 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zlatm3()

 complex*16 function zlatm3 ( integer M, integer N, integer I, integer J, integer ISUB, integer JSUB, integer KL, integer KU, integer IDIST, integer, dimension( 4 ) ISEED, complex*16, dimension( * ) D, integer IGRADE, complex*16, dimension( * ) DL, complex*16, dimension( * ) DR, integer IPVTNG, integer, dimension( * ) IWORK, double precision SPARSE )

ZLATM3

Purpose:
```    ZLATM3 returns the (ISUB,JSUB) entry of a random matrix of
dimension (M, N) described by the other parameters. (ISUB,JSUB)
is the final position of the (I,J) entry after pivoting
according to IPVTNG and IWORK. ZLATM3 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 ZLATM3 differs from CLATM2 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
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.```
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 unpivoted entry to be returned. Not modified.``` [in] J ``` J is INTEGER Column of unpivoted entry to be returned. Not modified.``` [in,out] ISUB ``` ISUB is INTEGER Row of pivoted entry to be returned. Changed on exit.``` [in,out] JSUB ``` JSUB is INTEGER Column of pivoted entry to be returned. Changed on exit.``` [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*16 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*16 array ( I or J, as appropriate ) Left scale factors for grading matrix. Not modified.``` [in] DR ``` DR is COMPLEX*16 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.``` [in] IWORK ``` IWORK is 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 ZLATM2. Not modified.``` [in] SPARSE ``` SPARSE is DOUBLE PRECISION 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 226 of file zlatm3.f.

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 DOUBLE PRECISION SPARSE
239* ..
240*
241* .. Array Arguments ..
242*
243 INTEGER ISEED( 4 ), IWORK( * )
244 COMPLEX*16 D( * ), DL( * ), DR( * )
245* ..
246*
247* =====================================================================
248*
249* .. Parameters ..
250*
251 DOUBLE PRECISION ZERO
252 parameter( zero = 0.0d0 )
253 COMPLEX*16 CZERO
254 parameter( czero = ( 0.0d0, 0.0d0 ) )
255* ..
256*
257* .. Local Scalars ..
258*
259 COMPLEX*16 CTEMP
260* ..
261*
262* .. External Functions ..
263*
264 DOUBLE PRECISION DLARAN
265 COMPLEX*16 ZLARND
266 EXTERNAL dlaran, zlarnd
267* ..
268*
269* .. Intrinsic Functions ..
270*
271 INTRINSIC dconjg
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 zlatm3 = 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 zlatm3 = czero
308 RETURN
309 END IF
310*
311* Check for sparsity
312*
313 IF( sparse.GT.zero ) THEN
314 IF( dlaran( iseed ).LT.sparse ) THEN
315 zlatm3 = czero
316 RETURN
317 END IF
318 END IF
319*
321*
322 IF( i.EQ.j ) THEN
323 ctemp = d( i )
324 ELSE
325 ctemp = zlarnd( idist, iseed )
326 END IF
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 )*dconjg( dl( j ) )
337 ELSE IF( igrade.EQ.6 ) THEN
338 ctemp = ctemp*dl( i )*dl( j )
339 END IF
340 zlatm3 = ctemp
341 RETURN
342*
343* End of ZLATM3
344*
double precision function dlaran(ISEED)
DLARAN
Definition: dlaran.f:67
complex *16 function zlatm3(M, N, I, J, ISUB, JSUB, KL, KU, IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE)
ZLATM3
Definition: zlatm3.f:229
complex *16 function zlarnd(IDIST, ISEED)
ZLARND
Definition: zlarnd.f:75
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