LAPACK  3.10.0
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 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 210 of file clatm2.f.

212 *
213 * -- LAPACK auxiliary routine --
214 * -- LAPACK is a software package provided by Univ. of Tennessee, --
215 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
216 *
217 * .. Scalar Arguments ..
218 *
219  INTEGER I, IDIST, IGRADE, IPVTNG, J, KL, KU, M, N
220  REAL SPARSE
221 * ..
222 *
223 * .. Array Arguments ..
224 *
225  INTEGER ISEED( 4 ), IWORK( * )
226  COMPLEX D( * ), DL( * ), DR( * )
227 * ..
228 *
229 * =====================================================================
230 *
231 * .. Parameters ..
232 *
233  COMPLEX CZERO
234  parameter( czero = ( 0.0e0, 0.0e0 ) )
235  REAL ZERO
236  parameter( zero = 0.0e0 )
237 * ..
238 *
239 * .. Local Scalars ..
240 *
241  INTEGER ISUB, JSUB
242  COMPLEX CTEMP
243 * ..
244 *
245 * .. External Functions ..
246 *
247  REAL SLARAN
248  COMPLEX CLARND
249  EXTERNAL slaran, clarnd
250 * ..
251 *
252 * .. Intrinsic Functions ..
253 *
254  INTRINSIC conjg
255 * ..
256 *
257 *-----------------------------------------------------------------------
258 *
259 * .. Executable Statements ..
260 *
261 *
262 * Check for I and J in range
263 *
264  IF( i.LT.1 .OR. i.GT.m .OR. j.LT.1 .OR. j.GT.n ) THEN
265  clatm2 = czero
266  RETURN
267  END IF
268 *
269 * Check for banding
270 *
271  IF( j.GT.i+ku .OR. j.LT.i-kl ) THEN
272  clatm2 = czero
273  RETURN
274  END IF
275 *
276 * Check for sparsity
277 *
278  IF( sparse.GT.zero ) THEN
279  IF( slaran( iseed ).LT.sparse ) THEN
280  clatm2 = czero
281  RETURN
282  END IF
283  END IF
284 *
285 * Compute subscripts depending on IPVTNG
286 *
287  IF( ipvtng.EQ.0 ) THEN
288  isub = i
289  jsub = j
290  ELSE IF( ipvtng.EQ.1 ) THEN
291  isub = iwork( i )
292  jsub = j
293  ELSE IF( ipvtng.EQ.2 ) THEN
294  isub = i
295  jsub = iwork( j )
296  ELSE IF( ipvtng.EQ.3 ) THEN
297  isub = iwork( i )
298  jsub = iwork( j )
299  END IF
300 *
301 * Compute entry and grade it according to IGRADE
302 *
303  IF( isub.EQ.jsub ) THEN
304  ctemp = d( isub )
305  ELSE
306  ctemp = clarnd( idist, iseed )
307  END IF
308  IF( igrade.EQ.1 ) THEN
309  ctemp = ctemp*dl( isub )
310  ELSE IF( igrade.EQ.2 ) THEN
311  ctemp = ctemp*dr( jsub )
312  ELSE IF( igrade.EQ.3 ) THEN
313  ctemp = ctemp*dl( isub )*dr( jsub )
314  ELSE IF( igrade.EQ.4 .AND. isub.NE.jsub ) THEN
315  ctemp = ctemp*dl( isub ) / dl( jsub )
316  ELSE IF( igrade.EQ.5 ) THEN
317  ctemp = ctemp*dl( isub )*conjg( dl( jsub ) )
318  ELSE IF( igrade.EQ.6 ) THEN
319  ctemp = ctemp*dl( isub )*dl( jsub )
320  END IF
321  clatm2 = ctemp
322  RETURN
323 *
324 * End of CLATM2
325 *
complex function clatm2(M, N, I, J, KL, KU, IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE)
CLATM2
Definition: clatm2.f:212
complex function clarnd(IDIST, ISEED)
CLARND
Definition: clarnd.f:75
real function slaran(ISEED)
SLARAN
Definition: slaran.f:67
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