LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ clavhp()

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

CLAVHP

Purpose:
```    CLAVHP  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 CHPTRF.
CHPTRF 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', CLAVHP multiplies either by U or U * D
(or L or L * D).
If TRANS = 'C' or 'c', CLAVHP 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 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 CSPTRF or CHPTRF.
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 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 clavhp.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 A( * ), B( LDB, * )
143 * ..
144 *
145 * =====================================================================
146 *
147 * .. Parameters ..
148  COMPLEX ONE
149  parameter( one = ( 1.0e+0, 0.0e+0 ) )
150 * ..
151 * .. Local Scalars ..
152  LOGICAL NOUNIT
153  INTEGER J, K, KC, KCNEXT, KP
154  COMPLEX D11, D12, D21, D22, T1, T2
155 * ..
156 * .. External Functions ..
157  LOGICAL LSAME
158  EXTERNAL lsame
159 * ..
160 * .. External Subroutines ..
161  EXTERNAL cgemv, cgeru, clacgv, cscal, cswap, xerbla
162 * ..
163 * .. Intrinsic Functions ..
164  INTRINSIC abs, conjg, 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( 'CLAVHP ', -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 cscal( 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 cgeru( 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 cswap( 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 = conjg( 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 cgeru( k-1, nrhs, one, a( kc ), 1, b( k, 1 ),
269  \$ ldb, b( 1, 1 ), ldb )
270  CALL cgeru( 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 cswap( 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 cscal( 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 cgeru( 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 cswap( 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 = conjg( 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 cgeru( n-k, nrhs, one, a( kc+1 ), 1, b( k, 1 ),
357  \$ ldb, b( k+1, 1 ), ldb )
358  CALL cgeru( 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 cswap( 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 IF( k.LT.1 )
392  \$ GO TO 90
393  kc = kc - k
394 *
395 * 1 x 1 pivot block.
396 *
397  IF( ipiv( k ).GT.0 ) THEN
398  IF( k.GT.1 ) THEN
399 *
400 * Interchange if P(K) != I.
401 *
402  kp = ipiv( k )
403  IF( kp.NE.k )
404  \$ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
405 *
406 * Apply the transformation:
407 * y := y - B' * conjg(x)
408 * where x is a column of A and y is a row of B.
409 *
410  CALL clacgv( nrhs, b( k, 1 ), ldb )
411  CALL cgemv( 'Conjugate', k-1, nrhs, one, b, ldb,
412  \$ a( kc ), 1, one, b( k, 1 ), ldb )
413  CALL clacgv( nrhs, b( k, 1 ), ldb )
414  END IF
415  IF( nounit )
416  \$ CALL cscal( nrhs, a( kc+k-1 ), b( k, 1 ), ldb )
417  k = k - 1
418 *
419 * 2 x 2 pivot block.
420 *
421  ELSE
422  kcnext = kc - ( k-1 )
423  IF( k.GT.2 ) THEN
424 *
425 * Interchange if P(K) != I.
426 *
427  kp = abs( ipiv( k ) )
428  IF( kp.NE.k-1 )
429  \$ CALL cswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ),
430  \$ ldb )
431 *
432 * Apply the transformations.
433 *
434  CALL clacgv( nrhs, b( k, 1 ), ldb )
435  CALL cgemv( 'Conjugate', k-2, nrhs, one, b, ldb,
436  \$ a( kc ), 1, one, b( k, 1 ), ldb )
437  CALL clacgv( nrhs, b( k, 1 ), ldb )
438 *
439  CALL clacgv( nrhs, b( k-1, 1 ), ldb )
440  CALL cgemv( 'Conjugate', k-2, nrhs, one, b, ldb,
441  \$ a( kcnext ), 1, one, b( k-1, 1 ), ldb )
442  CALL clacgv( nrhs, b( k-1, 1 ), ldb )
443  END IF
444 *
445 * Multiply by the diagonal block if non-unit.
446 *
447  IF( nounit ) THEN
448  d11 = a( kc-1 )
449  d22 = a( kc+k-1 )
450  d12 = a( kc+k-2 )
451  d21 = conjg( d12 )
452  DO 80 j = 1, nrhs
453  t1 = b( k-1, j )
454  t2 = b( k, j )
455  b( k-1, j ) = d11*t1 + d12*t2
456  b( k, j ) = d21*t1 + d22*t2
457  80 CONTINUE
458  END IF
459  kc = kcnext
460  k = k - 2
461  END IF
462  GO TO 70
463  90 CONTINUE
464 *
465 * Form B := L^H*B
466 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m))
467 * and L^H = inv(L(m))*P(m)* ... *inv(L(1))*P(1)
468 *
469  ELSE
470 *
471 * Loop forward applying the L-transformations.
472 *
473  k = 1
474  kc = 1
475  100 CONTINUE
476  IF( k.GT.n )
477  \$ GO TO 120
478 *
479 * 1 x 1 pivot block
480 *
481  IF( ipiv( k ).GT.0 ) THEN
482  IF( k.LT.n ) THEN
483 *
484 * Interchange if P(K) != I.
485 *
486  kp = ipiv( k )
487  IF( kp.NE.k )
488  \$ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
489 *
490 * Apply the transformation
491 *
492  CALL clacgv( nrhs, b( k, 1 ), ldb )
493  CALL cgemv( 'Conjugate', n-k, nrhs, one, b( k+1, 1 ),
494  \$ ldb, a( kc+1 ), 1, one, b( k, 1 ), ldb )
495  CALL clacgv( nrhs, b( k, 1 ), ldb )
496  END IF
497  IF( nounit )
498  \$ CALL cscal( nrhs, a( kc ), b( k, 1 ), ldb )
499  kc = kc + n - k + 1
500  k = k + 1
501 *
502 * 2 x 2 pivot block.
503 *
504  ELSE
505  kcnext = kc + n - k + 1
506  IF( k.LT.n-1 ) THEN
507 *
508 * Interchange if P(K) != I.
509 *
510  kp = abs( ipiv( k ) )
511  IF( kp.NE.k+1 )
512  \$ CALL cswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ),
513  \$ ldb )
514 *
515 * Apply the transformation
516 *
517  CALL clacgv( nrhs, b( k+1, 1 ), ldb )
518  CALL cgemv( 'Conjugate', n-k-1, nrhs, one,
519  \$ b( k+2, 1 ), ldb, a( kcnext+1 ), 1, one,
520  \$ b( k+1, 1 ), ldb )
521  CALL clacgv( nrhs, b( k+1, 1 ), ldb )
522 *
523  CALL clacgv( nrhs, b( k, 1 ), ldb )
524  CALL cgemv( 'Conjugate', n-k-1, nrhs, one,
525  \$ b( k+2, 1 ), ldb, a( kc+2 ), 1, one,
526  \$ b( k, 1 ), ldb )
527  CALL clacgv( nrhs, b( k, 1 ), ldb )
528  END IF
529 *
530 * Multiply by the diagonal block if non-unit.
531 *
532  IF( nounit ) THEN
533  d11 = a( kc )
534  d22 = a( kcnext )
535  d21 = a( kc+1 )
536  d12 = conjg( d21 )
537  DO 110 j = 1, nrhs
538  t1 = b( k, j )
539  t2 = b( k+1, j )
540  b( k, j ) = d11*t1 + d12*t2
541  b( k+1, j ) = d21*t1 + d22*t2
542  110 CONTINUE
543  END IF
544  kc = kcnext + ( n-k )
545  k = k + 2
546  END IF
547  GO TO 100
548  120 CONTINUE
549  END IF
550 *
551  END IF
552  RETURN
553 *
554 * End of CLAVHP
555 *
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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