LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ dlatm5()

subroutine dlatm5 ( integer  PRTYPE,
integer  M,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( ldc, * )  C,
integer  LDC,
double precision, dimension( ldd, * )  D,
integer  LDD,
double precision, dimension( lde, * )  E,
integer  LDE,
double precision, dimension( ldf, * )  F,
integer  LDF,
double precision, dimension( ldr, * )  R,
integer  LDR,
double precision, dimension( ldl, * )  L,
integer  LDL,
double precision  ALPHA,
integer  QBLCKA,
integer  QBLCKB 
)

DLATM5

Purpose:
 DLATM5 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
          "Points" 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION
          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 dlatm5.f.

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 DOUBLE PRECISION ALPHA
277* ..
278* .. Array Arguments ..
279 DOUBLE PRECISION 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 DOUBLE PRECISION ONE, ZERO, TWENTY, HALF, TWO
288 parameter( one = 1.0d+0, zero = 0.0d+0, twenty = 2.0d+1,
289 $ half = 0.5d+0, two = 2.0d+0 )
290* ..
291* .. Local Scalars ..
292 INTEGER I, J, K
293 DOUBLE PRECISION IMEPS, REEPS
294* ..
295* .. Intrinsic Functions ..
296 INTRINSIC dble, mod, sin
297* ..
298* .. External Subroutines ..
299 EXTERNAL dgemm
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( dble( 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( dble( i ) ) )*two
346 d( i, j ) = ( half-sin( dble( 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( dble( i+j ) ) )*two
358 e( i, j ) = ( half-sin( dble( 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( dble( i*j ) ) )*twenty
369 l( i, j ) = ( half-sin( dble( 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( dble( i*j ) ) )*twenty
393 d( i, j ) = ( half-sin( dble( 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( dble( i+j ) ) )*twenty
400 e( i, j ) = ( half-sin( dble( 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( dble( j / i ) ) )*twenty
407 l( i, j ) = ( half-sin( dble( 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( dble( i*j ) ) )*alpha / twenty
417 l( i, j ) = ( half-sin( dble( 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 dgemm( 'N', 'N', m, n, m, one, a, lda, r, ldr, zero, c, ldc )
492 CALL dgemm( 'N', 'N', m, n, n, -one, l, ldl, b, ldb, one, c, ldc )
493 CALL dgemm( 'N', 'N', m, n, m, one, d, ldd, r, ldr, zero, f, ldf )
494 CALL dgemm( 'N', 'N', m, n, n, -one, l, ldl, e, lde, one, f, ldf )
495*
496* End of DLATM5
497*
logical function lde(RI, RJ, LR)
Definition: dblat2.f:2970
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
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