LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ clatm2()

 complex function clatm2 ( integer m, integer n, integer i, integer j, integer kl, integer ku, integer idist, integer, dimension( 4 ) iseed, complex, dimension( * ) d, integer igrade, complex, dimension( * ) dl, complex, dimension( * ) dr, integer ipvtng, integer, dimension( * ) iwork, real sparse )

CLATM2

Purpose:
```    CLATM2 returns the (I,J) entry of a random matrix of dimension
(M, N) described by the other parameters. It 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 CLATM2 differs from CLATM3 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

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.```
Parameters
 [in] M ``` M is INTEGER Number of rows of matrix. Not modified.``` [in] N ``` N is INTEGER Number of columns of matrix. Not modified.``` [in] I ``` I is INTEGER Row of entry to be returned. Not modified.``` [in] J ``` J is INTEGER Column of entry to be returned. Not modified.``` [in] KL ``` KL is INTEGER Lower bandwidth. Not modified.``` [in] KU ``` KU is INTEGER Upper bandwidth. Not modified.``` [in] IDIST ``` IDIST is 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.``` [in,out] ISEED ``` ISEED is INTEGER array of dimension ( 4 ) Seed for random number generator. Changed on exit.``` [in] D ``` D is COMPLEX array of dimension ( MIN( I , J ) ) Diagonal entries of matrix. Not modified.``` [in] IGRADE ``` IGRADE is 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.``` [in] DL ``` DL is COMPLEX array ( I or J, as appropriate ) Left scale factors for grading matrix. Not modified.``` [in] DR ``` DR is COMPLEX array ( I or J, as appropriate ) Right scale factors for grading matrix. Not modified.``` [in] IPVTNG ``` IPVTNG is 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.``` [out] IWORK ``` IWORK is 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 CLATM3. Not modified.``` [in] SPARSE ``` SPARSE is REAL Value between 0. and 1. On entry specifies the sparsity of the matrix if sparse matrix 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.```

Definition at line 210 of file clatm2.f.

212*
213* -- LAPACK auxiliary routine --
214* -- LAPACK is a software package provided by Univ. of Tennessee, --
215* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
216*
217* .. Scalar Arguments ..
218*
219 INTEGER I, IDIST, IGRADE, IPVTNG, J, KL, KU, M, N
220 REAL SPARSE
221* ..
222*
223* .. Array Arguments ..
224*
225 INTEGER ISEED( 4 ), IWORK( * )
226 COMPLEX D( * ), DL( * ), DR( * )
227* ..
228*
229* =====================================================================
230*
231* .. Parameters ..
232*
233 COMPLEX CZERO
234 parameter( czero = ( 0.0e0, 0.0e0 ) )
235 REAL ZERO
236 parameter( zero = 0.0e0 )
237* ..
238*
239* .. Local Scalars ..
240*
241 INTEGER ISUB, JSUB
242 COMPLEX CTEMP
243* ..
244*
245* .. External Functions ..
246*
247 REAL SLARAN
248 COMPLEX CLARND
249 EXTERNAL slaran, clarnd
250* ..
251*
252* .. Intrinsic Functions ..
253*
254 INTRINSIC conjg
255* ..
256*
257*-----------------------------------------------------------------------
258*
259* .. Executable Statements ..
260*
261*
262* Check for I and J in range
263*
264 IF( i.LT.1 .OR. i.GT.m .OR. j.LT.1 .OR. j.GT.n ) THEN
265 clatm2 = czero
266 RETURN
267 END IF
268*
269* Check for banding
270*
271 IF( j.GT.i+ku .OR. j.LT.i-kl ) THEN
272 clatm2 = czero
273 RETURN
274 END IF
275*
276* Check for sparsity
277*
278 IF( sparse.GT.zero ) THEN
279 IF( slaran( iseed ).LT.sparse ) THEN
280 clatm2 = czero
281 RETURN
282 END IF
283 END IF
284*
285* Compute subscripts depending on IPVTNG
286*
287 IF( ipvtng.EQ.0 ) THEN
288 isub = i
289 jsub = j
290 ELSE IF( ipvtng.EQ.1 ) THEN
291 isub = iwork( i )
292 jsub = j
293 ELSE IF( ipvtng.EQ.2 ) THEN
294 isub = i
295 jsub = iwork( j )
296 ELSE IF( ipvtng.EQ.3 ) THEN
297 isub = iwork( i )
298 jsub = iwork( j )
299 END IF
300*
302*
303 IF( isub.EQ.jsub ) THEN
304 ctemp = d( isub )
305 ELSE
306 ctemp = clarnd( idist, iseed )
307 END IF
309 ctemp = ctemp*dl( isub )
310 ELSE IF( igrade.EQ.2 ) THEN
311 ctemp = ctemp*dr( jsub )
312 ELSE IF( igrade.EQ.3 ) THEN
313 ctemp = ctemp*dl( isub )*dr( jsub )
314 ELSE IF( igrade.EQ.4 .AND. isub.NE.jsub ) THEN
315 ctemp = ctemp*dl( isub ) / dl( jsub )
316 ELSE IF( igrade.EQ.5 ) THEN
317 ctemp = ctemp*dl( isub )*conjg( dl( jsub ) )
318 ELSE IF( igrade.EQ.6 ) THEN
319 ctemp = ctemp*dl( isub )*dl( jsub )
320 END IF
321 clatm2 = ctemp
322 RETURN
323*
324* End of CLATM2
325*
complex function clarnd(idist, iseed)
CLARND
Definition clarnd.f:75
complex function clatm2(m, n, i, j, kl, ku, idist, iseed, d, igrade, dl, dr, ipvtng, iwork, sparse)
CLATM2
Definition clatm2.f:212
real function slaran(iseed)
SLARAN
Definition slaran.f:67
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