
154*>
155*> \param[in] DR
156*> \verbatim
157*> DR is REAL array ( I or J, as appropriate )
158*> Right scale factors for grading matrix. Not modified.
159*> \endverbatim
160*>
161*> \param[in] IPVTNG
162*> \verbatim
163*> IPVTNG is INTEGER
164*> On entry specifies pivoting permutations as follows:
165*> 0 => none.
166*> 1 => row pivoting.
167*> 2 => column pivoting.
168*> 3 => full pivoting, i.e., on both sides.
169*> Not modified.
170*> \endverbatim
171*>
172*> \param[out] IWORK
173*> \verbatim
174*> IWORK is INTEGER array ( I or J, as appropriate )
175*> This array specifies the permutation used. The
176*> row (or column) in position K was originally in
177*> position IWORK( K ).
178*> This differs from IWORK for SLATM3. Not modified.
179*> \endverbatim
180*>
181*> \param[in] SPARSE
182*> \verbatim
183*> SPARSE is REAL between 0. and 1.
184*> On entry specifies the sparsity of the matrix
185*> if sparse matrix is to be generated.
186*> SPARSE should lie between 0 and 1.
187*> A uniform ( 0, 1 ) random number x is generated and
188*> compared to SPARSE; if x is larger the matrix entry
189*> is unchanged and if x is smaller the entry is set
190*> to zero. Thus on the average a fraction SPARSE of the
191*> entries will be set to zero.
192*> Not modified.
193*> \endverbatim
194*
195* Authors:
196* ========
197*
198*> \author Univ. of Tennessee
199*> \author Univ. of California Berkeley
200*> \author Univ. of Colorado Denver
201*> \author NAG Ltd.
202*
203*> \ingroup real_matgen
204*
205* =====================================================================
206 REAL function slatm2( m, n, i, j, kl, ku, idist,
207 $ iseed, d, igrade, dl, dr, ipvtng, iwork, sparse )
208*
209* -- LAPACK auxiliary routine --
210* -- LAPACK is a software package provided by Univ. of Tennessee, --
211* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
212*
213* .. Scalar Arguments ..
214*
215 INTEGER i, idist, igrade, ipvtng, j, kl, ku, m, n
216 REAL sparse
217* ..
218*
219* .. Array Arguments ..
220*
221 INTEGER iseed( 4 ), iwork( * )
222 REAL d( * ), dl( * ), dr( * )
223* ..
224*
225* =====================================================================
226*
227* .. Parameters ..
228*
229 REAL zero
230 parameter( zero = 0.0e0 )
231* ..
232*
233* .. Local Scalars ..
234*
235 INTEGER isub, jsub
236 REAL temp
237* ..
238*
239* .. External Functions ..
240*
241 REAL slaran, slarnd
242 EXTERNAL slaran, slarnd
243* ..
244*
245*-----------------------------------------------------------------------
246*
247* .. Executable Statements ..
248*
249*
250* Check for I and J in range
251*
252 IF( i.LT.1 .OR. i.GT.m .OR. j.LT.1 .OR. j.GT.n ) THEN
253 slatm2 = zero
254 RETURN
255 END IF
256*
257* Check for banding
258*
259 IF( j.GT.i+ku .OR. j.LT.i-kl ) THEN
260 slatm2 = zero
261 RETURN
262 END IF
263*
264* Check for sparsity
265*
266 IF( sparse.GT.zero ) THEN
267 IF( slaran( iseed ).LT.sparse ) THEN
268 slatm2 = zero
269 RETURN
270 END IF
271 END IF
272*
273* Compute subscripts depending on IPVTNG
274*
275 IF( ipvtng.EQ.0 ) THEN
276 isub = i
277 jsub = j
278 ELSE IF( ipvtng.EQ.1 ) THEN
279 isub = iwork( i )
280 jsub = j
281 ELSE IF( ipvtng.EQ.2 ) THEN
282 isub = i
283 jsub = iwork( j )
284 ELSE IF( ipvtng.EQ.3 ) THEN
285 isub = iwork( i )
286 jsub = iwork( j )
287 END IF
288*
289* Compute entry and grade it according to IGRADE
290*
291 IF( isub.EQ.jsub ) THEN
292 temp = d( isub )
293 ELSE
294 temp = slarnd( idist, iseed )
295 END IF
296 IF( igrade.EQ.1 ) THEN
297 temp = temp*dl( isub )
298 ELSE IF( igrade.EQ.2 ) THEN
299 temp = temp*dr( jsub )
300 ELSE IF( igrade.EQ.3 ) THEN
301 temp = temp*dl( isub )*dr( jsub )
302 ELSE IF( igrade.EQ.4 .AND. isub.NE.jsub ) THEN
303 temp = temp*dl( isub ) / dl( jsub )
304 ELSE IF( igrade.EQ.5 ) THEN
305 temp = temp*dl( isub )*dl( jsub )
306 END IF
307 slatm2 = temp
308 RETURN
309*
310* End of SLATM2
311*
312 END
real function slaran(ISEED)
SLARAN
Definition: slaran.f:67
real function slatm2(M, N, I, J, KL, KU, IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE)
SLATM2
Definition: slatm2.f:208
real function slarnd(IDIST, ISEED)
SLARND
Definition: slarnd.f:73