 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ 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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