 LAPACK  3.8.0 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 matix 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.```
Date
June 2016

Definition at line 231 of file zlatm3.f.

231 *
232 * -- LAPACK auxiliary routine (version 3.7.0) --
233 * -- LAPACK is a software package provided by Univ. of Tennessee, --
234 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
235 * June 2016
236 *
237 * .. Scalar Arguments ..
238 *
239  INTEGER i, idist, igrade, ipvtng, isub, j, jsub, kl,
240  \$ ku, m, n
241  DOUBLE PRECISION sparse
242 * ..
243 *
244 * .. Array Arguments ..
245 *
246  INTEGER iseed( 4 ), iwork( * )
247  COMPLEX*16 d( * ), dl( * ), dr( * )
248 * ..
249 *
250 * =====================================================================
251 *
252 * .. Parameters ..
253 *
254  DOUBLE PRECISION zero
255  parameter( zero = 0.0d0 )
256  COMPLEX*16 czero
257  parameter( czero = ( 0.0d0, 0.0d0 ) )
258 * ..
259 *
260 * .. Local Scalars ..
261 *
262  COMPLEX*16 ctemp
263 * ..
264 *
265 * .. External Functions ..
266 *
267  DOUBLE PRECISION dlaran
268  COMPLEX*16 zlarnd
269  EXTERNAL dlaran, zlarnd
270 * ..
271 *
272 * .. Intrinsic Functions ..
273 *
274  INTRINSIC dconjg
275 * ..
276 *
277 *-----------------------------------------------------------------------
278 *
279 * .. Executable Statements ..
280 *
281 *
282 * Check for I and J in range
283 *
284  IF( i.LT.1 .OR. i.GT.m .OR. j.LT.1 .OR. j.GT.n ) THEN
285  isub = i
286  jsub = j
287  zlatm3 = czero
288  RETURN
289  END IF
290 *
291 * Compute subscripts depending on IPVTNG
292 *
293  IF( ipvtng.EQ.0 ) THEN
294  isub = i
295  jsub = j
296  ELSE IF( ipvtng.EQ.1 ) THEN
297  isub = iwork( i )
298  jsub = j
299  ELSE IF( ipvtng.EQ.2 ) THEN
300  isub = i
301  jsub = iwork( j )
302  ELSE IF( ipvtng.EQ.3 ) THEN
303  isub = iwork( i )
304  jsub = iwork( j )
305  END IF
306 *
307 * Check for banding
308 *
309  IF( jsub.GT.isub+ku .OR. jsub.LT.isub-kl ) THEN
310  zlatm3 = czero
311  RETURN
312  END IF
313 *
314 * Check for sparsity
315 *
316  IF( sparse.GT.zero ) THEN
317  IF( dlaran( iseed ).LT.sparse ) THEN
318  zlatm3 = czero
319  RETURN
320  END IF
321  END IF
322 *
324 *
325  IF( i.EQ.j ) THEN
326  ctemp = d( i )
327  ELSE
328  ctemp = zlarnd( idist, iseed )
329  END IF
331  ctemp = ctemp*dl( i )
332  ELSE IF( igrade.EQ.2 ) THEN
333  ctemp = ctemp*dr( j )
334  ELSE IF( igrade.EQ.3 ) THEN
335  ctemp = ctemp*dl( i )*dr( j )
336  ELSE IF( igrade.EQ.4 .AND. i.NE.j ) THEN
337  ctemp = ctemp*dl( i ) / dl( j )
338  ELSE IF( igrade.EQ.5 ) THEN
339  ctemp = ctemp*dl( i )*dconjg( dl( j ) )
340  ELSE IF( igrade.EQ.6 ) THEN
341  ctemp = ctemp*dl( i )*dl( j )
342  END IF
343  zlatm3 = ctemp
344  RETURN
345 *
346 * End of ZLATM3
347 *
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:231
complex *16 function zlarnd(IDIST, ISEED)
ZLARND
Definition: zlarnd.f:77
double precision function dlaran(ISEED)
DLARAN
Definition: dlaran.f:69