LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ clatm3()

complex function clatm3 ( integer  M,
integer  N,
integer  I,
integer  J,
integer  ISUB,
integer  JSUB,
integer  KL,
integer  KU,
integer  IDIST,
integer, dimension( 4 )  ISEED,
complex, dimension( * )  D,
integer  IGRADE,
complex, dimension( * )  DL,
complex, dimension( * )  DR,
integer  IPVTNG,
integer, dimension( * )  IWORK,
real  SPARSE 
)

CLATM3

Purpose:
    CLATM3 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. CLATM3 is called by the
    CLATMR 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 CLATMR which has already checked the parameters.

    Use of CLATM3 differs from CLATM2 in the order in which the random
    number generator is called to fill in random matrix entries.
    With CLATM2, the generator is called to fill in the pivoted matrix
    columnwise. With CLATM3, the generator is called to fill in the
    matrix columnwise, after which it is pivoted. Thus, CLATM3 can
    be used to construct random matrices which differ only in their
    order of rows and/or columns. CLATM2 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 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 array ( I or J, as appropriate )
           Left scale factors for grading matrix.  Not modified.
[in]DR
          DR is COMPLEX 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 CLATM2. Not modified.
[in]SPARSE
          SPARSE is REAL 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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
June 2016

Definition at line 231 of file clatm3.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  REAL sparse
242 * ..
243 *
244 * .. Array Arguments ..
245 *
246  INTEGER iseed( 4 ), iwork( * )
247  COMPLEX d( * ), dl( * ), dr( * )
248 * ..
249 *
250 * =====================================================================
251 *
252 * .. Parameters ..
253 *
254  REAL zero
255  parameter( zero = 0.0e0 )
256  COMPLEX czero
257  parameter( czero = ( 0.0e0, 0.0e0 ) )
258 * ..
259 *
260 * .. Local Scalars ..
261 *
262  COMPLEX ctemp
263 * ..
264 *
265 * .. External Functions ..
266 *
267  REAL slaran
268  COMPLEX clarnd
269  EXTERNAL slaran, clarnd
270 * ..
271 *
272 * .. Intrinsic Functions ..
273 *
274  INTRINSIC conjg
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  clatm3 = 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  clatm3 = czero
311  RETURN
312  END IF
313 *
314 * Check for sparsity
315 *
316  IF( sparse.GT.zero ) THEN
317  IF( slaran( iseed ).LT.sparse ) THEN
318  clatm3 = czero
319  RETURN
320  END IF
321  END IF
322 *
323 * Compute entry and grade it according to IGRADE
324 *
325  IF( i.EQ.j ) THEN
326  ctemp = d( i )
327  ELSE
328  ctemp = clarnd( idist, iseed )
329  END IF
330  IF( igrade.EQ.1 ) THEN
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 )*conjg( dl( j ) )
340  ELSE IF( igrade.EQ.6 ) THEN
341  ctemp = ctemp*dl( i )*dl( j )
342  END IF
343  clatm3 = ctemp
344  RETURN
345 *
346 * End of CLATM3
347 *
complex function clarnd(IDIST, ISEED)
CLARND
Definition: clarnd.f:77
complex function clatm3(M, N, I, J, ISUB, JSUB, KL, KU, IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE)
CLATM3
Definition: clatm3.f:231
real function slaran(ISEED)
SLARAN
Definition: slaran.f:69