LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ clavhe()

 subroutine clavhe ( 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 )

CLAVHE

Purpose:
``` CLAVHE performs one of the matrix-vector operations
x := A*x  or  x := A^H*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 CHETRF.

If TRANS = 'N', multiplies by U  or U * D  (or L  or L * D)
If TRANS = 'C', 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 = 'C': x := A^H*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 CHETRF_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 CHETRF. 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) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged, 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) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged, 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 151 of file clavhe.f.

153 *
154 * -- LAPACK test routine --
155 * -- LAPACK is a software package provided by Univ. of Tennessee, --
156 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
157 *
158 * .. Scalar Arguments ..
159  CHARACTER DIAG, TRANS, UPLO
160  INTEGER INFO, LDA, LDB, N, NRHS
161 * ..
162 * .. Array Arguments ..
163  INTEGER IPIV( * )
164  COMPLEX A( LDA, * ), B( LDB, * )
165 * ..
166 *
167 * =====================================================================
168 *
169 * .. Parameters ..
170  COMPLEX ONE
171  parameter( one = ( 1.0e+0, 0.0e+0 ) )
172 * ..
173 * .. Local Scalars ..
174  LOGICAL NOUNIT
175  INTEGER J, K, KP
176  COMPLEX D11, D12, D21, D22, T1, T2
177 * ..
178 * .. External Functions ..
179  LOGICAL LSAME
180  EXTERNAL lsame
181 * ..
182 * .. External Subroutines ..
183  EXTERNAL cgemv, cgeru, clacgv, cscal, cswap, xerbla
184 * ..
185 * .. Intrinsic Functions ..
186  INTRINSIC abs, conjg, max
187 * ..
188 * .. Executable Statements ..
189 *
190 * Test the input parameters.
191 *
192  info = 0
193  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
194  info = -1
195  ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.lsame( trans, 'C' ) )
196  \$ THEN
197  info = -2
198  ELSE IF( .NOT.lsame( diag, 'U' ) .AND. .NOT.lsame( diag, 'N' ) )
199  \$ THEN
200  info = -3
201  ELSE IF( n.LT.0 ) THEN
202  info = -4
203  ELSE IF( lda.LT.max( 1, n ) ) THEN
204  info = -6
205  ELSE IF( ldb.LT.max( 1, n ) ) THEN
206  info = -9
207  END IF
208  IF( info.NE.0 ) THEN
209  CALL xerbla( 'CLAVHE ', -info )
210  RETURN
211  END IF
212 *
213 * Quick return if possible.
214 *
215  IF( n.EQ.0 )
216  \$ RETURN
217 *
218  nounit = lsame( diag, 'N' )
219 *------------------------------------------
220 *
221 * Compute B := A * B (No transpose)
222 *
223 *------------------------------------------
224  IF( lsame( trans, 'N' ) ) THEN
225 *
226 * Compute B := U*B
227 * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
228 *
229  IF( lsame( uplo, 'U' ) ) THEN
230 *
231 * Loop forward applying the transformations.
232 *
233  k = 1
234  10 CONTINUE
235  IF( k.GT.n )
236  \$ GO TO 30
237  IF( ipiv( k ).GT.0 ) THEN
238 *
239 * 1 x 1 pivot block
240 *
241 * Multiply by the diagonal element if forming U * D.
242 *
243  IF( nounit )
244  \$ CALL cscal( nrhs, a( k, k ), b( k, 1 ), ldb )
245 *
246 * Multiply by P(K) * inv(U(K)) if K > 1.
247 *
248  IF( k.GT.1 ) THEN
249 *
250 * Apply the transformation.
251 *
252  CALL cgeru( k-1, nrhs, one, a( 1, k ), 1, b( k, 1 ),
253  \$ ldb, b( 1, 1 ), ldb )
254 *
255 * Interchange if P(K) != I.
256 *
257  kp = ipiv( k )
258  IF( kp.NE.k )
259  \$ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
260  END IF
261  k = k + 1
262  ELSE
263 *
264 * 2 x 2 pivot block
265 *
266 * Multiply by the diagonal block if forming U * D.
267 *
268  IF( nounit ) THEN
269  d11 = a( k, k )
270  d22 = a( k+1, k+1 )
271  d12 = a( k, k+1 )
272  d21 = conjg( d12 )
273  DO 20 j = 1, nrhs
274  t1 = b( k, j )
275  t2 = b( k+1, j )
276  b( k, j ) = d11*t1 + d12*t2
277  b( k+1, j ) = d21*t1 + d22*t2
278  20 CONTINUE
279  END IF
280 *
281 * Multiply by P(K) * inv(U(K)) if K > 1.
282 *
283  IF( k.GT.1 ) THEN
284 *
285 * Apply the transformations.
286 *
287  CALL cgeru( k-1, nrhs, one, a( 1, k ), 1, b( k, 1 ),
288  \$ ldb, b( 1, 1 ), ldb )
289  CALL cgeru( k-1, nrhs, one, a( 1, k+1 ), 1,
290  \$ b( k+1, 1 ), ldb, b( 1, 1 ), ldb )
291 *
292 * Interchange if P(K) != I.
293 *
294  kp = abs( ipiv( k ) )
295  IF( kp.NE.k )
296  \$ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
297  END IF
298  k = k + 2
299  END IF
300  GO TO 10
301  30 CONTINUE
302 *
303 * Compute B := L*B
304 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) .
305 *
306  ELSE
307 *
308 * Loop backward applying the transformations to B.
309 *
310  k = n
311  40 CONTINUE
312  IF( k.LT.1 )
313  \$ GO TO 60
314 *
315 * Test the pivot index. If greater than zero, a 1 x 1
316 * pivot was used, otherwise a 2 x 2 pivot was used.
317 *
318  IF( ipiv( k ).GT.0 ) THEN
319 *
320 * 1 x 1 pivot block:
321 *
322 * Multiply by the diagonal element if forming L * D.
323 *
324  IF( nounit )
325  \$ CALL cscal( nrhs, a( k, k ), b( k, 1 ), ldb )
326 *
327 * Multiply by P(K) * inv(L(K)) if K < N.
328 *
329  IF( k.NE.n ) THEN
330  kp = ipiv( k )
331 *
332 * Apply the transformation.
333 *
334  CALL cgeru( n-k, nrhs, one, a( k+1, k ), 1,
335  \$ b( k, 1 ), ldb, b( k+1, 1 ), ldb )
336 *
337 * Interchange if a permutation was applied at the
338 * K-th step of the factorization.
339 *
340  IF( kp.NE.k )
341  \$ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
342  END IF
343  k = k - 1
344 *
345  ELSE
346 *
347 * 2 x 2 pivot block:
348 *
349 * Multiply by the diagonal block if forming L * D.
350 *
351  IF( nounit ) THEN
352  d11 = a( k-1, k-1 )
353  d22 = a( k, k )
354  d21 = a( k, k-1 )
355  d12 = conjg( d21 )
356  DO 50 j = 1, nrhs
357  t1 = b( k-1, j )
358  t2 = b( k, j )
359  b( k-1, j ) = d11*t1 + d12*t2
360  b( k, j ) = d21*t1 + d22*t2
361  50 CONTINUE
362  END IF
363 *
364 * Multiply by P(K) * inv(L(K)) if K < N.
365 *
366  IF( k.NE.n ) THEN
367 *
368 * Apply the transformation.
369 *
370  CALL cgeru( n-k, nrhs, one, a( k+1, k ), 1,
371  \$ b( k, 1 ), ldb, b( k+1, 1 ), ldb )
372  CALL cgeru( n-k, nrhs, one, a( k+1, k-1 ), 1,
373  \$ b( k-1, 1 ), ldb, b( k+1, 1 ), ldb )
374 *
375 * Interchange if a permutation was applied at the
376 * K-th step of the factorization.
377 *
378  kp = abs( ipiv( k ) )
379  IF( kp.NE.k )
380  \$ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
381  END IF
382  k = k - 2
383  END IF
384  GO TO 40
385  60 CONTINUE
386  END IF
387 *--------------------------------------------------
388 *
389 * Compute B := A^H * B (conjugate transpose)
390 *
391 *--------------------------------------------------
392  ELSE
393 *
394 * Form B := U^H*B
395 * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
396 * and U^H = inv(U^H(1))*P(1)* ... *inv(U^H(m))*P(m)
397 *
398  IF( lsame( uplo, 'U' ) ) THEN
399 *
400 * Loop backward applying the transformations.
401 *
402  k = n
403  70 IF( k.LT.1 )
404  \$ GO TO 90
405 *
406 * 1 x 1 pivot block.
407 *
408  IF( ipiv( k ).GT.0 ) THEN
409  IF( k.GT.1 ) THEN
410 *
411 * Interchange if P(K) != I.
412 *
413  kp = ipiv( k )
414  IF( kp.NE.k )
415  \$ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
416 *
417 * Apply the transformation
418 * y = y - B' conjg(x),
419 * where x is a column of A and y is a row of B.
420 *
421  CALL clacgv( nrhs, b( k, 1 ), ldb )
422  CALL cgemv( 'Conjugate', k-1, nrhs, one, b, ldb,
423  \$ a( 1, k ), 1, one, b( k, 1 ), ldb )
424  CALL clacgv( nrhs, b( k, 1 ), ldb )
425  END IF
426  IF( nounit )
427  \$ CALL cscal( nrhs, a( k, k ), b( k, 1 ), ldb )
428  k = k - 1
429 *
430 * 2 x 2 pivot block.
431 *
432  ELSE
433  IF( k.GT.2 ) THEN
434 *
435 * Interchange if P(K) != I.
436 *
437  kp = abs( ipiv( k ) )
438  IF( kp.NE.k-1 )
439  \$ CALL cswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ),
440  \$ ldb )
441 *
442 * Apply the transformations
443 * y = y - B' conjg(x),
444 * where x is a block column of A and y is a block
445 * row of B.
446 *
447  CALL clacgv( nrhs, b( k, 1 ), ldb )
448  CALL cgemv( 'Conjugate', k-2, nrhs, one, b, ldb,
449  \$ a( 1, k ), 1, one, b( k, 1 ), ldb )
450  CALL clacgv( nrhs, b( k, 1 ), ldb )
451 *
452  CALL clacgv( nrhs, b( k-1, 1 ), ldb )
453  CALL cgemv( 'Conjugate', k-2, nrhs, one, b, ldb,
454  \$ a( 1, k-1 ), 1, one, b( k-1, 1 ), ldb )
455  CALL clacgv( nrhs, b( k-1, 1 ), ldb )
456  END IF
457 *
458 * Multiply by the diagonal block if non-unit.
459 *
460  IF( nounit ) THEN
461  d11 = a( k-1, k-1 )
462  d22 = a( k, k )
463  d12 = a( k-1, k )
464  d21 = conjg( d12 )
465  DO 80 j = 1, nrhs
466  t1 = b( k-1, j )
467  t2 = b( k, j )
468  b( k-1, j ) = d11*t1 + d12*t2
469  b( k, j ) = d21*t1 + d22*t2
470  80 CONTINUE
471  END IF
472  k = k - 2
473  END IF
474  GO TO 70
475  90 CONTINUE
476 *
477 * Form B := L^H*B
478 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m))
479 * and L^H = inv(L^H(m))*P(m)* ... *inv(L^H(1))*P(1)
480 *
481  ELSE
482 *
483 * Loop forward applying the L-transformations.
484 *
485  k = 1
486  100 CONTINUE
487  IF( k.GT.n )
488  \$ GO TO 120
489 *
490 * 1 x 1 pivot block
491 *
492  IF( ipiv( k ).GT.0 ) THEN
493  IF( k.LT.n ) THEN
494 *
495 * Interchange if P(K) != I.
496 *
497  kp = ipiv( k )
498  IF( kp.NE.k )
499  \$ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
500 *
501 * Apply the transformation
502 *
503  CALL clacgv( nrhs, b( k, 1 ), ldb )
504  CALL cgemv( 'Conjugate', n-k, nrhs, one, b( k+1, 1 ),
505  \$ ldb, a( k+1, k ), 1, one, b( k, 1 ), ldb )
506  CALL clacgv( nrhs, b( k, 1 ), ldb )
507  END IF
508  IF( nounit )
509  \$ CALL cscal( nrhs, a( k, k ), b( k, 1 ), ldb )
510  k = k + 1
511 *
512 * 2 x 2 pivot block.
513 *
514  ELSE
515  IF( k.LT.n-1 ) THEN
516 *
517 * Interchange if P(K) != I.
518 *
519  kp = abs( ipiv( k ) )
520  IF( kp.NE.k+1 )
521  \$ CALL cswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ),
522  \$ ldb )
523 *
524 * Apply the transformation
525 *
526  CALL clacgv( nrhs, b( k+1, 1 ), ldb )
527  CALL cgemv( 'Conjugate', n-k-1, nrhs, one,
528  \$ b( k+2, 1 ), ldb, a( k+2, k+1 ), 1, one,
529  \$ b( k+1, 1 ), ldb )
530  CALL clacgv( nrhs, b( k+1, 1 ), ldb )
531 *
532  CALL clacgv( nrhs, b( k, 1 ), ldb )
533  CALL cgemv( 'Conjugate', n-k-1, nrhs, one,
534  \$ b( k+2, 1 ), ldb, a( k+2, k ), 1, one,
535  \$ b( k, 1 ), ldb )
536  CALL clacgv( nrhs, b( k, 1 ), ldb )
537  END IF
538 *
539 * Multiply by the diagonal block if non-unit.
540 *
541  IF( nounit ) THEN
542  d11 = a( k, k )
543  d22 = a( k+1, k+1 )
544  d21 = a( k+1, k )
545  d12 = conjg( d21 )
546  DO 110 j = 1, nrhs
547  t1 = b( k, j )
548  t2 = b( k+1, j )
549  b( k, j ) = d11*t1 + d12*t2
550  b( k+1, j ) = d21*t1 + d22*t2
551  110 CONTINUE
552  END IF
553  k = k + 2
554  END IF
555  GO TO 100
556  120 CONTINUE
557  END IF
558 *
559  END IF
560  RETURN
561 *
562 * End of CLAVHE
563 *
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
subroutine clacgv(N, X, INCX)
CLACGV conjugates a complex vector.
Definition: clacgv.f:74
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