 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ dlatm3()

 double precision function dlatm3 ( integer M, integer N, integer I, integer J, integer ISUB, integer JSUB, 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 )

DLATM3

Purpose:
```    DLATM3 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. DLATM3 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 DLATM3 differs from SLATM2 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
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 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.``` [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 DLATM2. 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 223 of file dlatm3.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  DOUBLE PRECISION SPARSE
236 * ..
237 *
238 * .. Array Arguments ..
239 *
240  INTEGER ISEED( 4 ), IWORK( * )
241  DOUBLE PRECISION D( * ), DL( * ), DR( * )
242 * ..
243 *
244 * =====================================================================
245 *
246 * .. Parameters ..
247 *
248  DOUBLE PRECISION ZERO
249  parameter( zero = 0.0d0 )
250 * ..
251 *
252 * .. Local Scalars ..
253 *
254  DOUBLE PRECISION TEMP
255 * ..
256 *
257 * .. External Functions ..
258 *
259  DOUBLE PRECISION DLARAN, DLARND
260  EXTERNAL dlaran, dlarnd
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  dlatm3 = 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  dlatm3 = zero
297  RETURN
298  END IF
299 *
300 * Check for sparsity
301 *
302  IF( sparse.GT.zero ) THEN
303  IF( dlaran( iseed ).LT.sparse ) THEN
304  dlatm3 = zero
305  RETURN
306  END IF
307  END IF
308 *
310 *
311  IF( i.EQ.j ) THEN
312  temp = d( i )
313  ELSE
314  temp = dlarnd( idist, iseed )
315  END IF
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  dlatm3 = temp
328  RETURN
329 *
330 * End of DLATM3
331 *
double precision function dlaran(ISEED)
DLARAN
Definition: dlaran.f:67
double precision function dlatm3(M, N, I, J, ISUB, JSUB, KL, KU, IDIST, ISEED, D, IGRADE, DL, DR, IPVTNG, IWORK, SPARSE)
DLATM3
Definition: dlatm3.f:226
double precision function dlarnd(IDIST, ISEED)
DLARND
Definition: dlarnd.f:73
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