LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
slatm5.f
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1 *> \brief \b SLATM5
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE SLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD,
12 * E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA,
13 * QBLCKB )
14 *
15 * .. Scalar Arguments ..
16 * INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N,
17 * \$ PRTYPE, QBLCKA, QBLCKB
18 * REAL ALPHA
19 * ..
20 * .. Array Arguments ..
21 * REAL A( LDA, * ), B( LDB, * ), C( LDC, * ),
22 * \$ D( LDD, * ), E( LDE, * ), F( LDF, * ),
23 * \$ L( LDL, * ), R( LDR, * )
24 * ..
25 *
26 *
27 *> \par Purpose:
28 * =============
29 *>
30 *> \verbatim
31 *>
32 *> SLATM5 generates matrices involved in the Generalized Sylvester
33 *> equation:
34 *>
35 *> A * R - L * B = C
36 *> D * R - L * E = F
37 *>
38 *> They also satisfy (the diagonalization condition)
39 *>
40 *> [ I -L ] ( [ A -C ], [ D -F ] ) [ I R ] = ( [ A ], [ D ] )
41 *> [ I ] ( [ B ] [ E ] ) [ I ] ( [ B ] [ E ] )
42 *>
43 *> \endverbatim
44 *
45 * Arguments:
46 * ==========
47 *
48 *> \param[in] PRTYPE
49 *> \verbatim
50 *> PRTYPE is INTEGER
51 *> "Points" to a certain type of the matrices to generate
52 *> (see further details).
53 *> \endverbatim
54 *>
55 *> \param[in] M
56 *> \verbatim
57 *> M is INTEGER
58 *> Specifies the order of A and D and the number of rows in
59 *> C, F, R and L.
60 *> \endverbatim
61 *>
62 *> \param[in] N
63 *> \verbatim
64 *> N is INTEGER
65 *> Specifies the order of B and E and the number of columns in
66 *> C, F, R and L.
67 *> \endverbatim
68 *>
69 *> \param[out] A
70 *> \verbatim
71 *> A is REAL array, dimension (LDA, M).
72 *> On exit A M-by-M is initialized according to PRTYPE.
73 *> \endverbatim
74 *>
75 *> \param[in] LDA
76 *> \verbatim
77 *> LDA is INTEGER
78 *> The leading dimension of A.
79 *> \endverbatim
80 *>
81 *> \param[out] B
82 *> \verbatim
83 *> B is REAL array, dimension (LDB, N).
84 *> On exit B N-by-N is initialized according to PRTYPE.
85 *> \endverbatim
86 *>
87 *> \param[in] LDB
88 *> \verbatim
89 *> LDB is INTEGER
90 *> The leading dimension of B.
91 *> \endverbatim
92 *>
93 *> \param[out] C
94 *> \verbatim
95 *> C is REAL array, dimension (LDC, N).
96 *> On exit C M-by-N is initialized according to PRTYPE.
97 *> \endverbatim
98 *>
99 *> \param[in] LDC
100 *> \verbatim
101 *> LDC is INTEGER
102 *> The leading dimension of C.
103 *> \endverbatim
104 *>
105 *> \param[out] D
106 *> \verbatim
107 *> D is REAL array, dimension (LDD, M).
108 *> On exit D M-by-M is initialized according to PRTYPE.
109 *> \endverbatim
110 *>
111 *> \param[in] LDD
112 *> \verbatim
113 *> LDD is INTEGER
114 *> The leading dimension of D.
115 *> \endverbatim
116 *>
117 *> \param[out] E
118 *> \verbatim
119 *> E is REAL array, dimension (LDE, N).
120 *> On exit E N-by-N is initialized according to PRTYPE.
121 *> \endverbatim
122 *>
123 *> \param[in] LDE
124 *> \verbatim
125 *> LDE is INTEGER
126 *> The leading dimension of E.
127 *> \endverbatim
128 *>
129 *> \param[out] F
130 *> \verbatim
131 *> F is REAL array, dimension (LDF, N).
132 *> On exit F M-by-N is initialized according to PRTYPE.
133 *> \endverbatim
134 *>
135 *> \param[in] LDF
136 *> \verbatim
137 *> LDF is INTEGER
138 *> The leading dimension of F.
139 *> \endverbatim
140 *>
141 *> \param[out] R
142 *> \verbatim
143 *> R is REAL array, dimension (LDR, N).
144 *> On exit R M-by-N is initialized according to PRTYPE.
145 *> \endverbatim
146 *>
147 *> \param[in] LDR
148 *> \verbatim
149 *> LDR is INTEGER
150 *> The leading dimension of R.
151 *> \endverbatim
152 *>
153 *> \param[out] L
154 *> \verbatim
155 *> L is REAL array, dimension (LDL, N).
156 *> On exit L M-by-N is initialized according to PRTYPE.
157 *> \endverbatim
158 *>
159 *> \param[in] LDL
160 *> \verbatim
161 *> LDL is INTEGER
162 *> The leading dimension of L.
163 *> \endverbatim
164 *>
165 *> \param[in] ALPHA
166 *> \verbatim
167 *> ALPHA is REAL
168 *> Parameter used in generating PRTYPE = 1 and 5 matrices.
169 *> \endverbatim
170 *>
171 *> \param[in] QBLCKA
172 *> \verbatim
173 *> QBLCKA is INTEGER
174 *> When PRTYPE = 3, specifies the distance between 2-by-2
175 *> blocks on the diagonal in A. Otherwise, QBLCKA is not
176 *> referenced. QBLCKA > 1.
177 *> \endverbatim
178 *>
179 *> \param[in] QBLCKB
180 *> \verbatim
181 *> QBLCKB is INTEGER
182 *> When PRTYPE = 3, specifies the distance between 2-by-2
183 *> blocks on the diagonal in B. Otherwise, QBLCKB is not
184 *> referenced. QBLCKB > 1.
185 *> \endverbatim
186 *
187 * Authors:
188 * ========
189 *
190 *> \author Univ. of Tennessee
191 *> \author Univ. of California Berkeley
192 *> \author Univ. of Colorado Denver
193 *> \author NAG Ltd.
194 *
195 *> \ingroup real_matgen
196 *
197 *> \par Further Details:
198 * =====================
199 *>
200 *> \verbatim
201 *>
202 *> PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices
203 *>
204 *> A : if (i == j) then A(i, j) = 1.0
205 *> if (j == i + 1) then A(i, j) = -1.0
206 *> else A(i, j) = 0.0, i, j = 1...M
207 *>
208 *> B : if (i == j) then B(i, j) = 1.0 - ALPHA
209 *> if (j == i + 1) then B(i, j) = 1.0
210 *> else B(i, j) = 0.0, i, j = 1...N
211 *>
212 *> D : if (i == j) then D(i, j) = 1.0
213 *> else D(i, j) = 0.0, i, j = 1...M
214 *>
215 *> E : if (i == j) then E(i, j) = 1.0
216 *> else E(i, j) = 0.0, i, j = 1...N
217 *>
218 *> L = R are chosen from [-10...10],
219 *> which specifies the right hand sides (C, F).
220 *>
221 *> PRTYPE = 2 or 3: Triangular and/or quasi- triangular.
222 *>
223 *> A : if (i <= j) then A(i, j) = [-1...1]
224 *> else A(i, j) = 0.0, i, j = 1...M
225 *>
226 *> if (PRTYPE = 3) then
227 *> A(k + 1, k + 1) = A(k, k)
228 *> A(k + 1, k) = [-1...1]
229 *> sign(A(k, k + 1) = -(sin(A(k + 1, k))
230 *> k = 1, M - 1, QBLCKA
231 *>
232 *> B : if (i <= j) then B(i, j) = [-1...1]
233 *> else B(i, j) = 0.0, i, j = 1...N
234 *>
235 *> if (PRTYPE = 3) then
236 *> B(k + 1, k + 1) = B(k, k)
237 *> B(k + 1, k) = [-1...1]
238 *> sign(B(k, k + 1) = -(sign(B(k + 1, k))
239 *> k = 1, N - 1, QBLCKB
240 *>
241 *> D : if (i <= j) then D(i, j) = [-1...1].
242 *> else D(i, j) = 0.0, i, j = 1...M
243 *>
244 *>
245 *> E : if (i <= j) then D(i, j) = [-1...1]
246 *> else E(i, j) = 0.0, i, j = 1...N
247 *>
248 *> L, R are chosen from [-10...10],
249 *> which specifies the right hand sides (C, F).
250 *>
251 *> PRTYPE = 4 Full
252 *> A(i, j) = [-10...10]
253 *> D(i, j) = [-1...1] i,j = 1...M
254 *> B(i, j) = [-10...10]
255 *> E(i, j) = [-1...1] i,j = 1...N
256 *> R(i, j) = [-10...10]
257 *> L(i, j) = [-1...1] i = 1..M ,j = 1...N
258 *>
259 *> L, R specifies the right hand sides (C, F).
260 *>
261 *> PRTYPE = 5 special case common and/or close eigs.
262 *> \endverbatim
263 *>
264 * =====================================================================
265  SUBROUTINE slatm5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD,
266  \$ E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA,
267  \$ QBLCKB )
268 *
269 * -- LAPACK computational routine --
270 * -- LAPACK is a software package provided by Univ. of Tennessee, --
271 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
272 *
273 * .. Scalar Arguments ..
274  INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N,
275  \$ PRTYPE, QBLCKA, QBLCKB
276  REAL ALPHA
277 * ..
278 * .. Array Arguments ..
279  REAL A( LDA, * ), B( LDB, * ), C( LDC, * ),
280  \$ D( LDD, * ), E( LDE, * ), F( LDF, * ),
281  \$ l( ldl, * ), r( ldr, * )
282 * ..
283 *
284 * =====================================================================
285 *
286 * .. Parameters ..
287  REAL ONE, ZERO, TWENTY, HALF, TWO
288  PARAMETER ( ONE = 1.0e+0, zero = 0.0e+0, twenty = 2.0e+1,
289  \$ half = 0.5e+0, two = 2.0e+0 )
290 * ..
291 * .. Local Scalars ..
292  INTEGER I, J, K
293  REAL IMEPS, REEPS
294 * ..
295 * .. Intrinsic Functions ..
296  INTRINSIC mod, real, sin
297 * ..
298 * .. External Subroutines ..
299  EXTERNAL sgemm
300 * ..
301 * .. Executable Statements ..
302 *
303  IF( prtype.EQ.1 ) THEN
304  DO 20 i = 1, m
305  DO 10 j = 1, m
306  IF( i.EQ.j ) THEN
307  a( i, j ) = one
308  d( i, j ) = one
309  ELSE IF( i.EQ.j-1 ) THEN
310  a( i, j ) = -one
311  d( i, j ) = zero
312  ELSE
313  a( i, j ) = zero
314  d( i, j ) = zero
315  END IF
316  10 CONTINUE
317  20 CONTINUE
318 *
319  DO 40 i = 1, n
320  DO 30 j = 1, n
321  IF( i.EQ.j ) THEN
322  b( i, j ) = one - alpha
323  e( i, j ) = one
324  ELSE IF( i.EQ.j-1 ) THEN
325  b( i, j ) = one
326  e( i, j ) = zero
327  ELSE
328  b( i, j ) = zero
329  e( i, j ) = zero
330  END IF
331  30 CONTINUE
332  40 CONTINUE
333 *
334  DO 60 i = 1, m
335  DO 50 j = 1, n
336  r( i, j ) = ( half-sin( real( i / j ) ) )*twenty
337  l( i, j ) = r( i, j )
338  50 CONTINUE
339  60 CONTINUE
340 *
341  ELSE IF( prtype.EQ.2 .OR. prtype.EQ.3 ) THEN
342  DO 80 i = 1, m
343  DO 70 j = 1, m
344  IF( i.LE.j ) THEN
345  a( i, j ) = ( half-sin( real( i ) ) )*two
346  d( i, j ) = ( half-sin( real( i*j ) ) )*two
347  ELSE
348  a( i, j ) = zero
349  d( i, j ) = zero
350  END IF
351  70 CONTINUE
352  80 CONTINUE
353 *
354  DO 100 i = 1, n
355  DO 90 j = 1, n
356  IF( i.LE.j ) THEN
357  b( i, j ) = ( half-sin( real( i+j ) ) )*two
358  e( i, j ) = ( half-sin( real( j ) ) )*two
359  ELSE
360  b( i, j ) = zero
361  e( i, j ) = zero
362  END IF
363  90 CONTINUE
364  100 CONTINUE
365 *
366  DO 120 i = 1, m
367  DO 110 j = 1, n
368  r( i, j ) = ( half-sin( real( i*j ) ) )*twenty
369  l( i, j ) = ( half-sin( real( i+j ) ) )*twenty
370  110 CONTINUE
371  120 CONTINUE
372 *
373  IF( prtype.EQ.3 ) THEN
374  IF( qblcka.LE.1 )
375  \$ qblcka = 2
376  DO 130 k = 1, m - 1, qblcka
377  a( k+1, k+1 ) = a( k, k )
378  a( k+1, k ) = -sin( a( k, k+1 ) )
379  130 CONTINUE
380 *
381  IF( qblckb.LE.1 )
382  \$ qblckb = 2
383  DO 140 k = 1, n - 1, qblckb
384  b( k+1, k+1 ) = b( k, k )
385  b( k+1, k ) = -sin( b( k, k+1 ) )
386  140 CONTINUE
387  END IF
388 *
389  ELSE IF( prtype.EQ.4 ) THEN
390  DO 160 i = 1, m
391  DO 150 j = 1, m
392  a( i, j ) = ( half-sin( real( i*j ) ) )*twenty
393  d( i, j ) = ( half-sin( real( i+j ) ) )*two
394  150 CONTINUE
395  160 CONTINUE
396 *
397  DO 180 i = 1, n
398  DO 170 j = 1, n
399  b( i, j ) = ( half-sin( real( i+j ) ) )*twenty
400  e( i, j ) = ( half-sin( real( i*j ) ) )*two
401  170 CONTINUE
402  180 CONTINUE
403 *
404  DO 200 i = 1, m
405  DO 190 j = 1, n
406  r( i, j ) = ( half-sin( real( j / i ) ) )*twenty
407  l( i, j ) = ( half-sin( real( i*j ) ) )*two
408  190 CONTINUE
409  200 CONTINUE
410 *
411  ELSE IF( prtype.GE.5 ) THEN
412  reeps = half*two*twenty / alpha
413  imeps = ( half-two ) / alpha
414  DO 220 i = 1, m
415  DO 210 j = 1, n
416  r( i, j ) = ( half-sin( real( i*j ) ) )*alpha / twenty
417  l( i, j ) = ( half-sin( real( i+j ) ) )*alpha / twenty
418  210 CONTINUE
419  220 CONTINUE
420 *
421  DO 230 i = 1, m
422  d( i, i ) = one
423  230 CONTINUE
424 *
425  DO 240 i = 1, m
426  IF( i.LE.4 ) THEN
427  a( i, i ) = one
428  IF( i.GT.2 )
429  \$ a( i, i ) = one + reeps
430  IF( mod( i, 2 ).NE.0 .AND. i.LT.m ) THEN
431  a( i, i+1 ) = imeps
432  ELSE IF( i.GT.1 ) THEN
433  a( i, i-1 ) = -imeps
434  END IF
435  ELSE IF( i.LE.8 ) THEN
436  IF( i.LE.6 ) THEN
437  a( i, i ) = reeps
438  ELSE
439  a( i, i ) = -reeps
440  END IF
441  IF( mod( i, 2 ).NE.0 .AND. i.LT.m ) THEN
442  a( i, i+1 ) = one
443  ELSE IF( i.GT.1 ) THEN
444  a( i, i-1 ) = -one
445  END IF
446  ELSE
447  a( i, i ) = one
448  IF( mod( i, 2 ).NE.0 .AND. i.LT.m ) THEN
449  a( i, i+1 ) = imeps*2
450  ELSE IF( i.GT.1 ) THEN
451  a( i, i-1 ) = -imeps*2
452  END IF
453  END IF
454  240 CONTINUE
455 *
456  DO 250 i = 1, n
457  e( i, i ) = one
458  IF( i.LE.4 ) THEN
459  b( i, i ) = -one
460  IF( i.GT.2 )
461  \$ b( i, i ) = one - reeps
462  IF( mod( i, 2 ).NE.0 .AND. i.LT.n ) THEN
463  b( i, i+1 ) = imeps
464  ELSE IF( i.GT.1 ) THEN
465  b( i, i-1 ) = -imeps
466  END IF
467  ELSE IF( i.LE.8 ) THEN
468  IF( i.LE.6 ) THEN
469  b( i, i ) = reeps
470  ELSE
471  b( i, i ) = -reeps
472  END IF
473  IF( mod( i, 2 ).NE.0 .AND. i.LT.n ) THEN
474  b( i, i+1 ) = one + imeps
475  ELSE IF( i.GT.1 ) THEN
476  b( i, i-1 ) = -one - imeps
477  END IF
478  ELSE
479  b( i, i ) = one - reeps
480  IF( mod( i, 2 ).NE.0 .AND. i.LT.n ) THEN
481  b( i, i+1 ) = imeps*2
482  ELSE IF( i.GT.1 ) THEN
483  b( i, i-1 ) = -imeps*2
484  END IF
485  END IF
486  250 CONTINUE
487  END IF
488 *
489 * Compute rhs (C, F)
490 *
491  CALL sgemm( 'N', 'N', m, n, m, one, a, lda, r, ldr, zero, c, ldc )
492  CALL sgemm( 'N', 'N', m, n, n, -one, l, ldl, b, ldb, one, c, ldc )
493  CALL sgemm( 'N', 'N', m, n, m, one, d, ldd, r, ldr, zero, f, ldf )
494  CALL sgemm( 'N', 'N', m, n, n, -one, l, ldl, e, lde, one, f, ldf )
495 *
496 * End of SLATM5
497 *
498  END
subroutine slatm5(PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD, E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA, QBLCKB)
SLATM5
Definition: slatm5.f:268
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187