LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches

◆ clatm4()

subroutine clatm4 ( integer  ITYPE,
integer  N,
integer  NZ1,
integer  NZ2,
logical  RSIGN,
real  AMAGN,
real  RCOND,
real  TRIANG,
integer  IDIST,
integer, dimension( 4 )  ISEED,
complex, dimension( lda, * )  A,
integer  LDA 
)

CLATM4

Purpose:
 CLATM4 generates basic square matrices, which may later be
 multiplied by others in order to produce test matrices.  It is
 intended mainly to be used to test the generalized eigenvalue
 routines.

 It first generates the diagonal and (possibly) subdiagonal,
 according to the value of ITYPE, NZ1, NZ2, RSIGN, AMAGN, and RCOND.
 It then fills in the upper triangle with random numbers, if TRIANG is
 non-zero.
Parameters
[in]ITYPE
          ITYPE is INTEGER
          The "type" of matrix on the diagonal and sub-diagonal.
          If ITYPE < 0, then type abs(ITYPE) is generated and then
             swapped end for end (A(I,J) := A'(N-J,N-I).)  See also
             the description of AMAGN and RSIGN.

          Special types:
          = 0:  the zero matrix.
          = 1:  the identity.
          = 2:  a transposed Jordan block.
          = 3:  If N is odd, then a k+1 x k+1 transposed Jordan block
                followed by a k x k identity block, where k=(N-1)/2.
                If N is even, then k=(N-2)/2, and a zero diagonal entry
                is tacked onto the end.

          Diagonal types.  The diagonal consists of NZ1 zeros, then
             k=N-NZ1-NZ2 nonzeros.  The subdiagonal is zero.  ITYPE
             specifies the nonzero diagonal entries as follows:
          = 4:  1, ..., k
          = 5:  1, RCOND, ..., RCOND
          = 6:  1, ..., 1, RCOND
          = 7:  1, a, a^2, ..., a^(k-1)=RCOND
          = 8:  1, 1-d, 1-2*d, ..., 1-(k-1)*d=RCOND
          = 9:  random numbers chosen from (RCOND,1)
          = 10: random numbers with distribution IDIST (see CLARND.)
[in]N
          N is INTEGER
          The order of the matrix.
[in]NZ1
          NZ1 is INTEGER
          If abs(ITYPE) > 3, then the first NZ1 diagonal entries will
          be zero.
[in]NZ2
          NZ2 is INTEGER
          If abs(ITYPE) > 3, then the last NZ2 diagonal entries will
          be zero.
[in]RSIGN
          RSIGN is LOGICAL
          = .TRUE.:  The diagonal and subdiagonal entries will be
                     multiplied by random numbers of magnitude 1.
          = .FALSE.: The diagonal and subdiagonal entries will be
                     left as they are (usually non-negative real.)
[in]AMAGN
          AMAGN is REAL
          The diagonal and subdiagonal entries will be multiplied by
          AMAGN.
[in]RCOND
          RCOND is REAL
          If abs(ITYPE) > 4, then the smallest diagonal entry will be
          RCOND.  RCOND must be between 0 and 1.
[in]TRIANG
          TRIANG is REAL
          The entries above the diagonal will be random numbers with
          magnitude bounded by TRIANG (i.e., random numbers multiplied
          by TRIANG.)
[in]IDIST
          IDIST is INTEGER
          On entry, DIST specifies the type of distribution to be used
          to generate a random matrix .
          = 1: real and imaginary parts each UNIFORM( 0, 1 )
          = 2: real and imaginary parts each UNIFORM( -1, 1 )
          = 3: real and imaginary parts each NORMAL( 0, 1 )
          = 4: complex number uniform in DISK( 0, 1 )
[in,out]ISEED
          ISEED is INTEGER array, dimension (4)
          On entry ISEED specifies the seed of the random number
          generator.  The values of ISEED are changed on exit, and can
          be used in the next call to CLATM4 to continue the same
          random number sequence.
          Note: ISEED(4) should be odd, for the random number generator
          used at present.
[out]A
          A is COMPLEX array, dimension (LDA, N)
          Array to be computed.
[in]LDA
          LDA is INTEGER
          Leading dimension of A.  Must be at least 1 and at least N.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 169 of file clatm4.f.

171*
172* -- LAPACK test routine --
173* -- LAPACK is a software package provided by Univ. of Tennessee, --
174* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175*
176* .. Scalar Arguments ..
177 LOGICAL RSIGN
178 INTEGER IDIST, ITYPE, LDA, N, NZ1, NZ2
179 REAL AMAGN, RCOND, TRIANG
180* ..
181* .. Array Arguments ..
182 INTEGER ISEED( 4 )
183 COMPLEX A( LDA, * )
184* ..
185*
186* =====================================================================
187*
188* .. Parameters ..
189 REAL ZERO, ONE
190 parameter( zero = 0.0e+0, one = 1.0e+0 )
191 COMPLEX CZERO, CONE
192 parameter( czero = ( 0.0e+0, 0.0e+0 ),
193 $ cone = ( 1.0e+0, 0.0e+0 ) )
194* ..
195* .. Local Scalars ..
196 INTEGER I, ISDB, ISDE, JC, JD, JR, K, KBEG, KEND, KLEN
197 REAL ALPHA
198 COMPLEX CTEMP
199* ..
200* .. External Functions ..
201 REAL SLARAN
202 COMPLEX CLARND
203 EXTERNAL slaran, clarnd
204* ..
205* .. External Subroutines ..
206 EXTERNAL claset
207* ..
208* .. Intrinsic Functions ..
209 INTRINSIC abs, cmplx, exp, log, max, min, mod, real
210* ..
211* .. Executable Statements ..
212*
213 IF( n.LE.0 )
214 $ RETURN
215 CALL claset( 'Full', n, n, czero, czero, a, lda )
216*
217* Insure a correct ISEED
218*
219 IF( mod( iseed( 4 ), 2 ).NE.1 )
220 $ iseed( 4 ) = iseed( 4 ) + 1
221*
222* Compute diagonal and subdiagonal according to ITYPE, NZ1, NZ2,
223* and RCOND
224*
225 IF( itype.NE.0 ) THEN
226 IF( abs( itype ).GE.4 ) THEN
227 kbeg = max( 1, min( n, nz1+1 ) )
228 kend = max( kbeg, min( n, n-nz2 ) )
229 klen = kend + 1 - kbeg
230 ELSE
231 kbeg = 1
232 kend = n
233 klen = n
234 END IF
235 isdb = 1
236 isde = 0
237 GO TO ( 10, 30, 50, 80, 100, 120, 140, 160,
238 $ 180, 200 )abs( itype )
239*
240* abs(ITYPE) = 1: Identity
241*
242 10 CONTINUE
243 DO 20 jd = 1, n
244 a( jd, jd ) = cone
245 20 CONTINUE
246 GO TO 220
247*
248* abs(ITYPE) = 2: Transposed Jordan block
249*
250 30 CONTINUE
251 DO 40 jd = 1, n - 1
252 a( jd+1, jd ) = cone
253 40 CONTINUE
254 isdb = 1
255 isde = n - 1
256 GO TO 220
257*
258* abs(ITYPE) = 3: Transposed Jordan block, followed by the
259* identity.
260*
261 50 CONTINUE
262 k = ( n-1 ) / 2
263 DO 60 jd = 1, k
264 a( jd+1, jd ) = cone
265 60 CONTINUE
266 isdb = 1
267 isde = k
268 DO 70 jd = k + 2, 2*k + 1
269 a( jd, jd ) = cone
270 70 CONTINUE
271 GO TO 220
272*
273* abs(ITYPE) = 4: 1,...,k
274*
275 80 CONTINUE
276 DO 90 jd = kbeg, kend
277 a( jd, jd ) = cmplx( jd-nz1 )
278 90 CONTINUE
279 GO TO 220
280*
281* abs(ITYPE) = 5: One large D value:
282*
283 100 CONTINUE
284 DO 110 jd = kbeg + 1, kend
285 a( jd, jd ) = cmplx( rcond )
286 110 CONTINUE
287 a( kbeg, kbeg ) = cone
288 GO TO 220
289*
290* abs(ITYPE) = 6: One small D value:
291*
292 120 CONTINUE
293 DO 130 jd = kbeg, kend - 1
294 a( jd, jd ) = cone
295 130 CONTINUE
296 a( kend, kend ) = cmplx( rcond )
297 GO TO 220
298*
299* abs(ITYPE) = 7: Exponentially distributed D values:
300*
301 140 CONTINUE
302 a( kbeg, kbeg ) = cone
303 IF( klen.GT.1 ) THEN
304 alpha = rcond**( one / real( klen-1 ) )
305 DO 150 i = 2, klen
306 a( nz1+i, nz1+i ) = cmplx( alpha**real( i-1 ) )
307 150 CONTINUE
308 END IF
309 GO TO 220
310*
311* abs(ITYPE) = 8: Arithmetically distributed D values:
312*
313 160 CONTINUE
314 a( kbeg, kbeg ) = cone
315 IF( klen.GT.1 ) THEN
316 alpha = ( one-rcond ) / real( klen-1 )
317 DO 170 i = 2, klen
318 a( nz1+i, nz1+i ) = cmplx( real( klen-i )*alpha+rcond )
319 170 CONTINUE
320 END IF
321 GO TO 220
322*
323* abs(ITYPE) = 9: Randomly distributed D values on ( RCOND, 1):
324*
325 180 CONTINUE
326 alpha = log( rcond )
327 DO 190 jd = kbeg, kend
328 a( jd, jd ) = exp( alpha*slaran( iseed ) )
329 190 CONTINUE
330 GO TO 220
331*
332* abs(ITYPE) = 10: Randomly distributed D values from DIST
333*
334 200 CONTINUE
335 DO 210 jd = kbeg, kend
336 a( jd, jd ) = clarnd( idist, iseed )
337 210 CONTINUE
338*
339 220 CONTINUE
340*
341* Scale by AMAGN
342*
343 DO 230 jd = kbeg, kend
344 a( jd, jd ) = amagn*real( a( jd, jd ) )
345 230 CONTINUE
346 DO 240 jd = isdb, isde
347 a( jd+1, jd ) = amagn*real( a( jd+1, jd ) )
348 240 CONTINUE
349*
350* If RSIGN = .TRUE., assign random signs to diagonal and
351* subdiagonal
352*
353 IF( rsign ) THEN
354 DO 250 jd = kbeg, kend
355 IF( real( a( jd, jd ) ).NE.zero ) THEN
356 ctemp = clarnd( 3, iseed )
357 ctemp = ctemp / abs( ctemp )
358 a( jd, jd ) = ctemp*real( a( jd, jd ) )
359 END IF
360 250 CONTINUE
361 DO 260 jd = isdb, isde
362 IF( real( a( jd+1, jd ) ).NE.zero ) THEN
363 ctemp = clarnd( 3, iseed )
364 ctemp = ctemp / abs( ctemp )
365 a( jd+1, jd ) = ctemp*real( a( jd+1, jd ) )
366 END IF
367 260 CONTINUE
368 END IF
369*
370* Reverse if ITYPE < 0
371*
372 IF( itype.LT.0 ) THEN
373 DO 270 jd = kbeg, ( kbeg+kend-1 ) / 2
374 ctemp = a( jd, jd )
375 a( jd, jd ) = a( kbeg+kend-jd, kbeg+kend-jd )
376 a( kbeg+kend-jd, kbeg+kend-jd ) = ctemp
377 270 CONTINUE
378 DO 280 jd = 1, ( n-1 ) / 2
379 ctemp = a( jd+1, jd )
380 a( jd+1, jd ) = a( n+1-jd, n-jd )
381 a( n+1-jd, n-jd ) = ctemp
382 280 CONTINUE
383 END IF
384*
385 END IF
386*
387* Fill in upper triangle
388*
389 IF( triang.NE.zero ) THEN
390 DO 300 jc = 2, n
391 DO 290 jr = 1, jc - 1
392 a( jr, jc ) = triang*clarnd( idist, iseed )
393 290 CONTINUE
394 300 CONTINUE
395 END IF
396*
397 RETURN
398*
399* End of CLATM4
400*
complex function clarnd(IDIST, ISEED)
CLARND
Definition: clarnd.f:75
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: claset.f:106
real function slaran(ISEED)
SLARAN
Definition: slaran.f:67
Here is the call graph for this function:
Here is the caller graph for this function: