LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
zlavsp.f
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1 *> \brief \b ZLAVSP
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 ZLAVSP( 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*16 A( * ), B( LDB, * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> ZLAVSP 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 ZSPTRF.
33 *> ZSPTRF 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', ZLAVSP multiplies either by U or U * D
43 *> (or L or L * D).
44 *> If TRANS = 'C' or 'c', ZLAVSP 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*16 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 ZSPTRF.
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*16 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 *> \date December 2016
127 *
128 *> \ingroup complex16_lin
129 *
130 * =====================================================================
131  SUBROUTINE zlavsp( UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB,
132  \$ INFO )
133 *
134 * -- LAPACK test routine (version 3.7.0) --
135 * -- LAPACK is a software package provided by Univ. of Tennessee, --
136 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
137 * December 2016
138 *
139 * .. Scalar Arguments ..
140  CHARACTER DIAG, TRANS, UPLO
141  INTEGER INFO, LDB, N, NRHS
142 * ..
143 * .. Array Arguments ..
144  INTEGER IPIV( * )
145  COMPLEX*16 A( * ), B( ldb, * )
146 * ..
147 *
148 * =====================================================================
149 *
150 * .. Parameters ..
151  COMPLEX*16 ONE
152  parameter( one = ( 1.0d+0, 0.0d+0 ) )
153 * ..
154 * .. Local Scalars ..
155  LOGICAL NOUNIT
156  INTEGER J, K, KC, KCNEXT, KP
157  COMPLEX*16 D11, D12, D21, D22, T1, T2
158 * ..
159 * .. External Functions ..
160  LOGICAL LSAME
161  EXTERNAL lsame
162 * ..
163 * .. External Subroutines ..
164  EXTERNAL xerbla, zgemv, zgeru, zscal, zswap
165 * ..
166 * .. Intrinsic Functions ..
167  INTRINSIC abs, max
168 * ..
169 * .. Executable Statements ..
170 *
171 * Test the input parameters.
172 *
173  info = 0
174  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
175  info = -1
176  ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.lsame( trans, 'T' ) )
177  \$ THEN
178  info = -2
179  ELSE IF( .NOT.lsame( diag, 'U' ) .AND. .NOT.lsame( diag, 'N' ) )
180  \$ THEN
181  info = -3
182  ELSE IF( n.LT.0 ) THEN
183  info = -4
184  ELSE IF( ldb.LT.max( 1, n ) ) THEN
185  info = -8
186  END IF
187  IF( info.NE.0 ) THEN
188  CALL xerbla( 'ZLAVSP ', -info )
189  RETURN
190  END IF
191 *
192 * Quick return if possible.
193 *
194  IF( n.EQ.0 )
195  \$ RETURN
196 *
197  nounit = lsame( diag, 'N' )
198 *------------------------------------------
199 *
200 * Compute B := A * B (No transpose)
201 *
202 *------------------------------------------
203  IF( lsame( trans, 'N' ) ) THEN
204 *
205 * Compute B := U*B
206 * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
207 *
208  IF( lsame( uplo, 'U' ) ) THEN
209 *
210 * Loop forward applying the transformations.
211 *
212  k = 1
213  kc = 1
214  10 CONTINUE
215  IF( k.GT.n )
216  \$ GO TO 30
217 *
218 * 1 x 1 pivot block
219 *
220  IF( ipiv( k ).GT.0 ) THEN
221 *
222 * Multiply by the diagonal element if forming U * D.
223 *
224  IF( nounit )
225  \$ CALL zscal( nrhs, a( kc+k-1 ), b( k, 1 ), ldb )
226 *
227 * Multiply by P(K) * inv(U(K)) if K > 1.
228 *
229  IF( k.GT.1 ) THEN
230 *
231 * Apply the transformation.
232 *
233  CALL zgeru( k-1, nrhs, one, a( kc ), 1, b( k, 1 ),
234  \$ ldb, b( 1, 1 ), ldb )
235 *
236 * Interchange if P(K) != I.
237 *
238  kp = ipiv( k )
239  IF( kp.NE.k )
240  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
241  END IF
242  kc = kc + k
243  k = k + 1
244  ELSE
245 *
246 * 2 x 2 pivot block
247 *
248  kcnext = kc + k
249 *
250 * Multiply by the diagonal block if forming U * D.
251 *
252  IF( nounit ) THEN
253  d11 = a( kcnext-1 )
254  d22 = a( kcnext+k )
255  d12 = a( kcnext+k-1 )
256  d21 = d12
257  DO 20 j = 1, nrhs
258  t1 = b( k, j )
259  t2 = b( k+1, j )
260  b( k, j ) = d11*t1 + d12*t2
261  b( k+1, j ) = d21*t1 + d22*t2
262  20 CONTINUE
263  END IF
264 *
265 * Multiply by P(K) * inv(U(K)) if K > 1.
266 *
267  IF( k.GT.1 ) THEN
268 *
269 * Apply the transformations.
270 *
271  CALL zgeru( k-1, nrhs, one, a( kc ), 1, b( k, 1 ),
272  \$ ldb, b( 1, 1 ), ldb )
273  CALL zgeru( k-1, nrhs, one, a( kcnext ), 1,
274  \$ b( k+1, 1 ), ldb, b( 1, 1 ), ldb )
275 *
276 * Interchange if P(K) != I.
277 *
278  kp = abs( ipiv( k ) )
279  IF( kp.NE.k )
280  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
281  END IF
282  kc = kcnext + k + 1
283  k = k + 2
284  END IF
285  GO TO 10
286  30 CONTINUE
287 *
288 * Compute B := L*B
289 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) .
290 *
291  ELSE
292 *
293 * Loop backward applying the transformations to B.
294 *
295  k = n
296  kc = n*( n+1 ) / 2 + 1
297  40 CONTINUE
298  IF( k.LT.1 )
299  \$ GO TO 60
300  kc = kc - ( n-k+1 )
301 *
302 * Test the pivot index. If greater than zero, a 1 x 1
303 * pivot was used, otherwise a 2 x 2 pivot was used.
304 *
305  IF( ipiv( k ).GT.0 ) THEN
306 *
307 * 1 x 1 pivot block:
308 *
309 * Multiply by the diagonal element if forming L * D.
310 *
311  IF( nounit )
312  \$ CALL zscal( nrhs, a( kc ), b( k, 1 ), ldb )
313 *
314 * Multiply by P(K) * inv(L(K)) if K < N.
315 *
316  IF( k.NE.n ) THEN
317  kp = ipiv( k )
318 *
319 * Apply the transformation.
320 *
321  CALL zgeru( n-k, nrhs, one, a( kc+1 ), 1, b( k, 1 ),
322  \$ ldb, b( k+1, 1 ), ldb )
323 *
324 * Interchange if a permutation was applied at the
325 * K-th step of the factorization.
326 *
327  IF( kp.NE.k )
328  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
329  END IF
330  k = k - 1
331 *
332  ELSE
333 *
334 * 2 x 2 pivot block:
335 *
336  kcnext = kc - ( n-k+2 )
337 *
338 * Multiply by the diagonal block if forming L * D.
339 *
340  IF( nounit ) THEN
341  d11 = a( kcnext )
342  d22 = a( kc )
343  d21 = a( kcnext+1 )
344  d12 = d21
345  DO 50 j = 1, nrhs
346  t1 = b( k-1, j )
347  t2 = b( k, j )
348  b( k-1, j ) = d11*t1 + d12*t2
349  b( k, j ) = d21*t1 + d22*t2
350  50 CONTINUE
351  END IF
352 *
353 * Multiply by P(K) * inv(L(K)) if K < N.
354 *
355  IF( k.NE.n ) THEN
356 *
357 * Apply the transformation.
358 *
359  CALL zgeru( n-k, nrhs, one, a( kc+1 ), 1, b( k, 1 ),
360  \$ ldb, b( k+1, 1 ), ldb )
361  CALL zgeru( n-k, nrhs, one, a( kcnext+2 ), 1,
362  \$ b( k-1, 1 ), ldb, b( k+1, 1 ), ldb )
363 *
364 * Interchange if a permutation was applied at the
365 * K-th step of the factorization.
366 *
367  kp = abs( ipiv( k ) )
368  IF( kp.NE.k )
369  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
370  END IF
371  kc = kcnext
372  k = k - 2
373  END IF
374  GO TO 40
375  60 CONTINUE
376  END IF
377 *-------------------------------------------------
378 *
379 * Compute B := A^T * B (transpose)
380 *
381 *-------------------------------------------------
382  ELSE
383 *
384 * Form B := U^T*B
385 * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
386 * and U^T = inv(U^T(1))*P(1)* ... *inv(U^T(m))*P(m)
387 *
388  IF( lsame( uplo, 'U' ) ) THEN
389 *
390 * Loop backward applying the transformations.
391 *
392  k = n
393  kc = n*( n+1 ) / 2 + 1
394  70 CONTINUE
395  IF( k.LT.1 )
396  \$ GO TO 90
397  kc = kc - k
398 *
399 * 1 x 1 pivot block.
400 *
401  IF( ipiv( k ).GT.0 ) THEN
402  IF( k.GT.1 ) THEN
403 *
404 * Interchange if P(K) != I.
405 *
406  kp = ipiv( k )
407  IF( kp.NE.k )
408  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
409 *
410 * Apply the transformation:
411 * y := y - B' * conjg(x)
412 * where x is a column of A and y is a row of B.
413 *
414  CALL zgemv( 'Transpose', k-1, nrhs, one, b, ldb,
415  \$ a( kc ), 1, one, b( k, 1 ), ldb )
416  END IF
417  IF( nounit )
418  \$ CALL zscal( nrhs, a( kc+k-1 ), b( k, 1 ), ldb )
419  k = k - 1
420 *
421 * 2 x 2 pivot block.
422 *
423  ELSE
424  kcnext = kc - ( k-1 )
425  IF( k.GT.2 ) THEN
426 *
427 * Interchange if P(K) != I.
428 *
429  kp = abs( ipiv( k ) )
430  IF( kp.NE.k-1 )
431  \$ CALL zswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ),
432  \$ ldb )
433 *
434 * Apply the transformations.
435 *
436  CALL zgemv( 'Transpose', k-2, nrhs, one, b, ldb,
437  \$ a( kc ), 1, one, b( k, 1 ), ldb )
438 *
439  CALL zgemv( 'Transpose', k-2, nrhs, one, b, ldb,
440  \$ a( kcnext ), 1, one, b( k-1, 1 ), ldb )
441  END IF
442 *
443 * Multiply by the diagonal block if non-unit.
444 *
445  IF( nounit ) THEN
446  d11 = a( kc-1 )
447  d22 = a( kc+k-1 )
448  d12 = a( kc+k-2 )
449  d21 = d12
450  DO 80 j = 1, nrhs
451  t1 = b( k-1, j )
452  t2 = b( k, j )
453  b( k-1, j ) = d11*t1 + d12*t2
454  b( k, j ) = d21*t1 + d22*t2
455  80 CONTINUE
456  END IF
457  kc = kcnext
458  k = k - 2
459  END IF
460  GO TO 70
461  90 CONTINUE
462 *
463 * Form B := L^T*B
464 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m))
465 * and L^T = inv(L(m))*P(m)* ... *inv(L(1))*P(1)
466 *
467  ELSE
468 *
469 * Loop forward applying the L-transformations.
470 *
471  k = 1
472  kc = 1
473  100 CONTINUE
474  IF( k.GT.n )
475  \$ GO TO 120
476 *
477 * 1 x 1 pivot block
478 *
479  IF( ipiv( k ).GT.0 ) THEN
480  IF( k.LT.n ) THEN
481 *
482 * Interchange if P(K) != I.
483 *
484  kp = ipiv( k )
485  IF( kp.NE.k )
486  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
487 *
488 * Apply the transformation
489 *
490  CALL zgemv( 'Transpose', n-k, nrhs, one, b( k+1, 1 ),
491  \$ ldb, a( kc+1 ), 1, one, b( k, 1 ), ldb )
492  END IF
493  IF( nounit )
494  \$ CALL zscal( nrhs, a( kc ), b( k, 1 ), ldb )
495  kc = kc + n - k + 1
496  k = k + 1
497 *
498 * 2 x 2 pivot block.
499 *
500  ELSE
501  kcnext = kc + n - k + 1
502  IF( k.LT.n-1 ) THEN
503 *
504 * Interchange if P(K) != I.
505 *
506  kp = abs( ipiv( k ) )
507  IF( kp.NE.k+1 )
508  \$ CALL zswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ),
509  \$ ldb )
510 *
511 * Apply the transformation
512 *
513  CALL zgemv( 'Transpose', n-k-1, nrhs, one,
514  \$ b( k+2, 1 ), ldb, a( kcnext+1 ), 1, one,
515  \$ b( k+1, 1 ), ldb )
516 *
517  CALL zgemv( 'Transpose', n-k-1, nrhs, one,
518  \$ b( k+2, 1 ), ldb, a( kc+2 ), 1, one,
519  \$ b( k, 1 ), ldb )
520  END IF
521 *
522 * Multiply by the diagonal block if non-unit.
523 *
524  IF( nounit ) THEN
525  d11 = a( kc )
526  d22 = a( kcnext )
527  d21 = a( kc+1 )
528  d12 = d21
529  DO 110 j = 1, nrhs
530  t1 = b( k, j )
531  t2 = b( k+1, j )
532  b( k, j ) = d11*t1 + d12*t2
533  b( k+1, j ) = d21*t1 + d22*t2
534  110 CONTINUE
535  END IF
536  kc = kcnext + ( n-k )
537  k = k + 2
538  END IF
539  GO TO 100
540  120 CONTINUE
541  END IF
542 *
543  END IF
544  RETURN
545 *
546 * End of ZLAVSP
547 *
548  END
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:83
subroutine zscal(N, ZA, ZX, INCX)
ZSCAL
Definition: zscal.f:80
subroutine zgeru(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
ZGERU
Definition: zgeru.f:132
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zlavsp(UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, INFO)
ZLAVSP
Definition: zlavsp.f:133
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:160