 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ 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.```

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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