 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ clavsy_rook()

 subroutine clavsy_rook ( character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex, dimension( ldb, * ) B, integer LDB, integer INFO )

CLAVSY_ROOK

Purpose:
``` CLAVSY_ROOK performs one of the matrix-vector operations
x := A*x  or  x := A'*x,
where x is an N element vector and  A is one of the factors
from the block U*D*U' or L*D*L' factorization computed by CSYTRF_ROOK.

If TRANS = 'N', multiplies by U  or U * D  (or L  or L * D)
If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L')```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the factor stored in A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular``` [in] TRANS ``` TRANS is CHARACTER*1 Specifies the operation to be performed: = 'N': x := A*x = 'T': x := A'*x``` [in] DIAG ``` DIAG is CHARACTER*1 Specifies whether or not the diagonal blocks are unit matrices. If the diagonal blocks are assumed to be unit, then A = U or A = L, otherwise A = U*D or A = L*D. = 'U': Diagonal blocks are assumed to be unit matrices. = 'N': Diagonal blocks are assumed to be non-unit matrices.``` [in] N ``` N is INTEGER The number of rows and columns of the matrix A. N >= 0.``` [in] NRHS ``` NRHS is INTEGER The number of right hand sides, i.e., the number of vectors x to be multiplied by A. NRHS >= 0.``` [in] A ``` A is COMPLEX array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF_ROOK. Stored as a 2-D triangular matrix.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D, as determined by CSYTRF_ROOK. If UPLO = 'U': If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. (If IPIV( k ) = k, no interchange was done). If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were inerchaged, D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L': If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. (If IPIV( k ) = k, no interchange was done). If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were inerchaged, D(k:k+1,k:k+1) is a 2-by-2 diagonal block.``` [in,out] B ``` B is COMPLEX array, dimension (LDB,NRHS) On entry, B contains NRHS vectors of length N. On exit, B is overwritten with the product A * B.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -k, the k-th argument had an illegal value```

Definition at line 153 of file clavsy_rook.f.

155 *
156 * -- LAPACK test routine --
157 * -- LAPACK is a software package provided by Univ. of Tennessee, --
158 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
159 *
160 * .. Scalar Arguments ..
161  CHARACTER DIAG, TRANS, UPLO
162  INTEGER INFO, LDA, LDB, N, NRHS
163 * ..
164 * .. Array Arguments ..
165  INTEGER IPIV( * )
166  COMPLEX A( LDA, * ), B( LDB, * )
167 * ..
168 *
169 * =====================================================================
170 *
171 * .. Parameters ..
172  COMPLEX CONE
173  parameter( cone = ( 1.0e+0, 0.0e+0 ) )
174 * ..
175 * .. Local Scalars ..
176  LOGICAL NOUNIT
177  INTEGER J, K, KP
178  COMPLEX D11, D12, D21, D22, T1, T2
179 * ..
180 * .. External Functions ..
181  LOGICAL LSAME
182  EXTERNAL lsame
183 * ..
184 * .. External Subroutines ..
185  EXTERNAL cgemv, cgeru, cscal, cswap, xerbla
186 * ..
187 * .. Intrinsic Functions ..
188  INTRINSIC abs, max
189 * ..
190 * .. Executable Statements ..
191 *
192 * Test the input parameters.
193 *
194  info = 0
195  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
196  info = -1
197  ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.lsame( trans, 'T' ) )
198  \$ THEN
199  info = -2
200  ELSE IF( .NOT.lsame( diag, 'U' ) .AND. .NOT.lsame( diag, 'N' ) )
201  \$ THEN
202  info = -3
203  ELSE IF( n.LT.0 ) THEN
204  info = -4
205  ELSE IF( lda.LT.max( 1, n ) ) THEN
206  info = -6
207  ELSE IF( ldb.LT.max( 1, n ) ) THEN
208  info = -9
209  END IF
210  IF( info.NE.0 ) THEN
211  CALL xerbla( 'CLAVSY_ROOK ', -info )
212  RETURN
213  END IF
214 *
215 * Quick return if possible.
216 *
217  IF( n.EQ.0 )
218  \$ RETURN
219 *
220  nounit = lsame( diag, 'N' )
221 *------------------------------------------
222 *
223 * Compute B := A * B (No transpose)
224 *
225 *------------------------------------------
226  IF( lsame( trans, 'N' ) ) THEN
227 *
228 * Compute B := U*B
229 * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
230 *
231  IF( lsame( uplo, 'U' ) ) THEN
232 *
233 * Loop forward applying the transformations.
234 *
235  k = 1
236  10 CONTINUE
237  IF( k.GT.n )
238  \$ GO TO 30
239  IF( ipiv( k ).GT.0 ) THEN
240 *
241 * 1 x 1 pivot block
242 *
243 * Multiply by the diagonal element if forming U * D.
244 *
245  IF( nounit )
246  \$ CALL cscal( nrhs, a( k, k ), b( k, 1 ), ldb )
247 *
248 * Multiply by P(K) * inv(U(K)) if K > 1.
249 *
250  IF( k.GT.1 ) THEN
251 *
252 * Apply the transformation.
253 *
254  CALL cgeru( k-1, nrhs, cone, a( 1, k ), 1, b( k, 1 ),
255  \$ ldb, b( 1, 1 ), ldb )
256 *
257 * Interchange if P(K) != I.
258 *
259  kp = ipiv( k )
260  IF( kp.NE.k )
261  \$ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
262  END IF
263  k = k + 1
264  ELSE
265 *
266 * 2 x 2 pivot block
267 *
268 * Multiply by the diagonal block if forming U * D.
269 *
270  IF( nounit ) THEN
271  d11 = a( k, k )
272  d22 = a( k+1, k+1 )
273  d12 = a( k, k+1 )
274  d21 = d12
275  DO 20 j = 1, nrhs
276  t1 = b( k, j )
277  t2 = b( k+1, j )
278  b( k, j ) = d11*t1 + d12*t2
279  b( k+1, j ) = d21*t1 + d22*t2
280  20 CONTINUE
281  END IF
282 *
283 * Multiply by P(K) * inv(U(K)) if K > 1.
284 *
285  IF( k.GT.1 ) THEN
286 *
287 * Apply the transformations.
288 *
289  CALL cgeru( k-1, nrhs, cone, a( 1, k ), 1, b( k, 1 ),
290  \$ ldb, b( 1, 1 ), ldb )
291  CALL cgeru( k-1, nrhs, cone, a( 1, k+1 ), 1,
292  \$ b( k+1, 1 ), ldb, b( 1, 1 ), ldb )
293 *
294 * Interchange if a permutation was applied at the
295 * K-th step of the factorization.
296 *
297 * Swap the first of pair with IMAXth
298 *
299  kp = abs( ipiv( k ) )
300  IF( kp.NE.k )
301  \$ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
302 *
303 * NOW swap the first of pair with Pth
304 *
305  kp = abs( ipiv( k+1 ) )
306  IF( kp.NE.k+1 )
307  \$ CALL cswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ),
308  \$ ldb )
309  END IF
310  k = k + 2
311  END IF
312  GO TO 10
313  30 CONTINUE
314 *
315 * Compute B := L*B
316 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) .
317 *
318  ELSE
319 *
320 * Loop backward applying the transformations to B.
321 *
322  k = n
323  40 CONTINUE
324  IF( k.LT.1 )
325  \$ GO TO 60
326 *
327 * Test the pivot index. If greater than zero, a 1 x 1
328 * pivot was used, otherwise a 2 x 2 pivot was used.
329 *
330  IF( ipiv( k ).GT.0 ) THEN
331 *
332 * 1 x 1 pivot block:
333 *
334 * Multiply by the diagonal element if forming L * D.
335 *
336  IF( nounit )
337  \$ CALL cscal( nrhs, a( k, k ), b( k, 1 ), ldb )
338 *
339 * Multiply by P(K) * inv(L(K)) if K < N.
340 *
341  IF( k.NE.n ) THEN
342  kp = ipiv( k )
343 *
344 * Apply the transformation.
345 *
346  CALL cgeru( n-k, nrhs, cone, a( k+1, k ), 1,
347  \$ b( k, 1 ), ldb, b( k+1, 1 ), ldb )
348 *
349 * Interchange if a permutation was applied at the
350 * K-th step of the factorization.
351 *
352  IF( kp.NE.k )
353  \$ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
354  END IF
355  k = k - 1
356 *
357  ELSE
358 *
359 * 2 x 2 pivot block:
360 *
361 * Multiply by the diagonal block if forming L * D.
362 *
363  IF( nounit ) THEN
364  d11 = a( k-1, k-1 )
365  d22 = a( k, k )
366  d21 = a( k, k-1 )
367  d12 = d21
368  DO 50 j = 1, nrhs
369  t1 = b( k-1, j )
370  t2 = b( k, j )
371  b( k-1, j ) = d11*t1 + d12*t2
372  b( k, j ) = d21*t1 + d22*t2
373  50 CONTINUE
374  END IF
375 *
376 * Multiply by P(K) * inv(L(K)) if K < N.
377 *
378  IF( k.NE.n ) THEN
379 *
380 * Apply the transformation.
381 *
382  CALL cgeru( n-k, nrhs, cone, a( k+1, k ), 1,
383  \$ b( k, 1 ), ldb, b( k+1, 1 ), ldb )
384  CALL cgeru( n-k, nrhs, cone, a( k+1, k-1 ), 1,
385  \$ b( k-1, 1 ), ldb, b( k+1, 1 ), ldb )
386 *
387 * Interchange if a permutation was applied at the
388 * K-th step of the factorization.
389 *
390 * Swap the second of pair with IMAXth
391 *
392  kp = abs( ipiv( k ) )
393  IF( kp.NE.k )
394  \$ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
395 *
396 * NOW swap the first of pair with Pth
397 *
398  kp = abs( ipiv( k-1 ) )
399  IF( kp.NE.k-1 )
400  \$ CALL cswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ),
401  \$ ldb )
402  END IF
403  k = k - 2
404  END IF
405  GO TO 40
406  60 CONTINUE
407  END IF
408 *----------------------------------------
409 *
410 * Compute B := A' * B (transpose)
411 *
412 *----------------------------------------
413  ELSE IF( lsame( trans, 'T' ) ) THEN
414 *
415 * Form B := U'*B
416 * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
417 * and U' = inv(U'(1))*P(1)* ... *inv(U'(m))*P(m)
418 *
419  IF( lsame( uplo, 'U' ) ) THEN
420 *
421 * Loop backward applying the transformations.
422 *
423  k = n
424  70 IF( k.LT.1 )
425  \$ GO TO 90
426 *
427 * 1 x 1 pivot block.
428 *
429  IF( ipiv( k ).GT.0 ) THEN
430  IF( k.GT.1 ) THEN
431 *
432 * Interchange if P(K) != I.
433 *
434  kp = ipiv( k )
435  IF( kp.NE.k )
436  \$ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
437 *
438 * Apply the transformation
439 *
440  CALL cgemv( 'Transpose', k-1, nrhs, cone, b, ldb,
441  \$ a( 1, k ), 1, cone, b( k, 1 ), ldb )
442  END IF
443  IF( nounit )
444  \$ CALL cscal( nrhs, a( k, k ), b( k, 1 ), ldb )
445  k = k - 1
446 *
447 * 2 x 2 pivot block.
448 *
449  ELSE
450  IF( k.GT.2 ) THEN
451 *
452 * Swap the second of pair with Pth
453 *
454  kp = abs( ipiv( k ) )
455  IF( kp.NE.k )
456  \$ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
457 *
458 * Now swap the first of pair with IMAX(r)th
459 *
460  kp = abs( ipiv( k-1 ) )
461  IF( kp.NE.k-1 )
462  \$ CALL cswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ),
463  \$ ldb )
464 *
465 * Apply the transformations
466 *
467  CALL cgemv( 'Transpose', k-2, nrhs, cone, b, ldb,
468  \$ a( 1, k ), 1, cone, b( k, 1 ), ldb )
469  CALL cgemv( 'Transpose', k-2, nrhs, cone, b, ldb,
470  \$ a( 1, k-1 ), 1, cone, b( k-1, 1 ), ldb )
471  END IF
472 *
473 * Multiply by the diagonal block if non-unit.
474 *
475  IF( nounit ) THEN
476  d11 = a( k-1, k-1 )
477  d22 = a( k, k )
478  d12 = a( k-1, k )
479  d21 = d12
480  DO 80 j = 1, nrhs
481  t1 = b( k-1, j )
482  t2 = b( k, j )
483  b( k-1, j ) = d11*t1 + d12*t2
484  b( k, j ) = d21*t1 + d22*t2
485  80 CONTINUE
486  END IF
487  k = k - 2
488  END IF
489  GO TO 70
490  90 CONTINUE
491 *
492 * Form B := L'*B
493 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m))
494 * and L' = inv(L'(m))*P(m)* ... *inv(L'(1))*P(1)
495 *
496  ELSE
497 *
498 * Loop forward applying the L-transformations.
499 *
500  k = 1
501  100 CONTINUE
502  IF( k.GT.n )
503  \$ GO TO 120
504 *
505 * 1 x 1 pivot block
506 *
507  IF( ipiv( k ).GT.0 ) THEN
508  IF( k.LT.n ) THEN
509 *
510 * Interchange if P(K) != I.
511 *
512  kp = ipiv( k )
513  IF( kp.NE.k )
514  \$ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
515 *
516 * Apply the transformation
517 *
518  CALL cgemv( 'Transpose', n-k, nrhs, cone, b( k+1, 1 ),
519  \$ ldb, a( k+1, k ), 1, cone, b( k, 1 ), ldb )
520  END IF
521  IF( nounit )
522  \$ CALL cscal( nrhs, a( k, k ), b( k, 1 ), ldb )
523  k = k + 1
524 *
525 * 2 x 2 pivot block.
526 *
527  ELSE
528  IF( k.LT.n-1 ) THEN
529 *
530 * Swap the first of pair with Pth
531 *
532  kp = abs( ipiv( k ) )
533  IF( kp.NE.k )
534  \$ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
535 *
536 * Now swap the second of pair with IMAX(r)th
537 *
538  kp = abs( ipiv( k+1 ) )
539  IF( kp.NE.k+1 )
540  \$ CALL cswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ),
541  \$ ldb )
542 *
543 * Apply the transformation
544 *
545  CALL cgemv( 'Transpose', n-k-1, nrhs, cone,
546  \$ b( k+2, 1 ), ldb, a( k+2, k+1 ), 1, cone,
547  \$ b( k+1, 1 ), ldb )
548  CALL cgemv( 'Transpose', n-k-1, nrhs, cone,
549  \$ b( k+2, 1 ), ldb, a( k+2, k ), 1, cone,
550  \$ b( k, 1 ), ldb )
551  END IF
552 *
553 * Multiply by the diagonal block if non-unit.
554 *
555  IF( nounit ) THEN
556  d11 = a( k, k )
557  d22 = a( k+1, k+1 )
558  d21 = a( k+1, k )
559  d12 = d21
560  DO 110 j = 1, nrhs
561  t1 = b( k, j )
562  t2 = b( k+1, j )
563  b( k, j ) = d11*t1 + d12*t2
564  b( k+1, j ) = d21*t1 + d22*t2
565  110 CONTINUE
566  END IF
567  k = k + 2
568  END IF
569  GO TO 100
570  120 CONTINUE
571  END IF
572  END IF
573  RETURN
574 *
575 * End of CLAVSY_ROOK
576 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cswap(N, CX, INCX, CY, INCY)
CSWAP
Definition: cswap.f:81
subroutine cscal(N, CA, CX, INCX)
CSCAL
Definition: cscal.f:78
subroutine cgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CGEMV
Definition: cgemv.f:158
subroutine cgeru(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
CGERU
Definition: cgeru.f:130
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