LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ clavsp()

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

CLAVSP

Purpose:
    CLAVSP  performs one of the matrix-vector operations
       x := A*x  or  x := A^T*x,
    where x is an N element vector and  A is one of the factors
    from the symmetric factorization computed by CSPTRF.
    CSPTRF produces a factorization of the form
         U * D * U^T     or     L * D * L^T,
    where U (or L) is a product of permutation and unit upper (lower)
    triangular matrices, U^T (or L^T) is the transpose of
    U (or L), and D is symmetric 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', CLAVSP multiplies either by U or U * D
    (or L or L * D).
    If TRANS = 'C' or 'c', CLAVSP multiplies either by U^T or D * U^T
    (or L^T or D * L^T ).
  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 = 'T' or 't'   x := A^T*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.
           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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 129 of file clavsp.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, cscal, cswap, xerbla
162* ..
163* .. Intrinsic Functions ..
164 INTRINSIC abs, 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, 'T' ) )
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( 'CLAVSP ', -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 = 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 = 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^T * B (transpose)
377*
378*-------------------------------------------------
379 ELSE
380*
381* Form B := U^T*B
382* where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
383* and U^T = inv(U^T(1))*P(1)* ... *inv(U^T(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 cgemv( 'Transpose', k-1, nrhs, one, b, ldb,
411 $ a( kc ), 1, one, b( k, 1 ), ldb )
412 END IF
413 IF( nounit )
414 $ CALL cscal( nrhs, a( kc+k-1 ), b( k, 1 ), ldb )
415 k = k - 1
416*
417* 2 x 2 pivot block.
418*
419 ELSE
420 kcnext = kc - ( k-1 )
421 IF( k.GT.2 ) THEN
422*
423* Interchange if P(K) != I.
424*
425 kp = abs( ipiv( k ) )
426 IF( kp.NE.k-1 )
427 $ CALL cswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ),
428 $ ldb )
429*
430* Apply the transformations.
431*
432 CALL cgemv( 'Transpose', k-2, nrhs, one, b, ldb,
433 $ a( kc ), 1, one, b( k, 1 ), ldb )
434*
435 CALL cgemv( 'Transpose', k-2, nrhs, one, b, ldb,
436 $ a( kcnext ), 1, one, b( k-1, 1 ), ldb )
437 END IF
438*
439* Multiply by the diagonal block if non-unit.
440*
441 IF( nounit ) THEN
442 d11 = a( kc-1 )
443 d22 = a( kc+k-1 )
444 d12 = a( kc+k-2 )
445 d21 = d12
446 DO 80 j = 1, nrhs
447 t1 = b( k-1, j )
448 t2 = b( k, j )
449 b( k-1, j ) = d11*t1 + d12*t2
450 b( k, j ) = d21*t1 + d22*t2
451 80 CONTINUE
452 END IF
453 kc = kcnext
454 k = k - 2
455 END IF
456 GO TO 70
457 90 CONTINUE
458*
459* Form B := L^T*B
460* where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m))
461* and L^T = inv(L(m))*P(m)* ... *inv(L(1))*P(1)
462*
463 ELSE
464*
465* Loop forward applying the L-transformations.
466*
467 k = 1
468 kc = 1
469 100 CONTINUE
470 IF( k.GT.n )
471 $ GO TO 120
472*
473* 1 x 1 pivot block
474*
475 IF( ipiv( k ).GT.0 ) THEN
476 IF( k.LT.n ) THEN
477*
478* Interchange if P(K) != I.
479*
480 kp = ipiv( k )
481 IF( kp.NE.k )
482 $ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
483*
484* Apply the transformation
485*
486 CALL cgemv( 'Transpose', n-k, nrhs, one, b( k+1, 1 ),
487 $ ldb, a( kc+1 ), 1, one, b( k, 1 ), ldb )
488 END IF
489 IF( nounit )
490 $ CALL cscal( nrhs, a( kc ), b( k, 1 ), ldb )
491 kc = kc + n - k + 1
492 k = k + 1
493*
494* 2 x 2 pivot block.
495*
496 ELSE
497 kcnext = kc + n - k + 1
498 IF( k.LT.n-1 ) THEN
499*
500* Interchange if P(K) != I.
501*
502 kp = abs( ipiv( k ) )
503 IF( kp.NE.k+1 )
504 $ CALL cswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ),
505 $ ldb )
506*
507* Apply the transformation
508*
509 CALL cgemv( 'Transpose', n-k-1, nrhs, one,
510 $ b( k+2, 1 ), ldb, a( kcnext+1 ), 1, one,
511 $ b( k+1, 1 ), ldb )
512*
513 CALL cgemv( 'Transpose', n-k-1, nrhs, one,
514 $ b( k+2, 1 ), ldb, a( kc+2 ), 1, one,
515 $ b( k, 1 ), ldb )
516 END IF
517*
518* Multiply by the diagonal block if non-unit.
519*
520 IF( nounit ) THEN
521 d11 = a( kc )
522 d22 = a( kcnext )
523 d21 = a( kc+1 )
524 d12 = d21
525 DO 110 j = 1, nrhs
526 t1 = b( k, j )
527 t2 = b( k+1, j )
528 b( k, j ) = d11*t1 + d12*t2
529 b( k+1, j ) = d21*t1 + d22*t2
530 110 CONTINUE
531 END IF
532 kc = kcnext + ( n-k )
533 k = k + 2
534 END IF
535 GO TO 100
536 120 CONTINUE
537 END IF
538*
539 END IF
540 RETURN
541*
542* End of CLAVSP
543*
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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