 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ 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.```

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 *
290 *
291  IF( isub.EQ.jsub ) THEN
292  temp = d( isub )
293  ELSE
294  temp = slarnd( idist, iseed )
295  END IF
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 *
real function slaran(ISEED)
SLARAN
Definition: slaran.f:67
real function slatm2(M, N, I, J, KL, KU, IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE)
SLATM2
Definition: slatm2.f:208
real function slarnd(IDIST, ISEED)
SLARND
Definition: slarnd.f:73
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