LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ clatm5()

subroutine clatm5 ( integer prtype,
integer m,
integer n,
complex, dimension( lda, * ) a,
integer lda,
complex, dimension( ldb, * ) b,
integer ldb,
complex, dimension( ldc, * ) c,
integer ldc,
complex, dimension( ldd, * ) d,
integer ldd,
complex, dimension( lde, * ) e,
integer lde,
complex, dimension( ldf, * ) f,
integer ldf,
complex, dimension( ldr, * ) r,
integer ldr,
complex, dimension( ldl, * ) l,
integer ldl,
real alpha,
integer qblcka,
integer qblckb )

CLATM5

Purpose:
!>
!> CLATM5 generates matrices involved in the Generalized Sylvester
!> equation:
!>
!>     A * R - L * B = C
!>     D * R - L * E = F
!>
!> They also satisfy (the diagonalization condition)
!>
!>  [ I -L ] ( [ A  -C ], [ D -F ] ) [ I  R ] = ( [ A    ], [ D    ] )
!>  [    I ] ( [     B ]  [    E ] ) [    I ]   ( [    B ]  [    E ] )
!>
!>
Parameters
[in]PRTYPE
!>          PRTYPE is INTEGER
!>           to a certain type of the matrices to generate
!>          (see further details).
!>
[in]M
!>          M is INTEGER
!>          Specifies the order of A and D and the number of rows in
!>          C, F,  R and L.
!>
[in]N
!>          N is INTEGER
!>          Specifies the order of B and E and the number of columns in
!>          C, F, R and L.
!>
[out]A
!>          A is COMPLEX array, dimension (LDA, M).
!>          On exit A M-by-M is initialized according to PRTYPE.
!>
[in]LDA
!>          LDA is INTEGER
!>          The leading dimension of A.
!>
[out]B
!>          B is COMPLEX array, dimension (LDB, N).
!>          On exit B N-by-N is initialized according to PRTYPE.
!>
[in]LDB
!>          LDB is INTEGER
!>          The leading dimension of B.
!>
[out]C
!>          C is COMPLEX array, dimension (LDC, N).
!>          On exit C M-by-N is initialized according to PRTYPE.
!>
[in]LDC
!>          LDC is INTEGER
!>          The leading dimension of C.
!>
[out]D
!>          D is COMPLEX array, dimension (LDD, M).
!>          On exit D M-by-M is initialized according to PRTYPE.
!>
[in]LDD
!>          LDD is INTEGER
!>          The leading dimension of D.
!>
[out]E
!>          E is COMPLEX array, dimension (LDE, N).
!>          On exit E N-by-N is initialized according to PRTYPE.
!>
[in]LDE
!>          LDE is INTEGER
!>          The leading dimension of E.
!>
[out]F
!>          F is COMPLEX array, dimension (LDF, N).
!>          On exit F M-by-N is initialized according to PRTYPE.
!>
[in]LDF
!>          LDF is INTEGER
!>          The leading dimension of F.
!>
[out]R
!>          R is COMPLEX array, dimension (LDR, N).
!>          On exit R M-by-N is initialized according to PRTYPE.
!>
[in]LDR
!>          LDR is INTEGER
!>          The leading dimension of R.
!>
[out]L
!>          L is COMPLEX array, dimension (LDL, N).
!>          On exit L M-by-N is initialized according to PRTYPE.
!>
[in]LDL
!>          LDL is INTEGER
!>          The leading dimension of L.
!>
[in]ALPHA
!>          ALPHA is REAL
!>          Parameter used in generating PRTYPE = 1 and 5 matrices.
!>
[in]QBLCKA
!>          QBLCKA is INTEGER
!>          When PRTYPE = 3, specifies the distance between 2-by-2
!>          blocks on the diagonal in A. Otherwise, QBLCKA is not
!>          referenced. QBLCKA > 1.
!>
[in]QBLCKB
!>          QBLCKB is INTEGER
!>          When PRTYPE = 3, specifies the distance between 2-by-2
!>          blocks on the diagonal in B. Otherwise, QBLCKB is not
!>          referenced. QBLCKB > 1.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!>
!>  PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices
!>
!>             A : if (i == j) then A(i, j) = 1.0
!>                 if (j == i + 1) then A(i, j) = -1.0
!>                 else A(i, j) = 0.0,            i, j = 1...M
!>
!>             B : if (i == j) then B(i, j) = 1.0 - ALPHA
!>                 if (j == i + 1) then B(i, j) = 1.0
!>                 else B(i, j) = 0.0,            i, j = 1...N
!>
!>             D : if (i == j) then D(i, j) = 1.0
!>                 else D(i, j) = 0.0,            i, j = 1...M
!>
!>             E : if (i == j) then E(i, j) = 1.0
!>                 else E(i, j) = 0.0,            i, j = 1...N
!>
!>             L =  R are chosen from [-10...10],
!>                  which specifies the right hand sides (C, F).
!>
!>  PRTYPE = 2 or 3: Triangular and/or quasi- triangular.
!>
!>             A : if (i <= j) then A(i, j) = [-1...1]
!>                 else A(i, j) = 0.0,             i, j = 1...M
!>
!>                 if (PRTYPE = 3) then
!>                    A(k + 1, k + 1) = A(k, k)
!>                    A(k + 1, k) = [-1...1]
!>                    sign(A(k, k + 1) = -(sin(A(k + 1, k))
!>                        k = 1, M - 1, QBLCKA
!>
!>             B : if (i <= j) then B(i, j) = [-1...1]
!>                 else B(i, j) = 0.0,            i, j = 1...N
!>
!>                 if (PRTYPE = 3) then
!>                    B(k + 1, k + 1) = B(k, k)
!>                    B(k + 1, k) = [-1...1]
!>                    sign(B(k, k + 1) = -(sign(B(k + 1, k))
!>                        k = 1, N - 1, QBLCKB
!>
!>             D : if (i <= j) then D(i, j) = [-1...1].
!>                 else D(i, j) = 0.0,            i, j = 1...M
!>
!>
!>             E : if (i <= j) then D(i, j) = [-1...1]
!>                 else E(i, j) = 0.0,            i, j = 1...N
!>
!>                 L, R are chosen from [-10...10],
!>                 which specifies the right hand sides (C, F).
!>
!>  PRTYPE = 4 Full
!>             A(i, j) = [-10...10]
!>             D(i, j) = [-1...1]    i,j = 1...M
!>             B(i, j) = [-10...10]
!>             E(i, j) = [-1...1]    i,j = 1...N
!>             R(i, j) = [-10...10]
!>             L(i, j) = [-1...1]    i = 1..M ,j = 1...N
!>
!>             L, R specifies the right hand sides (C, F).
!>
!>  PRTYPE = 5 special case common and/or close eigs.
!>

Definition at line 265 of file clatm5.f.

269*
270* -- LAPACK computational routine --
271* -- LAPACK is a software package provided by Univ. of Tennessee, --
272* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
273*
274* .. Scalar Arguments ..
275 INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N,
276 $ PRTYPE, QBLCKA, QBLCKB
277 REAL ALPHA
278* ..
279* .. Array Arguments ..
280 COMPLEX A( LDA, * ), B( LDB, * ), C( LDC, * ),
281 $ D( LDD, * ), E( LDE, * ), F( LDF, * ),
282 $ L( LDL, * ), R( LDR, * )
283* ..
284*
285* =====================================================================
286*
287* .. Parameters ..
288 COMPLEX ONE, TWO, ZERO, HALF, TWENTY
289 parameter( one = ( 1.0e+0, 0.0e+0 ),
290 $ two = ( 2.0e+0, 0.0e+0 ),
291 $ zero = ( 0.0e+0, 0.0e+0 ),
292 $ half = ( 0.5e+0, 0.0e+0 ),
293 $ twenty = ( 2.0e+1, 0.0e+0 ) )
294* ..
295* .. Local Scalars ..
296 INTEGER I, J, K
297 COMPLEX IMEPS, REEPS
298* ..
299* .. Intrinsic Functions ..
300 INTRINSIC cmplx, mod, sin
301* ..
302* .. External Subroutines ..
303 EXTERNAL cgemm
304* ..
305* .. Executable Statements ..
306*
307 IF( prtype.EQ.1 ) THEN
308 DO 20 i = 1, m
309 DO 10 j = 1, m
310 IF( i.EQ.j ) THEN
311 a( i, j ) = one
312 d( i, j ) = one
313 ELSE IF( i.EQ.j-1 ) THEN
314 a( i, j ) = -one
315 d( i, j ) = zero
316 ELSE
317 a( i, j ) = zero
318 d( i, j ) = zero
319 END IF
320 10 CONTINUE
321 20 CONTINUE
322*
323 DO 40 i = 1, n
324 DO 30 j = 1, n
325 IF( i.EQ.j ) THEN
326 b( i, j ) = one - alpha
327 e( i, j ) = one
328 ELSE IF( i.EQ.j-1 ) THEN
329 b( i, j ) = one
330 e( i, j ) = zero
331 ELSE
332 b( i, j ) = zero
333 e( i, j ) = zero
334 END IF
335 30 CONTINUE
336 40 CONTINUE
337*
338 DO 60 i = 1, m
339 DO 50 j = 1, n
340 r( i, j ) = ( half-sin( cmplx( i / j ) ) )*twenty
341 l( i, j ) = r( i, j )
342 50 CONTINUE
343 60 CONTINUE
344*
345 ELSE IF( prtype.EQ.2 .OR. prtype.EQ.3 ) THEN
346 DO 80 i = 1, m
347 DO 70 j = 1, m
348 IF( i.LE.j ) THEN
349 a( i, j ) = ( half-sin( cmplx( i ) ) )*two
350 d( i, j ) = ( half-sin( cmplx( i*j ) ) )*two
351 ELSE
352 a( i, j ) = zero
353 d( i, j ) = zero
354 END IF
355 70 CONTINUE
356 80 CONTINUE
357*
358 DO 100 i = 1, n
359 DO 90 j = 1, n
360 IF( i.LE.j ) THEN
361 b( i, j ) = ( half-sin( cmplx( i+j ) ) )*two
362 e( i, j ) = ( half-sin( cmplx( j ) ) )*two
363 ELSE
364 b( i, j ) = zero
365 e( i, j ) = zero
366 END IF
367 90 CONTINUE
368 100 CONTINUE
369*
370 DO 120 i = 1, m
371 DO 110 j = 1, n
372 r( i, j ) = ( half-sin( cmplx( i*j ) ) )*twenty
373 l( i, j ) = ( half-sin( cmplx( i+j ) ) )*twenty
374 110 CONTINUE
375 120 CONTINUE
376*
377 IF( prtype.EQ.3 ) THEN
378 IF( qblcka.LE.1 )
379 $ qblcka = 2
380 DO 130 k = 1, m - 1, qblcka
381 a( k+1, k+1 ) = a( k, k )
382 a( k+1, k ) = -sin( a( k, k+1 ) )
383 130 CONTINUE
384*
385 IF( qblckb.LE.1 )
386 $ qblckb = 2
387 DO 140 k = 1, n - 1, qblckb
388 b( k+1, k+1 ) = b( k, k )
389 b( k+1, k ) = -sin( b( k, k+1 ) )
390 140 CONTINUE
391 END IF
392*
393 ELSE IF( prtype.EQ.4 ) THEN
394 DO 160 i = 1, m
395 DO 150 j = 1, m
396 a( i, j ) = ( half-sin( cmplx( i*j ) ) )*twenty
397 d( i, j ) = ( half-sin( cmplx( i+j ) ) )*two
398 150 CONTINUE
399 160 CONTINUE
400*
401 DO 180 i = 1, n
402 DO 170 j = 1, n
403 b( i, j ) = ( half-sin( cmplx( i+j ) ) )*twenty
404 e( i, j ) = ( half-sin( cmplx( i*j ) ) )*two
405 170 CONTINUE
406 180 CONTINUE
407*
408 DO 200 i = 1, m
409 DO 190 j = 1, n
410 r( i, j ) = ( half-sin( cmplx( j / i ) ) )*twenty
411 l( i, j ) = ( half-sin( cmplx( i*j ) ) )*two
412 190 CONTINUE
413 200 CONTINUE
414*
415 ELSE IF( prtype.GE.5 ) THEN
416 reeps = half*two*twenty / alpha
417 imeps = ( half-two ) / alpha
418 DO 220 i = 1, m
419 DO 210 j = 1, n
420 r( i, j ) = ( half-sin( cmplx( i*j ) ) )*alpha / twenty
421 l( i, j ) = ( half-sin( cmplx( i+j ) ) )*alpha / twenty
422 210 CONTINUE
423 220 CONTINUE
424*
425 DO 230 i = 1, m
426 d( i, i ) = one
427 230 CONTINUE
428*
429 DO 240 i = 1, m
430 IF( i.LE.4 ) THEN
431 a( i, i ) = one
432 IF( i.GT.2 )
433 $ a( i, i ) = one + reeps
434 IF( mod( i, 2 ).NE.0 .AND. i.LT.m ) THEN
435 a( i, i+1 ) = imeps
436 ELSE IF( i.GT.1 ) THEN
437 a( i, i-1 ) = -imeps
438 END IF
439 ELSE IF( i.LE.8 ) THEN
440 IF( i.LE.6 ) THEN
441 a( i, i ) = reeps
442 ELSE
443 a( i, i ) = -reeps
444 END IF
445 IF( mod( i, 2 ).NE.0 .AND. i.LT.m ) THEN
446 a( i, i+1 ) = one
447 ELSE IF( i.GT.1 ) THEN
448 a( i, i-1 ) = -one
449 END IF
450 ELSE
451 a( i, i ) = one
452 IF( mod( i, 2 ).NE.0 .AND. i.LT.m ) THEN
453 a( i, i+1 ) = imeps*2
454 ELSE IF( i.GT.1 ) THEN
455 a( i, i-1 ) = -imeps*2
456 END IF
457 END IF
458 240 CONTINUE
459*
460 DO 250 i = 1, n
461 e( i, i ) = one
462 IF( i.LE.4 ) THEN
463 b( i, i ) = -one
464 IF( i.GT.2 )
465 $ b( i, i ) = one - reeps
466 IF( mod( i, 2 ).NE.0 .AND. i.LT.n ) THEN
467 b( i, i+1 ) = imeps
468 ELSE IF( i.GT.1 ) THEN
469 b( i, i-1 ) = -imeps
470 END IF
471 ELSE IF( i.LE.8 ) THEN
472 IF( i.LE.6 ) THEN
473 b( i, i ) = reeps
474 ELSE
475 b( i, i ) = -reeps
476 END IF
477 IF( mod( i, 2 ).NE.0 .AND. i.LT.n ) THEN
478 b( i, i+1 ) = one + imeps
479 ELSE IF( i.GT.1 ) THEN
480 b( i, i-1 ) = -one - imeps
481 END IF
482 ELSE
483 b( i, i ) = one - reeps
484 IF( mod( i, 2 ).NE.0 .AND. i.LT.n ) THEN
485 b( i, i+1 ) = imeps*2
486 ELSE IF( i.GT.1 ) THEN
487 b( i, i-1 ) = -imeps*2
488 END IF
489 END IF
490 250 CONTINUE
491 END IF
492*
493* Compute rhs (C, F)
494*
495 CALL cgemm( 'N', 'N', m, n, m, one, a, lda, r, ldr, zero, c, ldc )
496 CALL cgemm( 'N', 'N', m, n, n, -one, l, ldl, b, ldb, one, c, ldc )
497 CALL cgemm( 'N', 'N', m, n, m, one, d, ldd, r, ldr, zero, f, ldf )
498 CALL cgemm( 'N', 'N', m, n, n, -one, l, ldl, e, lde, one, f, ldf )
499*
500* End of CLATM5
501*
lde
logical function lde(ri, rj, lr)
Definition dblat2.f:2970
cgemm
subroutine cgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
CGEMM
Definition cgemm.f:188
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