LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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 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.```
Date
June 2016

Definition at line 228 of file slatm3.f.

228 *
229 * -- LAPACK auxiliary routine (version 3.7.0) --
230 * -- LAPACK is a software package provided by Univ. of Tennessee, --
231 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
232 * June 2016
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  REAL d( * ), dl( * ), dr( * )
245 * ..
246 *
247 * =====================================================================
248 *
249 * .. Parameters ..
250 *
251  REAL zero
252  parameter( zero = 0.0e0 )
253 * ..
254 *
255 * .. Local Scalars ..
256 *
257  REAL temp
258 * ..
259 *
260 * .. External Functions ..
261 *
262  REAL slaran, slarnd
263  EXTERNAL slaran, slarnd
264 * ..
265 *
266 *-----------------------------------------------------------------------
267 *
268 * .. Executable Statements ..
269 *
270 *
271 * Check for I and J in range
272 *
273  IF( i.LT.1 .OR. i.GT.m .OR. j.LT.1 .OR. j.GT.n ) THEN
274  isub = i
275  jsub = j
276  slatm3 = zero
277  RETURN
278  END IF
279 *
280 * Compute subscripts depending on IPVTNG
281 *
282  IF( ipvtng.EQ.0 ) THEN
283  isub = i
284  jsub = j
285  ELSE IF( ipvtng.EQ.1 ) THEN
286  isub = iwork( i )
287  jsub = j
288  ELSE IF( ipvtng.EQ.2 ) THEN
289  isub = i
290  jsub = iwork( j )
291  ELSE IF( ipvtng.EQ.3 ) THEN
292  isub = iwork( i )
293  jsub = iwork( j )
294  END IF
295 *
296 * Check for banding
297 *
298  IF( jsub.GT.isub+ku .OR. jsub.LT.isub-kl ) THEN
299  slatm3 = zero
300  RETURN
301  END IF
302 *
303 * Check for sparsity
304 *
305  IF( sparse.GT.zero ) THEN
306  IF( slaran( iseed ).LT.sparse ) THEN
307  slatm3 = zero
308  RETURN
309  END IF
310  END IF
311 *
313 *
314  IF( i.EQ.j ) THEN
315  temp = d( i )
316  ELSE
317  temp = slarnd( idist, iseed )
318  END IF
320  temp = temp*dl( i )
321  ELSE IF( igrade.EQ.2 ) THEN
322  temp = temp*dr( j )
323  ELSE IF( igrade.EQ.3 ) THEN
324  temp = temp*dl( i )*dr( j )
325  ELSE IF( igrade.EQ.4 .AND. i.NE.j ) THEN
326  temp = temp*dl( i ) / dl( j )
327  ELSE IF( igrade.EQ.5 ) THEN
328  temp = temp*dl( i )*dl( j )
329  END IF
330  slatm3 = temp
331  RETURN
332 *
333 * End of SLATM3
334 *
real function slarnd(IDIST, ISEED)
SLARND
Definition: slarnd.f:75
real function slaran(ISEED)
SLARAN
Definition: slaran.f:69
real function slatm3(M, N, I, J, ISUB, JSUB, KL, KU, IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE)
SLATM3
Definition: slatm3.f:228
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