LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ slatm3()

real function slatm3 ( integer  m,
integer  n,
integer  i,
integer  j,
integer  isub,
integer  jsub,
integer  kl,
integer  ku,
integer  idist,
integer, dimension( 4 )  iseed,
real, dimension( * )  d,
integer  igrade,
real, dimension( * )  dl,
real, dimension( * )  dr,
integer  ipvtng,
integer, dimension( * )  iwork,
real  sparse 
)

SLATM3

Purpose:
    SLATM3 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. SLATM3 is called by the
    SLATMR 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 SLATMR which has already checked the parameters.

    Use of SLATM3 differs from SLATM2 in the order in which the random
    number generator is called to fill in random matrix entries.
    With SLATM2, the generator is called to fill in the pivoted matrix
    columnwise. With SLATM3, the generator is called to fill in the
    matrix columnwise, after which it is pivoted. Thus, SLATM3 can
    be used to construct random matrices which differ only in their
    order of rows and/or columns. SLATM2 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 => UNIFORM( 0, 1 )
           2 => UNIFORM( -1, 1 )
           3 => NORMAL( 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 REAL 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( DL )
           Not modified.
[in]DL
          DL is REAL array ( I or J, as appropriate )
           Left scale factors for grading matrix.  Not modified.
[in]DR
          DR is REAL 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 SLATM2. 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 223 of file slatm3.f.

226*
227* -- LAPACK auxiliary routine --
228* -- LAPACK is a software package provided by Univ. of Tennessee, --
229* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
230*
231* .. Scalar Arguments ..
232*
233 INTEGER I, IDIST, IGRADE, IPVTNG, ISUB, J, JSUB, KL,
234 $ KU, M, N
235 REAL SPARSE
236* ..
237*
238* .. Array Arguments ..
239*
240 INTEGER ISEED( 4 ), IWORK( * )
241 REAL D( * ), DL( * ), DR( * )
242* ..
243*
244* =====================================================================
245*
246* .. Parameters ..
247*
248 REAL ZERO
249 parameter( zero = 0.0e0 )
250* ..
251*
252* .. Local Scalars ..
253*
254 REAL TEMP
255* ..
256*
257* .. External Functions ..
258*
259 REAL SLARAN, SLARND
260 EXTERNAL slaran, slarnd
261* ..
262*
263*-----------------------------------------------------------------------
264*
265* .. Executable Statements ..
266*
267*
268* Check for I and J in range
269*
270 IF( i.LT.1 .OR. i.GT.m .OR. j.LT.1 .OR. j.GT.n ) THEN
271 isub = i
272 jsub = j
273 slatm3 = zero
274 RETURN
275 END IF
276*
277* Compute subscripts depending on IPVTNG
278*
279 IF( ipvtng.EQ.0 ) THEN
280 isub = i
281 jsub = j
282 ELSE IF( ipvtng.EQ.1 ) THEN
283 isub = iwork( i )
284 jsub = j
285 ELSE IF( ipvtng.EQ.2 ) THEN
286 isub = i
287 jsub = iwork( j )
288 ELSE IF( ipvtng.EQ.3 ) THEN
289 isub = iwork( i )
290 jsub = iwork( j )
291 END IF
292*
293* Check for banding
294*
295 IF( jsub.GT.isub+ku .OR. jsub.LT.isub-kl ) THEN
296 slatm3 = zero
297 RETURN
298 END IF
299*
300* Check for sparsity
301*
302 IF( sparse.GT.zero ) THEN
303 IF( slaran( iseed ).LT.sparse ) THEN
304 slatm3 = zero
305 RETURN
306 END IF
307 END IF
308*
309* Compute entry and grade it according to IGRADE
310*
311 IF( i.EQ.j ) THEN
312 temp = d( i )
313 ELSE
314 temp = slarnd( idist, iseed )
315 END IF
316 IF( igrade.EQ.1 ) THEN
317 temp = temp*dl( i )
318 ELSE IF( igrade.EQ.2 ) THEN
319 temp = temp*dr( j )
320 ELSE IF( igrade.EQ.3 ) THEN
321 temp = temp*dl( i )*dr( j )
322 ELSE IF( igrade.EQ.4 .AND. i.NE.j ) THEN
323 temp = temp*dl( i ) / dl( j )
324 ELSE IF( igrade.EQ.5 ) THEN
325 temp = temp*dl( i )*dl( j )
326 END IF
327 slatm3 = temp
328 RETURN
329*
330* End of SLATM3
331*
slaran
real function slaran(iseed)
SLARAN
Definition slaran.f:67
slarnd
real function slarnd(idist, iseed)
SLARND
Definition slarnd.f:73
slatm3
real function slatm3(m, n, i, j, isub, jsub, kl, ku, idist, iseed, d, igrade, dl, dr, ipvtng, iwork, sparse)
SLATM3
Definition slatm3.f:226
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