 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dlatm2()

 double precision function dlatm2 ( integer M, integer N, integer I, integer J, integer KL, integer KU, integer IDIST, integer, dimension( 4 ) ISEED, double precision, dimension( * ) D, integer IGRADE, double precision, dimension( * ) DL, double precision, dimension( * ) DR, integer IPVTNG, integer, dimension( * ) IWORK, double precision SPARSE )

DLATM2

Purpose:
```    DLATM2 returns the (I,J) entry of a random matrix of dimension
(M, N) described by the other parameters. It is called by the
DLATMR 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 DLATMR which has already checked the parameters.

Use of DLATM2 differs from SLATM3 in the order in which the random
number generator is called to fill in random matrix entries.
With DLATM2, the generator is called to fill in the pivoted matrix
columnwise. With DLATM3, the generator is called to fill in the
matrix columnwise, after which it is pivoted. Thus, DLATM3 can
be used to construct random matrices which differ only in their
order of rows and/or columns. DLATM2 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 DOUBLE PRECISION 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 DOUBLE PRECISION array ( I or J, as appropriate ) Left scale factors for grading matrix. Not modified.``` [in] DR ``` DR is DOUBLE PRECISION 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 DLATM3. Not modified.``` [in] SPARSE ``` SPARSE is DOUBLE PRECISION 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 dlatm2.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 DOUBLE PRECISION SPARSE
217* ..
218*
219* .. Array Arguments ..
220*
221 INTEGER ISEED( 4 ), IWORK( * )
222 DOUBLE PRECISION D( * ), DL( * ), DR( * )
223* ..
224*
225* =====================================================================
226*
227* .. Parameters ..
228*
229 DOUBLE PRECISION ZERO
230 parameter( zero = 0.0d0 )
231* ..
232*
233* .. Local Scalars ..
234*
235 INTEGER ISUB, JSUB
236 DOUBLE PRECISION TEMP
237* ..
238*
239* .. External Functions ..
240*
241 DOUBLE PRECISION DLARAN, DLARND
242 EXTERNAL dlaran, dlarnd
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 dlatm2 = 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 dlatm2 = zero
261 RETURN
262 END IF
263*
264* Check for sparsity
265*
266 IF( sparse.GT.zero ) THEN
267 IF( dlaran( iseed ).LT.sparse ) THEN
268 dlatm2 = 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 = dlarnd( 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 dlatm2 = temp
308 RETURN
309*
310* End of DLATM2
311*
double precision function dlaran(ISEED)
DLARAN
Definition: dlaran.f:67
double precision function dlarnd(IDIST, ISEED)
DLARND
Definition: dlarnd.f:73
double precision function dlatm2(M, N, I, J, KL, KU, IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE)
DLATM2
Definition: dlatm2.f:208
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