LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ 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  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*
clarnd
complex function clarnd(idist, iseed)
CLARND
Definition clarnd.f:75
claset
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:104
slaran
real function slaran(iseed)
SLARAN
Definition slaran.f:67
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