LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine zlatm5 ( integer PRTYPE, integer M, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( ldc, * ) C, integer LDC, complex*16, dimension( ldd, * ) D, integer LDD, complex*16, dimension( lde, * ) E, integer LDE, complex*16, dimension( ldf, * ) F, integer LDF, complex*16, dimension( ldr, * ) R, integer LDR, complex*16, dimension( ldl, * ) L, integer LDL, double precision ALPHA, integer QBLCKA, integer QBLCKB )

ZLATM5

Purpose:
``` ZLATM5 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 futher 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*16 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*16 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*16 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*16 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*16 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*16 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*16 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*16 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.```
Date
June 2016
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 270 of file zlatm5.f.

270 *
271 * -- LAPACK computational routine (version 3.6.1) --
272 * -- LAPACK is a software package provided by Univ. of Tennessee, --
273 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
274 * June 2016
275 *
276 * .. Scalar Arguments ..
277  INTEGER lda, ldb, ldc, ldd, lde, ldf, ldl, ldr, m, n,
278  \$ prtype, qblcka, qblckb
279  DOUBLE PRECISION alpha
280 * ..
281 * .. Array Arguments ..
282  COMPLEX*16 a( lda, * ), b( ldb, * ), c( ldc, * ),
283  \$ d( ldd, * ), e( lde, * ), f( ldf, * ),
284  \$ l( ldl, * ), r( ldr, * )
285 * ..
286 *
287 * =====================================================================
288 *
289 * .. Parameters ..
290  COMPLEX*16 one, two, zero, half, twenty
291  parameter ( one = ( 1.0d+0, 0.0d+0 ),
292  \$ two = ( 2.0d+0, 0.0d+0 ),
293  \$ zero = ( 0.0d+0, 0.0d+0 ),
294  \$ half = ( 0.5d+0, 0.0d+0 ),
295  \$ twenty = ( 2.0d+1, 0.0d+0 ) )
296 * ..
297 * .. Local Scalars ..
298  INTEGER i, j, k
299  COMPLEX*16 imeps, reeps
300 * ..
301 * .. Intrinsic Functions ..
302  INTRINSIC dcmplx, mod, sin
303 * ..
304 * .. External Subroutines ..
305  EXTERNAL zgemm
306 * ..
307 * .. Executable Statements ..
308 *
309  IF( prtype.EQ.1 ) THEN
310  DO 20 i = 1, m
311  DO 10 j = 1, m
312  IF( i.EQ.j ) THEN
313  a( i, j ) = one
314  d( i, j ) = one
315  ELSE IF( i.EQ.j-1 ) THEN
316  a( i, j ) = -one
317  d( i, j ) = zero
318  ELSE
319  a( i, j ) = zero
320  d( i, j ) = zero
321  END IF
322  10 CONTINUE
323  20 CONTINUE
324 *
325  DO 40 i = 1, n
326  DO 30 j = 1, n
327  IF( i.EQ.j ) THEN
328  b( i, j ) = one - alpha
329  e( i, j ) = one
330  ELSE IF( i.EQ.j-1 ) THEN
331  b( i, j ) = one
332  e( i, j ) = zero
333  ELSE
334  b( i, j ) = zero
335  e( i, j ) = zero
336  END IF
337  30 CONTINUE
338  40 CONTINUE
339 *
340  DO 60 i = 1, m
341  DO 50 j = 1, n
342  r( i, j ) = ( half-sin( dcmplx( i / j ) ) )*twenty
343  l( i, j ) = r( i, j )
344  50 CONTINUE
345  60 CONTINUE
346 *
347  ELSE IF( prtype.EQ.2 .OR. prtype.EQ.3 ) THEN
348  DO 80 i = 1, m
349  DO 70 j = 1, m
350  IF( i.LE.j ) THEN
351  a( i, j ) = ( half-sin( dcmplx( i ) ) )*two
352  d( i, j ) = ( half-sin( dcmplx( i*j ) ) )*two
353  ELSE
354  a( i, j ) = zero
355  d( i, j ) = zero
356  END IF
357  70 CONTINUE
358  80 CONTINUE
359 *
360  DO 100 i = 1, n
361  DO 90 j = 1, n
362  IF( i.LE.j ) THEN
363  b( i, j ) = ( half-sin( dcmplx( i+j ) ) )*two
364  e( i, j ) = ( half-sin( dcmplx( j ) ) )*two
365  ELSE
366  b( i, j ) = zero
367  e( i, j ) = zero
368  END IF
369  90 CONTINUE
370  100 CONTINUE
371 *
372  DO 120 i = 1, m
373  DO 110 j = 1, n
374  r( i, j ) = ( half-sin( dcmplx( i*j ) ) )*twenty
375  l( i, j ) = ( half-sin( dcmplx( i+j ) ) )*twenty
376  110 CONTINUE
377  120 CONTINUE
378 *
379  IF( prtype.EQ.3 ) THEN
380  IF( qblcka.LE.1 )
381  \$ qblcka = 2
382  DO 130 k = 1, m - 1, qblcka
383  a( k+1, k+1 ) = a( k, k )
384  a( k+1, k ) = -sin( a( k, k+1 ) )
385  130 CONTINUE
386 *
387  IF( qblckb.LE.1 )
388  \$ qblckb = 2
389  DO 140 k = 1, n - 1, qblckb
390  b( k+1, k+1 ) = b( k, k )
391  b( k+1, k ) = -sin( b( k, k+1 ) )
392  140 CONTINUE
393  END IF
394 *
395  ELSE IF( prtype.EQ.4 ) THEN
396  DO 160 i = 1, m
397  DO 150 j = 1, m
398  a( i, j ) = ( half-sin( dcmplx( i*j ) ) )*twenty
399  d( i, j ) = ( half-sin( dcmplx( i+j ) ) )*two
400  150 CONTINUE
401  160 CONTINUE
402 *
403  DO 180 i = 1, n
404  DO 170 j = 1, n
405  b( i, j ) = ( half-sin( dcmplx( i+j ) ) )*twenty
406  e( i, j ) = ( half-sin( dcmplx( i*j ) ) )*two
407  170 CONTINUE
408  180 CONTINUE
409 *
410  DO 200 i = 1, m
411  DO 190 j = 1, n
412  r( i, j ) = ( half-sin( dcmplx( j / i ) ) )*twenty
413  l( i, j ) = ( half-sin( dcmplx( i*j ) ) )*two
414  190 CONTINUE
415  200 CONTINUE
416 *
417  ELSE IF( prtype.GE.5 ) THEN
418  reeps = half*two*twenty / alpha
419  imeps = ( half-two ) / alpha
420  DO 220 i = 1, m
421  DO 210 j = 1, n
422  r( i, j ) = ( half-sin( dcmplx( i*j ) ) )*alpha / twenty
423  l( i, j ) = ( half-sin( dcmplx( i+j ) ) )*alpha / twenty
424  210 CONTINUE
425  220 CONTINUE
426 *
427  DO 230 i = 1, m
428  d( i, i ) = one
429  230 CONTINUE
430 *
431  DO 240 i = 1, m
432  IF( i.LE.4 ) THEN
433  a( i, i ) = one
434  IF( i.GT.2 )
435  \$ a( i, i ) = one + reeps
436  IF( mod( i, 2 ).NE.0 .AND. i.LT.m ) THEN
437  a( i, i+1 ) = imeps
438  ELSE IF( i.GT.1 ) THEN
439  a( i, i-1 ) = -imeps
440  END IF
441  ELSE IF( i.LE.8 ) THEN
442  IF( i.LE.6 ) THEN
443  a( i, i ) = reeps
444  ELSE
445  a( i, i ) = -reeps
446  END IF
447  IF( mod( i, 2 ).NE.0 .AND. i.LT.m ) THEN
448  a( i, i+1 ) = one
449  ELSE IF( i.GT.1 ) THEN
450  a( i, i-1 ) = -one
451  END IF
452  ELSE
453  a( i, i ) = one
454  IF( mod( i, 2 ).NE.0 .AND. i.LT.m ) THEN
455  a( i, i+1 ) = imeps*2
456  ELSE IF( i.GT.1 ) THEN
457  a( i, i-1 ) = -imeps*2
458  END IF
459  END IF
460  240 CONTINUE
461 *
462  DO 250 i = 1, n
463  e( i, i ) = one
464  IF( i.LE.4 ) THEN
465  b( i, i ) = -one
466  IF( i.GT.2 )
467  \$ b( i, i ) = one - reeps
468  IF( mod( i, 2 ).NE.0 .AND. i.LT.n ) THEN
469  b( i, i+1 ) = imeps
470  ELSE IF( i.GT.1 ) THEN
471  b( i, i-1 ) = -imeps
472  END IF
473  ELSE IF( i.LE.8 ) THEN
474  IF( i.LE.6 ) THEN
475  b( i, i ) = reeps
476  ELSE
477  b( i, i ) = -reeps
478  END IF
479  IF( mod( i, 2 ).NE.0 .AND. i.LT.n ) THEN
480  b( i, i+1 ) = one + imeps
481  ELSE IF( i.GT.1 ) THEN
482  b( i, i-1 ) = -one - imeps
483  END IF
484  ELSE
485  b( i, i ) = one - reeps
486  IF( mod( i, 2 ).NE.0 .AND. i.LT.n ) THEN
487  b( i, i+1 ) = imeps*2
488  ELSE IF( i.GT.1 ) THEN
489  b( i, i-1 ) = -imeps*2
490  END IF
491  END IF
492  250 CONTINUE
493  END IF
494 *
495 * Compute rhs (C, F)
496 *
497  CALL zgemm( 'N', 'N', m, n, m, one, a, lda, r, ldr, zero, c, ldc )
498  CALL zgemm( 'N', 'N', m, n, n, -one, l, ldl, b, ldb, one, c, ldc )
499  CALL zgemm( 'N', 'N', m, n, m, one, d, ldd, r, ldr, zero, f, ldf )
500  CALL zgemm( 'N', 'N', m, n, n, -one, l, ldl, e, lde, one, f, ldf )
501 *
502 * End of ZLATM5
503 *
logical function lde(RI, RJ, LR)
Definition: dblat2.f:2945
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:189

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