 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ zlatm2()

 complex*16 function zlatm2 ( integer M, integer N, integer I, integer J, 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 )

ZLATM2

Purpose:
ZLATM2 returns the (I,J) entry of a random matrix of dimension
(M, N) described by the other parameters. It 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 ZLATM2 differs from CLATM3 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

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*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. [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 ZLATM3. 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 209 of file zlatm2.f.

211 *
212 * -- LAPACK auxiliary routine --
213 * -- LAPACK is a software package provided by Univ. of Tennessee, --
214 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
215 *
216 * .. Scalar Arguments ..
217 *
218  INTEGER I, IDIST, IGRADE, IPVTNG, J, KL, KU, M, N
219  DOUBLE PRECISION SPARSE
220 * ..
221 *
222 * .. Array Arguments ..
223 *
224  INTEGER ISEED( 4 ), IWORK( * )
225  COMPLEX*16 D( * ), DL( * ), DR( * )
226 * ..
227 *
228 * =====================================================================
229 *
230 * .. Parameters ..
231 *
232  COMPLEX*16 CZERO
233  parameter( czero = ( 0.0d0, 0.0d0 ) )
234  DOUBLE PRECISION ZERO
235  parameter( zero = 0.0d0 )
236 * ..
237 *
238 * .. Local Scalars ..
239 *
240  INTEGER ISUB, JSUB
241  COMPLEX*16 CTEMP
242 * ..
243 *
244 * .. External Functions ..
245 *
246  DOUBLE PRECISION DLARAN
247  COMPLEX*16 ZLARND
248  EXTERNAL dlaran, zlarnd
249 * ..
250 *
251 * .. Intrinsic Functions ..
252 *
253  INTRINSIC dconjg
254 * ..
255 *
256 *-----------------------------------------------------------------------
257 *
258 * .. Executable Statements ..
259 *
260 *
261 * Check for I and J in range
262 *
263  IF( i.LT.1 .OR. i.GT.m .OR. j.LT.1 .OR. j.GT.n ) THEN
264  zlatm2 = czero
265  RETURN
266  END IF
267 *
268 * Check for banding
269 *
270  IF( j.GT.i+ku .OR. j.LT.i-kl ) THEN
271  zlatm2 = czero
272  RETURN
273  END IF
274 *
275 * Check for sparsity
276 *
277  IF( sparse.GT.zero ) THEN
278  IF( dlaran( iseed ).LT.sparse ) THEN
279  zlatm2 = czero
280  RETURN
281  END IF
282  END IF
283 *
284 * Compute subscripts depending on IPVTNG
285 *
286  IF( ipvtng.EQ.0 ) THEN
287  isub = i
288  jsub = j
289  ELSE IF( ipvtng.EQ.1 ) THEN
290  isub = iwork( i )
291  jsub = j
292  ELSE IF( ipvtng.EQ.2 ) THEN
293  isub = i
294  jsub = iwork( j )
295  ELSE IF( ipvtng.EQ.3 ) THEN
296  isub = iwork( i )
297  jsub = iwork( j )
298  END IF
299 *
301 *
302  IF( isub.EQ.jsub ) THEN
303  ctemp = d( isub )
304  ELSE
305  ctemp = zlarnd( idist, iseed )
306  END IF
308  ctemp = ctemp*dl( isub )
309  ELSE IF( igrade.EQ.2 ) THEN
310  ctemp = ctemp*dr( jsub )
311  ELSE IF( igrade.EQ.3 ) THEN
312  ctemp = ctemp*dl( isub )*dr( jsub )
313  ELSE IF( igrade.EQ.4 .AND. isub.NE.jsub ) THEN
314  ctemp = ctemp*dl( isub ) / dl( jsub )
315  ELSE IF( igrade.EQ.5 ) THEN
316  ctemp = ctemp*dl( isub )*dconjg( dl( jsub ) )
317  ELSE IF( igrade.EQ.6 ) THEN
318  ctemp = ctemp*dl( isub )*dl( jsub )
319  END IF
320  zlatm2 = ctemp
321  RETURN
322 *
323 * End of ZLATM2
324 *
double precision function dlaran(ISEED)
DLARAN
Definition: dlaran.f:67
complex *16 function zlatm2(M, N, I, J, KL, KU, IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE)
ZLATM2
Definition: zlatm2.f:211
complex *16 function zlarnd(IDIST, ISEED)
ZLARND
Definition: zlarnd.f:75
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