LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
clavsp.f
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1 *> \brief \b CLAVSP
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE CLAVSP( UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB,
12 * INFO )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER DIAG, TRANS, UPLO
16 * INTEGER INFO, LDB, N, NRHS
17 * ..
18 * .. Array Arguments ..
19 * INTEGER IPIV( * )
20 * COMPLEX A( * ), B( LDB, * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> CLAVSP performs one of the matrix-vector operations
30 *> x := A*x or x := A^T*x,
31 *> where x is an N element vector and A is one of the factors
32 *> from the symmetric factorization computed by CSPTRF.
33 *> CSPTRF produces a factorization of the form
34 *> U * D * U^T or L * D * L^T,
35 *> where U (or L) is a product of permutation and unit upper (lower)
36 *> triangular matrices, U^T (or L^T) is the transpose of
37 *> U (or L), and D is symmetric and block diagonal with 1 x 1 and
38 *> 2 x 2 diagonal blocks. The multipliers for the transformations
39 *> and the upper or lower triangular parts of the diagonal blocks
40 *> are stored columnwise in packed format in the linear array A.
41 *>
42 *> If TRANS = 'N' or 'n', CLAVSP multiplies either by U or U * D
43 *> (or L or L * D).
44 *> If TRANS = 'C' or 'c', CLAVSP multiplies either by U^T or D * U^T
45 *> (or L^T or D * L^T ).
46 *> \endverbatim
47 *
48 * Arguments:
49 * ==========
50 *
51 *> \verbatim
52 *> UPLO - CHARACTER*1
53 *> On entry, UPLO specifies whether the triangular matrix
54 *> stored in A is upper or lower triangular.
55 *> UPLO = 'U' or 'u' The matrix is upper triangular.
56 *> UPLO = 'L' or 'l' The matrix is lower triangular.
57 *> Unchanged on exit.
58 *>
59 *> TRANS - CHARACTER*1
60 *> On entry, TRANS specifies the operation to be performed as
61 *> follows:
62 *> TRANS = 'N' or 'n' x := A*x.
63 *> TRANS = 'T' or 't' x := A^T*x.
64 *> Unchanged on exit.
65 *>
66 *> DIAG - CHARACTER*1
67 *> On entry, DIAG specifies whether the diagonal blocks are
68 *> assumed to be unit matrices, as follows:
69 *> DIAG = 'U' or 'u' Diagonal blocks are unit matrices.
70 *> DIAG = 'N' or 'n' Diagonal blocks are non-unit.
71 *> Unchanged on exit.
72 *>
73 *> N - INTEGER
74 *> On entry, N specifies the order of the matrix A.
75 *> N must be at least zero.
76 *> Unchanged on exit.
77 *>
78 *> NRHS - INTEGER
79 *> On entry, NRHS specifies the number of right hand sides,
80 *> i.e., the number of vectors x to be multiplied by A.
81 *> NRHS must be at least zero.
82 *> Unchanged on exit.
83 *>
84 *> A - COMPLEX array, dimension( N*(N+1)/2 )
85 *> On entry, A contains a block diagonal matrix and the
86 *> multipliers of the transformations used to obtain it,
87 *> stored as a packed triangular matrix.
88 *> Unchanged on exit.
89 *>
90 *> IPIV - INTEGER array, dimension( N )
91 *> On entry, IPIV contains the vector of pivot indices as
92 *> determined by CSPTRF.
93 *> If IPIV( K ) = K, no interchange was done.
94 *> If IPIV( K ) <> K but IPIV( K ) > 0, then row K was inter-
95 *> changed with row IPIV( K ) and a 1 x 1 pivot block was used.
96 *> If IPIV( K ) < 0 and UPLO = 'U', then row K-1 was exchanged
97 *> with row | IPIV( K ) | and a 2 x 2 pivot block was used.
98 *> If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged
99 *> with row | IPIV( K ) | and a 2 x 2 pivot block was used.
100 *>
101 *> B - COMPLEX array, dimension( LDB, NRHS )
102 *> On entry, B contains NRHS vectors of length N.
103 *> On exit, B is overwritten with the product A * B.
104 *>
105 *> LDB - INTEGER
106 *> On entry, LDB contains the leading dimension of B as
107 *> declared in the calling program. LDB must be at least
108 *> max( 1, N ).
109 *> Unchanged on exit.
110 *>
111 *> INFO - INTEGER
112 *> INFO is the error flag.
113 *> On exit, a value of 0 indicates a successful exit.
114 *> A negative value, say -K, indicates that the K-th argument
115 *> has an illegal value.
116 *> \endverbatim
117 *
118 * Authors:
119 * ========
120 *
121 *> \author Univ. of Tennessee
122 *> \author Univ. of California Berkeley
123 *> \author Univ. of Colorado Denver
124 *> \author NAG Ltd.
125 *
126 *> \ingroup complex_lin
127 *
128 * =====================================================================
129  SUBROUTINE clavsp( UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB,
130  $ INFO )
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 *
544  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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 clavsp(UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, INFO)
CLAVSP
Definition: clavsp.f:131