LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ clatm2()

complex function clatm2 ( integer  M,
integer  N,
integer  I,
integer  J,
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 
)

CLATM2

Purpose:
    CLATM2 returns the (I,J) entry of a random matrix of dimension
    (M, N) described by the other parameters. It 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 CLATM2 differs from CLATM3 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

    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 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.
[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 CLATM3. Not modified.
[in]SPARSE
          SPARSE is REAL
           Value 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 214 of file clatm2.f.

214 *
215 * -- LAPACK auxiliary routine (version 3.7.0) --
216 * -- LAPACK is a software package provided by Univ. of Tennessee, --
217 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
218 * June 2016
219 *
220 * .. Scalar Arguments ..
221 *
222  INTEGER i, idist, igrade, ipvtng, j, kl, ku, m, n
223  REAL sparse
224 * ..
225 *
226 * .. Array Arguments ..
227 *
228  INTEGER iseed( 4 ), iwork( * )
229  COMPLEX d( * ), dl( * ), dr( * )
230 * ..
231 *
232 * =====================================================================
233 *
234 * .. Parameters ..
235 *
236  COMPLEX czero
237  parameter( czero = ( 0.0e0, 0.0e0 ) )
238  REAL zero
239  parameter( zero = 0.0e0 )
240 * ..
241 *
242 * .. Local Scalars ..
243 *
244  INTEGER isub, jsub
245  COMPLEX ctemp
246 * ..
247 *
248 * .. External Functions ..
249 *
250  REAL slaran
251  COMPLEX clarnd
252  EXTERNAL slaran, clarnd
253 * ..
254 *
255 * .. Intrinsic Functions ..
256 *
257  INTRINSIC conjg
258 * ..
259 *
260 *-----------------------------------------------------------------------
261 *
262 * .. Executable Statements ..
263 *
264 *
265 * Check for I and J in range
266 *
267  IF( i.LT.1 .OR. i.GT.m .OR. j.LT.1 .OR. j.GT.n ) THEN
268  clatm2 = czero
269  RETURN
270  END IF
271 *
272 * Check for banding
273 *
274  IF( j.GT.i+ku .OR. j.LT.i-kl ) THEN
275  clatm2 = czero
276  RETURN
277  END IF
278 *
279 * Check for sparsity
280 *
281  IF( sparse.GT.zero ) THEN
282  IF( slaran( iseed ).LT.sparse ) THEN
283  clatm2 = czero
284  RETURN
285  END IF
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 * Compute entry and grade it according to IGRADE
305 *
306  IF( isub.EQ.jsub ) THEN
307  ctemp = d( isub )
308  ELSE
309  ctemp = clarnd( idist, iseed )
310  END IF
311  IF( igrade.EQ.1 ) THEN
312  ctemp = ctemp*dl( isub )
313  ELSE IF( igrade.EQ.2 ) THEN
314  ctemp = ctemp*dr( jsub )
315  ELSE IF( igrade.EQ.3 ) THEN
316  ctemp = ctemp*dl( isub )*dr( jsub )
317  ELSE IF( igrade.EQ.4 .AND. isub.NE.jsub ) THEN
318  ctemp = ctemp*dl( isub ) / dl( jsub )
319  ELSE IF( igrade.EQ.5 ) THEN
320  ctemp = ctemp*dl( isub )*conjg( dl( jsub ) )
321  ELSE IF( igrade.EQ.6 ) THEN
322  ctemp = ctemp*dl( isub )*dl( jsub )
323  END IF
324  clatm2 = ctemp
325  RETURN
326 *
327 * End of CLATM2
328 *
complex function clarnd(IDIST, ISEED)
CLARND
Definition: clarnd.f:77
complex function clatm2(M, N, I, J, KL, KU, IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE)
CLATM2
Definition: clatm2.f:214
real function slaran(ISEED)
SLARAN
Definition: slaran.f:69