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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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 *
300 * Compute entry and grade it according to IGRADE
301 *
302  IF( isub.EQ.jsub ) THEN
303  ctemp = d( isub )
304  ELSE
305  ctemp = zlarnd( idist, iseed )
306  END IF
307  IF( igrade.EQ.1 ) THEN
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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