LAPACK  3.10.0
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 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 226 of file clatm3.f.

229 *
230 * -- LAPACK auxiliary routine --
231 * -- LAPACK is a software package provided by Univ. of Tennessee, --
232 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
233 *
234 * .. Scalar Arguments ..
235 *
236  INTEGER I, IDIST, IGRADE, IPVTNG, ISUB, J, JSUB, KL,
237  $ KU, M, N
238  REAL SPARSE
239 * ..
240 *
241 * .. Array Arguments ..
242 *
243  INTEGER ISEED( 4 ), IWORK( * )
244  COMPLEX D( * ), DL( * ), DR( * )
245 * ..
246 *
247 * =====================================================================
248 *
249 * .. Parameters ..
250 *
251  REAL ZERO
252  parameter( zero = 0.0e0 )
253  COMPLEX CZERO
254  parameter( czero = ( 0.0e0, 0.0e0 ) )
255 * ..
256 *
257 * .. Local Scalars ..
258 *
259  COMPLEX CTEMP
260 * ..
261 *
262 * .. External Functions ..
263 *
264  REAL SLARAN
265  COMPLEX CLARND
266  EXTERNAL slaran, clarnd
267 * ..
268 *
269 * .. Intrinsic Functions ..
270 *
271  INTRINSIC conjg
272 * ..
273 *
274 *-----------------------------------------------------------------------
275 *
276 * .. Executable Statements ..
277 *
278 *
279 * Check for I and J in range
280 *
281  IF( i.LT.1 .OR. i.GT.m .OR. j.LT.1 .OR. j.GT.n ) THEN
282  isub = i
283  jsub = j
284  clatm3 = czero
285  RETURN
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 * Check for banding
305 *
306  IF( jsub.GT.isub+ku .OR. jsub.LT.isub-kl ) THEN
307  clatm3 = czero
308  RETURN
309  END IF
310 *
311 * Check for sparsity
312 *
313  IF( sparse.GT.zero ) THEN
314  IF( slaran( iseed ).LT.sparse ) THEN
315  clatm3 = czero
316  RETURN
317  END IF
318  END IF
319 *
320 * Compute entry and grade it according to IGRADE
321 *
322  IF( i.EQ.j ) THEN
323  ctemp = d( i )
324  ELSE
325  ctemp = clarnd( idist, iseed )
326  END IF
327  IF( igrade.EQ.1 ) THEN
328  ctemp = ctemp*dl( i )
329  ELSE IF( igrade.EQ.2 ) THEN
330  ctemp = ctemp*dr( j )
331  ELSE IF( igrade.EQ.3 ) THEN
332  ctemp = ctemp*dl( i )*dr( j )
333  ELSE IF( igrade.EQ.4 .AND. i.NE.j ) THEN
334  ctemp = ctemp*dl( i ) / dl( j )
335  ELSE IF( igrade.EQ.5 ) THEN
336  ctemp = ctemp*dl( i )*conjg( dl( j ) )
337  ELSE IF( igrade.EQ.6 ) THEN
338  ctemp = ctemp*dl( i )*dl( j )
339  END IF
340  clatm3 = ctemp
341  RETURN
342 *
343 * End of CLATM3
344 *
complex function clatm3(M, N, I, J, ISUB, JSUB, KL, KU, IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE)
CLATM3
Definition: clatm3.f:229
complex function clarnd(IDIST, ISEED)
CLARND
Definition: clarnd.f:75
real function slaran(ISEED)
SLARAN
Definition: slaran.f:67
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