 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ zlavhp()

 subroutine zlavhp ( character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex*16, dimension( * ) A, integer, dimension( * ) IPIV, complex*16, dimension( ldb, * ) B, integer LDB, integer INFO )

ZLAVHP

Purpose:
ZLAVHP  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 symmetric factorization computed by ZHPTRF.
ZHPTRF produces a factorization of the form
U * D * U^H     or     L * D * L^H,
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, U^H (or L^H) is the conjugate transpose of
U (or L), and D is Hermitian and block diagonal with 1 x 1 and
2 x 2 diagonal blocks.  The multipliers for the transformations
and the upper or lower triangular parts of the diagonal blocks
are stored columnwise in packed format in the linear array A.

If TRANS = 'N' or 'n', ZLAVHP multiplies either by U or U * D
(or L or L * D).
If TRANS = 'C' or 'c', ZLAVHP multiplies either by U^H or D * U^H
(or L^H or D * L^H ).
UPLO   - CHARACTER*1
On entry, UPLO specifies whether the triangular matrix
stored in A is upper or lower triangular.
UPLO = 'U' or 'u'   The matrix is upper triangular.
UPLO = 'L' or 'l'   The matrix is lower triangular.
Unchanged on exit.

TRANS  - CHARACTER*1
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n'   x := A*x.
TRANS = 'C' or 'c'   x := A^H*x.
Unchanged on exit.

DIAG   - CHARACTER*1
On entry, DIAG specifies whether the diagonal blocks are
assumed to be unit matrices, as follows:
DIAG = 'U' or 'u'   Diagonal blocks are unit matrices.
DIAG = 'N' or 'n'   Diagonal blocks are non-unit.
Unchanged on exit.

N      - INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.

NRHS   - INTEGER
On entry, NRHS specifies the number of right hand sides,
i.e., the number of vectors x to be multiplied by A.
NRHS must be at least zero.
Unchanged on exit.

A      - COMPLEX*16 array, dimension( N*(N+1)/2 )
On entry, A contains a block diagonal matrix and the
multipliers of the transformations used to obtain it,
stored as a packed triangular matrix.
Unchanged on exit.

IPIV   - INTEGER array, dimension( N )
On entry, IPIV contains the vector of pivot indices as
determined by ZSPTRF or ZHPTRF.
If IPIV( K ) = K, no interchange was done.
If IPIV( K ) <> K but IPIV( K ) > 0, then row K was inter-
changed with row IPIV( K ) and a 1 x 1 pivot block was used.
If IPIV( K ) < 0 and UPLO = 'U', then row K-1 was exchanged
with row | IPIV( K ) | and a 2 x 2 pivot block was used.
If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged
with row | IPIV( K ) | and a 2 x 2 pivot block was used.

B      - COMPLEX*16 array, dimension( LDB, NRHS )
On entry, B contains NRHS vectors of length N.
On exit, B is overwritten with the product A * B.

LDB    - INTEGER
On entry, LDB contains the leading dimension of B as
declared in the calling program.  LDB must be at least
max( 1, N ).
Unchanged on exit.

INFO   - INTEGER
INFO is the error flag.
On exit, a value of 0 indicates a successful exit.
A negative value, say -K, indicates that the K-th argument
has an illegal value.

Definition at line 129 of file zlavhp.f.

131 *
132 * -- LAPACK test routine --
133 * -- LAPACK is a software package provided by Univ. of Tennessee, --
134 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
135 *
136 * .. Scalar Arguments ..
137  CHARACTER DIAG, TRANS, UPLO
138  INTEGER INFO, LDB, N, NRHS
139 * ..
140 * .. Array Arguments ..
141  INTEGER IPIV( * )
142  COMPLEX*16 A( * ), B( LDB, * )
143 * ..
144 *
145 * =====================================================================
146 *
147 * .. Parameters ..
148  COMPLEX*16 ONE
149  parameter( one = ( 1.0d+0, 0.0d+0 ) )
150 * ..
151 * .. Local Scalars ..
152  LOGICAL NOUNIT
153  INTEGER J, K, KC, KCNEXT, KP
154  COMPLEX*16 D11, D12, D21, D22, T1, T2
155 * ..
156 * .. External Functions ..
157  LOGICAL LSAME
158  EXTERNAL lsame
159 * ..
160 * .. External Subroutines ..
161  EXTERNAL xerbla, zgemv, zgeru, zlacgv, zscal, zswap
162 * ..
163 * .. Intrinsic Functions ..
164  INTRINSIC abs, dconjg, max
165 * ..
166 * .. Executable Statements ..
167 *
168 * Test the input parameters.
169 *
170  info = 0
171  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
172  info = -1
173  ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.lsame( trans, 'C' ) )
174  \$ THEN
175  info = -2
176  ELSE IF( .NOT.lsame( diag, 'U' ) .AND. .NOT.lsame( diag, 'N' ) )
177  \$ THEN
178  info = -3
179  ELSE IF( n.LT.0 ) THEN
180  info = -4
181  ELSE IF( ldb.LT.max( 1, n ) ) THEN
182  info = -8
183  END IF
184  IF( info.NE.0 ) THEN
185  CALL xerbla( 'ZLAVHP ', -info )
186  RETURN
187  END IF
188 *
189 * Quick return if possible.
190 *
191  IF( n.EQ.0 )
192  \$ RETURN
193 *
194  nounit = lsame( diag, 'N' )
195 *------------------------------------------
196 *
197 * Compute B := A * B (No transpose)
198 *
199 *------------------------------------------
200  IF( lsame( trans, 'N' ) ) THEN
201 *
202 * Compute B := U*B
203 * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
204 *
205  IF( lsame( uplo, 'U' ) ) THEN
206 *
207 * Loop forward applying the transformations.
208 *
209  k = 1
210  kc = 1
211  10 CONTINUE
212  IF( k.GT.n )
213  \$ GO TO 30
214 *
215 * 1 x 1 pivot block
216 *
217  IF( ipiv( k ).GT.0 ) THEN
218 *
219 * Multiply by the diagonal element if forming U * D.
220 *
221  IF( nounit )
222  \$ CALL zscal( nrhs, a( kc+k-1 ), b( k, 1 ), ldb )
223 *
224 * Multiply by P(K) * inv(U(K)) if K > 1.
225 *
226  IF( k.GT.1 ) THEN
227 *
228 * Apply the transformation.
229 *
230  CALL zgeru( k-1, nrhs, one, a( kc ), 1, b( k, 1 ),
231  \$ ldb, b( 1, 1 ), ldb )
232 *
233 * Interchange if P(K) != I.
234 *
235  kp = ipiv( k )
236  IF( kp.NE.k )
237  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
238  END IF
239  kc = kc + k
240  k = k + 1
241  ELSE
242 *
243 * 2 x 2 pivot block
244 *
245  kcnext = kc + k
246 *
247 * Multiply by the diagonal block if forming U * D.
248 *
249  IF( nounit ) THEN
250  d11 = a( kcnext-1 )
251  d22 = a( kcnext+k )
252  d12 = a( kcnext+k-1 )
253  d21 = dconjg( d12 )
254  DO 20 j = 1, nrhs
255  t1 = b( k, j )
256  t2 = b( k+1, j )
257  b( k, j ) = d11*t1 + d12*t2
258  b( k+1, j ) = d21*t1 + d22*t2
259  20 CONTINUE
260  END IF
261 *
262 * Multiply by P(K) * inv(U(K)) if K > 1.
263 *
264  IF( k.GT.1 ) THEN
265 *
266 * Apply the transformations.
267 *
268  CALL zgeru( k-1, nrhs, one, a( kc ), 1, b( k, 1 ),
269  \$ ldb, b( 1, 1 ), ldb )
270  CALL zgeru( k-1, nrhs, one, a( kcnext ), 1,
271  \$ b( k+1, 1 ), ldb, b( 1, 1 ), ldb )
272 *
273 * Interchange if P(K) != I.
274 *
275  kp = abs( ipiv( k ) )
276  IF( kp.NE.k )
277  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
278  END IF
279  kc = kcnext + k + 1
280  k = k + 2
281  END IF
282  GO TO 10
283  30 CONTINUE
284 *
285 * Compute B := L*B
286 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) .
287 *
288  ELSE
289 *
290 * Loop backward applying the transformations to B.
291 *
292  k = n
293  kc = n*( n+1 ) / 2 + 1
294  40 CONTINUE
295  IF( k.LT.1 )
296  \$ GO TO 60
297  kc = kc - ( n-k+1 )
298 *
299 * Test the pivot index. If greater than zero, a 1 x 1
300 * pivot was used, otherwise a 2 x 2 pivot was used.
301 *
302  IF( ipiv( k ).GT.0 ) THEN
303 *
304 * 1 x 1 pivot block:
305 *
306 * Multiply by the diagonal element if forming L * D.
307 *
308  IF( nounit )
309  \$ CALL zscal( nrhs, a( kc ), b( k, 1 ), ldb )
310 *
311 * Multiply by P(K) * inv(L(K)) if K < N.
312 *
313  IF( k.NE.n ) THEN
314  kp = ipiv( k )
315 *
316 * Apply the transformation.
317 *
318  CALL zgeru( n-k, nrhs, one, a( kc+1 ), 1, b( k, 1 ),
319  \$ ldb, b( k+1, 1 ), ldb )
320 *
321 * Interchange if a permutation was applied at the
322 * K-th step of the factorization.
323 *
324  IF( kp.NE.k )
325  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
326  END IF
327  k = k - 1
328 *
329  ELSE
330 *
331 * 2 x 2 pivot block:
332 *
333  kcnext = kc - ( n-k+2 )
334 *
335 * Multiply by the diagonal block if forming L * D.
336 *
337  IF( nounit ) THEN
338  d11 = a( kcnext )
339  d22 = a( kc )
340  d21 = a( kcnext+1 )
341  d12 = dconjg( d21 )
342  DO 50 j = 1, nrhs
343  t1 = b( k-1, j )
344  t2 = b( k, j )
345  b( k-1, j ) = d11*t1 + d12*t2
346  b( k, j ) = d21*t1 + d22*t2
347  50 CONTINUE
348  END IF
349 *
350 * Multiply by P(K) * inv(L(K)) if K < N.
351 *
352  IF( k.NE.n ) THEN
353 *
354 * Apply the transformation.
355 *
356  CALL zgeru( n-k, nrhs, one, a( kc+1 ), 1, b( k, 1 ),
357  \$ ldb, b( k+1, 1 ), ldb )
358  CALL zgeru( n-k, nrhs, one, a( kcnext+2 ), 1,
359  \$ b( k-1, 1 ), ldb, b( k+1, 1 ), ldb )
360 *
361 * Interchange if a permutation was applied at the
362 * K-th step of the factorization.
363 *
364  kp = abs( ipiv( k ) )
365  IF( kp.NE.k )
366  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
367  END IF
368  kc = kcnext
369  k = k - 2
370  END IF
371  GO TO 40
372  60 CONTINUE
373  END IF
374 *-------------------------------------------------
375 *
376 * Compute B := A^H * B (conjugate transpose)
377 *
378 *-------------------------------------------------
379  ELSE
380 *
381 * Form B := U^H*B
382 * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
383 * and U^H = inv(U^H(1))*P(1)* ... *inv(U^H(m))*P(m)
384 *
385  IF( lsame( uplo, 'U' ) ) THEN
386 *
387 * Loop backward applying the transformations.
388 *
389  k = n
390  kc = n*( n+1 ) / 2 + 1
391  70 CONTINUE
392  IF( k.LT.1 )
393  \$ GO TO 90
394  kc = kc - k
395 *
396 * 1 x 1 pivot block.
397 *
398  IF( ipiv( k ).GT.0 ) THEN
399  IF( k.GT.1 ) THEN
400 *
401 * Interchange if P(K) != I.
402 *
403  kp = ipiv( k )
404  IF( kp.NE.k )
405  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
406 *
407 * Apply the transformation:
408 * y := y - B' * conjg(x)
409 * where x is a column of A and y is a row of B.
410 *
411  CALL zlacgv( nrhs, b( k, 1 ), ldb )
412  CALL zgemv( 'Conjugate', k-1, nrhs, one, b, ldb,
413  \$ a( kc ), 1, one, b( k, 1 ), ldb )
414  CALL zlacgv( nrhs, b( k, 1 ), ldb )
415  END IF
416  IF( nounit )
417  \$ CALL zscal( nrhs, a( kc+k-1 ), b( k, 1 ), ldb )
418  k = k - 1
419 *
420 * 2 x 2 pivot block.
421 *
422  ELSE
423  kcnext = kc - ( k-1 )
424  IF( k.GT.2 ) THEN
425 *
426 * Interchange if P(K) != I.
427 *
428  kp = abs( ipiv( k ) )
429  IF( kp.NE.k-1 )
430  \$ CALL zswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ),
431  \$ ldb )
432 *
433 * Apply the transformations.
434 *
435  CALL zlacgv( nrhs, b( k, 1 ), ldb )
436  CALL zgemv( 'Conjugate', k-2, nrhs, one, b, ldb,
437  \$ a( kc ), 1, one, b( k, 1 ), ldb )
438  CALL zlacgv( nrhs, b( k, 1 ), ldb )
439 *
440  CALL zlacgv( nrhs, b( k-1, 1 ), ldb )
441  CALL zgemv( 'Conjugate', k-2, nrhs, one, b, ldb,
442  \$ a( kcnext ), 1, one, b( k-1, 1 ), ldb )
443  CALL zlacgv( nrhs, b( k-1, 1 ), ldb )
444  END IF
445 *
446 * Multiply by the diagonal block if non-unit.
447 *
448  IF( nounit ) THEN
449  d11 = a( kc-1 )
450  d22 = a( kc+k-1 )
451  d12 = a( kc+k-2 )
452  d21 = dconjg( d12 )
453  DO 80 j = 1, nrhs
454  t1 = b( k-1, j )
455  t2 = b( k, j )
456  b( k-1, j ) = d11*t1 + d12*t2
457  b( k, j ) = d21*t1 + d22*t2
458  80 CONTINUE
459  END IF
460  kc = kcnext
461  k = k - 2
462  END IF
463  GO TO 70
464  90 CONTINUE
465 *
466 * Form B := L^H*B
467 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m))
468 * and L^H = inv(L(m))*P(m)* ... *inv(L(1))*P(1)
469 *
470  ELSE
471 *
472 * Loop forward applying the L-transformations.
473 *
474  k = 1
475  kc = 1
476  100 CONTINUE
477  IF( k.GT.n )
478  \$ GO TO 120
479 *
480 * 1 x 1 pivot block
481 *
482  IF( ipiv( k ).GT.0 ) THEN
483  IF( k.LT.n ) THEN
484 *
485 * Interchange if P(K) != I.
486 *
487  kp = ipiv( k )
488  IF( kp.NE.k )
489  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
490 *
491 * Apply the transformation
492 *
493  CALL zlacgv( nrhs, b( k, 1 ), ldb )
494  CALL zgemv( 'Conjugate', n-k, nrhs, one, b( k+1, 1 ),
495  \$ ldb, a( kc+1 ), 1, one, b( k, 1 ), ldb )
496  CALL zlacgv( nrhs, b( k, 1 ), ldb )
497  END IF
498  IF( nounit )
499  \$ CALL zscal( nrhs, a( kc ), b( k, 1 ), ldb )
500  kc = kc + n - k + 1
501  k = k + 1
502 *
503 * 2 x 2 pivot block.
504 *
505  ELSE
506  kcnext = kc + n - k + 1
507  IF( k.LT.n-1 ) THEN
508 *
509 * Interchange if P(K) != I.
510 *
511  kp = abs( ipiv( k ) )
512  IF( kp.NE.k+1 )
513  \$ CALL zswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ),
514  \$ ldb )
515 *
516 * Apply the transformation
517 *
518  CALL zlacgv( nrhs, b( k+1, 1 ), ldb )
519  CALL zgemv( 'Conjugate', n-k-1, nrhs, one,
520  \$ b( k+2, 1 ), ldb, a( kcnext+1 ), 1, one,
521  \$ b( k+1, 1 ), ldb )
522  CALL zlacgv( nrhs, b( k+1, 1 ), ldb )
523 *
524  CALL zlacgv( nrhs, b( k, 1 ), ldb )
525  CALL zgemv( 'Conjugate', n-k-1, nrhs, one,
526  \$ b( k+2, 1 ), ldb, a( kc+2 ), 1, one,
527  \$ b( k, 1 ), ldb )
528  CALL zlacgv( nrhs, b( k, 1 ), ldb )
529  END IF
530 *
531 * Multiply by the diagonal block if non-unit.
532 *
533  IF( nounit ) THEN
534  d11 = a( kc )
535  d22 = a( kcnext )
536  d21 = a( kc+1 )
537  d12 = dconjg( d21 )
538  DO 110 j = 1, nrhs
539  t1 = b( k, j )
540  t2 = b( k+1, j )
541  b( k, j ) = d11*t1 + d12*t2
542  b( k+1, j ) = d21*t1 + d22*t2
543  110 CONTINUE
544  END IF
545  kc = kcnext + ( n-k )
546  k = k + 2
547  END IF
548  GO TO 100
549  120 CONTINUE
550  END IF
551 *
552  END IF
553  RETURN
554 *
555 * End of ZLAVHP
556 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:81
subroutine zscal(N, ZA, ZX, INCX)
ZSCAL
Definition: zscal.f:78
subroutine zgeru(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
ZGERU
Definition: zgeru.f:130
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:158
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:74
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