LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ slatm2()

real function slatm2 ( integer  m,
integer  n,
integer  i,
integer  j,
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 
)

SLATM2

Purpose:
    SLATM2 returns the (I,J) entry of a random matrix of dimension
    (M, N) described by the other parameters. It 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 SLATM2 differs from SLATM3 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

    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 => 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.
[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 SLATM3. 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 206 of file slatm2.f.

208*
209* -- LAPACK auxiliary routine --
210* -- LAPACK is a software package provided by Univ. of Tennessee, --
211* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
212*
213* .. Scalar Arguments ..
214*
215 INTEGER I, IDIST, IGRADE, IPVTNG, J, KL, KU, M, N
216 REAL SPARSE
217* ..
218*
219* .. Array Arguments ..
220*
221 INTEGER ISEED( 4 ), IWORK( * )
222 REAL D( * ), DL( * ), DR( * )
223* ..
224*
225* =====================================================================
226*
227* .. Parameters ..
228*
229 REAL ZERO
230 parameter( zero = 0.0e0 )
231* ..
232*
233* .. Local Scalars ..
234*
235 INTEGER ISUB, JSUB
236 REAL TEMP
237* ..
238*
239* .. External Functions ..
240*
241 REAL SLARAN, SLARND
242 EXTERNAL slaran, slarnd
243* ..
244*
245*-----------------------------------------------------------------------
246*
247* .. Executable Statements ..
248*
249*
250* Check for I and J in range
251*
252 IF( i.LT.1 .OR. i.GT.m .OR. j.LT.1 .OR. j.GT.n ) THEN
253 slatm2 = zero
254 RETURN
255 END IF
256*
257* Check for banding
258*
259 IF( j.GT.i+ku .OR. j.LT.i-kl ) THEN
260 slatm2 = zero
261 RETURN
262 END IF
263*
264* Check for sparsity
265*
266 IF( sparse.GT.zero ) THEN
267 IF( slaran( iseed ).LT.sparse ) THEN
268 slatm2 = zero
269 RETURN
270 END IF
271 END IF
272*
273* Compute subscripts depending on IPVTNG
274*
275 IF( ipvtng.EQ.0 ) THEN
276 isub = i
277 jsub = j
278 ELSE IF( ipvtng.EQ.1 ) THEN
279 isub = iwork( i )
280 jsub = j
281 ELSE IF( ipvtng.EQ.2 ) THEN
282 isub = i
283 jsub = iwork( j )
284 ELSE IF( ipvtng.EQ.3 ) THEN
285 isub = iwork( i )
286 jsub = iwork( j )
287 END IF
288*
289* Compute entry and grade it according to IGRADE
290*
291 IF( isub.EQ.jsub ) THEN
292 temp = d( isub )
293 ELSE
294 temp = slarnd( idist, iseed )
295 END IF
296 IF( igrade.EQ.1 ) THEN
297 temp = temp*dl( isub )
298 ELSE IF( igrade.EQ.2 ) THEN
299 temp = temp*dr( jsub )
300 ELSE IF( igrade.EQ.3 ) THEN
301 temp = temp*dl( isub )*dr( jsub )
302 ELSE IF( igrade.EQ.4 .AND. isub.NE.jsub ) THEN
303 temp = temp*dl( isub ) / dl( jsub )
304 ELSE IF( igrade.EQ.5 ) THEN
305 temp = temp*dl( isub )*dl( jsub )
306 END IF
307 slatm2 = temp
308 RETURN
309*
310* End of SLATM2
311*
slaran
real function slaran(iseed)
SLARAN
Definition slaran.f:67
slarnd
real function slarnd(idist, iseed)
SLARND
Definition slarnd.f:73
slatm2
real function slatm2(m, n, i, j, kl, ku, idist, iseed, d, igrade, dl, dr, ipvtng, iwork, sparse)
SLATM2
Definition slatm2.f:208
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