LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ slavsy_rook()

 subroutine slavsy_rook ( character UPLO, character TRANS, character DIAG, integer N, integer NRHS, real, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, real, dimension( ldb, * ) B, integer LDB, integer INFO )

SLAVSY_ROOK

Purpose:
``` SLAVSY_ROOK  performs one of the matrix-vector operations
x := A*x  or  x := A'*x,
where x is an N element vector and A is one of the factors
from the block U*D*U' or L*D*L' factorization computed by SSYTRF_ROOK.

If TRANS = 'N', multiplies by U  or U * D  (or L  or L * D)
If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L')
If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L')```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the factor stored in A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular``` [in] TRANS ``` TRANS is CHARACTER*1 Specifies the operation to be performed: = 'N': x := A*x = 'T': x := A'*x = 'C': x := A'*x``` [in] DIAG ``` DIAG is CHARACTER*1 Specifies whether or not the diagonal blocks are unit matrices. If the diagonal blocks are assumed to be unit, then A = U or A = L, otherwise A = U*D or A = L*D. = 'U': Diagonal blocks are assumed to be unit matrices. = 'N': Diagonal blocks are assumed to be non-unit matrices.``` [in] N ``` N is INTEGER The number of rows and columns of the matrix A. N >= 0.``` [in] NRHS ``` NRHS is INTEGER The number of right hand sides, i.e., the number of vectors x to be multiplied by A. NRHS >= 0.``` [in] A ``` A is REAL array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by SSYTRF_ROOK. Stored as a 2-D triangular matrix.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D, as determined by SSYTRF_ROOK. If UPLO = 'U': If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. (If IPIV( k ) = k, no interchange was done). If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were inerchaged, D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L': If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. (If IPIV( k ) = k, no interchange was done). If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were inerchaged, D(k:k+1,k:k+1) is a 2-by-2 diagonal block.``` [in,out] B ``` B is REAL array, dimension (LDB,NRHS) On entry, B contains NRHS vectors of length N. On exit, B is overwritten with the product A * B.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -k, the k-th argument had an illegal value```

Definition at line 155 of file slavsy_rook.f.

157 *
158 * -- LAPACK test routine --
159 * -- LAPACK is a software package provided by Univ. of Tennessee, --
160 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
161 *
162 * .. Scalar Arguments ..
163  CHARACTER DIAG, TRANS, UPLO
164  INTEGER INFO, LDA, LDB, N, NRHS
165 * ..
166 * .. Array Arguments ..
167  INTEGER IPIV( * )
168  REAL A( LDA, * ), B( LDB, * )
169 * ..
170 *
171 * =====================================================================
172 *
173 * .. Parameters ..
174  REAL ONE
175  parameter( one = 1.0e+0 )
176 * ..
177 * .. Local Scalars ..
178  LOGICAL NOUNIT
179  INTEGER J, K, KP
180  REAL D11, D12, D21, D22, T1, T2
181 * ..
182 * .. External Functions ..
183  LOGICAL LSAME
184  EXTERNAL lsame
185 * ..
186 * .. External Subroutines ..
187  EXTERNAL sgemv, sger, sscal, sswap, xerbla
188 * ..
189 * .. Intrinsic Functions ..
190  INTRINSIC abs, max
191 * ..
192 * .. Executable Statements ..
193 *
194 * Test the input parameters.
195 *
196  info = 0
197  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
198  info = -1
199  ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.
200  \$ lsame( trans, 'T' ) .AND. .NOT.lsame( trans, 'C' ) ) THEN
201  info = -2
202  ELSE IF( .NOT.lsame( diag, 'U' ) .AND. .NOT.lsame( diag, 'N' ) )
203  \$ THEN
204  info = -3
205  ELSE IF( n.LT.0 ) THEN
206  info = -4
207  ELSE IF( lda.LT.max( 1, n ) ) THEN
208  info = -6
209  ELSE IF( ldb.LT.max( 1, n ) ) THEN
210  info = -9
211  END IF
212  IF( info.NE.0 ) THEN
213  CALL xerbla( 'SLAVSY_ROOK ', -info )
214  RETURN
215  END IF
216 *
217 * Quick return if possible.
218 *
219  IF( n.EQ.0 )
220  \$ RETURN
221 *
222  nounit = lsame( diag, 'N' )
223 *------------------------------------------
224 *
225 * Compute B := A * B (No transpose)
226 *
227 *------------------------------------------
228  IF( lsame( trans, 'N' ) ) THEN
229 *
230 * Compute B := U*B
231 * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
232 *
233  IF( lsame( uplo, 'U' ) ) THEN
234 *
235 * Loop forward applying the transformations.
236 *
237  k = 1
238  10 CONTINUE
239  IF( k.GT.n )
240  \$ GO TO 30
241  IF( ipiv( k ).GT.0 ) THEN
242 *
243 * 1 x 1 pivot block
244 *
245 * Multiply by the diagonal element if forming U * D.
246 *
247  IF( nounit )
248  \$ CALL sscal( nrhs, a( k, k ), b( k, 1 ), ldb )
249 *
250 * Multiply by P(K) * inv(U(K)) if K > 1.
251 *
252  IF( k.GT.1 ) THEN
253 *
254 * Apply the transformation.
255 *
256  CALL sger( k-1, nrhs, one, a( 1, k ), 1, b( k, 1 ),
257  \$ ldb, b( 1, 1 ), ldb )
258 *
259 * Interchange if P(K) .ne. I.
260 *
261  kp = ipiv( k )
262  IF( kp.NE.k )
263  \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
264  END IF
265  k = k + 1
266  ELSE
267 *
268 * 2 x 2 pivot block
269 *
270 * Multiply by the diagonal block if forming U * D.
271 *
272  IF( nounit ) THEN
273  d11 = a( k, k )
274  d22 = a( k+1, k+1 )
275  d12 = a( k, k+1 )
276  d21 = d12
277  DO 20 j = 1, nrhs
278  t1 = b( k, j )
279  t2 = b( k+1, j )
280  b( k, j ) = d11*t1 + d12*t2
281  b( k+1, j ) = d21*t1 + d22*t2
282  20 CONTINUE
283  END IF
284 *
285 * Multiply by P(K) * inv(U(K)) if K > 1.
286 *
287  IF( k.GT.1 ) THEN
288 *
289 * Apply the transformations.
290 *
291  CALL sger( k-1, nrhs, one, a( 1, k ), 1, b( k, 1 ),
292  \$ ldb, b( 1, 1 ), ldb )
293  CALL sger( k-1, nrhs, one, a( 1, k+1 ), 1,
294  \$ b( k+1, 1 ), ldb, b( 1, 1 ), ldb )
295 *
296 * Interchange if a permutation was applied at the
297 * K-th step of the factorization.
298 *
299 * Swap the first of pair with IMAXth
300 *
301  kp = abs( ipiv( k ) )
302  IF( kp.NE.k )
303  \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
304 *
305 * NOW swap the first of pair with Pth
306 *
307  kp = abs( ipiv( k+1 ) )
308  IF( kp.NE.k+1 )
309  \$ CALL sswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ),
310  \$ ldb )
311  END IF
312  k = k + 2
313  END IF
314  GO TO 10
315  30 CONTINUE
316 *
317 * Compute B := L*B
318 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) .
319 *
320  ELSE
321 *
322 * Loop backward applying the transformations to B.
323 *
324  k = n
325  40 CONTINUE
326  IF( k.LT.1 )
327  \$ GO TO 60
328 *
329 * Test the pivot index. If greater than zero, a 1 x 1
330 * pivot was used, otherwise a 2 x 2 pivot was used.
331 *
332  IF( ipiv( k ).GT.0 ) THEN
333 *
334 * 1 x 1 pivot block:
335 *
336 * Multiply by the diagonal element if forming L * D.
337 *
338  IF( nounit )
339  \$ CALL sscal( nrhs, a( k, k ), b( k, 1 ), ldb )
340 *
341 * Multiply by P(K) * inv(L(K)) if K < N.
342 *
343  IF( k.NE.n ) THEN
344  kp = ipiv( k )
345 *
346 * Apply the transformation.
347 *
348  CALL sger( n-k, nrhs, one, a( k+1, k ), 1, b( k, 1 ),
349  \$ ldb, b( k+1, 1 ), ldb )
350 *
351 * Interchange if a permutation was applied at the
352 * K-th step of the factorization.
353 *
354  IF( kp.NE.k )
355  \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
356  END IF
357  k = k - 1
358 *
359  ELSE
360 *
361 * 2 x 2 pivot block:
362 *
363 * Multiply by the diagonal block if forming L * D.
364 *
365  IF( nounit ) THEN
366  d11 = a( k-1, k-1 )
367  d22 = a( k, k )
368  d21 = a( k, k-1 )
369  d12 = d21
370  DO 50 j = 1, nrhs
371  t1 = b( k-1, j )
372  t2 = b( k, j )
373  b( k-1, j ) = d11*t1 + d12*t2
374  b( k, j ) = d21*t1 + d22*t2
375  50 CONTINUE
376  END IF
377 *
378 * Multiply by P(K) * inv(L(K)) if K < N.
379 *
380  IF( k.NE.n ) THEN
381 *
382 * Apply the transformation.
383 *
384  CALL sger( n-k, nrhs, one, a( k+1, k ), 1, b( k, 1 ),
385  \$ ldb, b( k+1, 1 ), ldb )
386  CALL sger( n-k, nrhs, one, a( k+1, k-1 ), 1,
387  \$ b( k-1, 1 ), ldb, b( k+1, 1 ), ldb )
388 *
389 * Interchange if a permutation was applied at the
390 * K-th step of the factorization.
391 *
392 * Swap the second of pair with IMAXth
393 *
394  kp = abs( ipiv( k ) )
395  IF( kp.NE.k )
396  \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
397 *
398 * NOW swap the first of pair with Pth
399 *
400  kp = abs( ipiv( k-1 ) )
401  IF( kp.NE.k-1 )
402  \$ CALL sswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ),
403  \$ ldb )
404  END IF
405  k = k - 2
406  END IF
407  GO TO 40
408  60 CONTINUE
409  END IF
410 *----------------------------------------
411 *
412 * Compute B := A' * B (transpose)
413 *
414 *----------------------------------------
415  ELSE
416 *
417 * Form B := U'*B
418 * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
419 * and U' = inv(U'(1))*P(1)* ... *inv(U'(m))*P(m)
420 *
421  IF( lsame( uplo, 'U' ) ) THEN
422 *
423 * Loop backward applying the transformations.
424 *
425  k = n
426  70 CONTINUE
427  IF( k.LT.1 )
428  \$ GO TO 90
429 *
430 * 1 x 1 pivot block.
431 *
432  IF( ipiv( k ).GT.0 ) THEN
433  IF( k.GT.1 ) THEN
434 *
435 * Interchange if P(K) .ne. I.
436 *
437  kp = ipiv( k )
438  IF( kp.NE.k )
439  \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
440 *
441 * Apply the transformation
442 *
443  CALL sgemv( 'Transpose', k-1, nrhs, one, b, ldb,
444  \$ a( 1, k ), 1, one, b( k, 1 ), ldb )
445  END IF
446  IF( nounit )
447  \$ CALL sscal( nrhs, a( k, k ), b( k, 1 ), ldb )
448  k = k - 1
449 *
450 * 2 x 2 pivot block.
451 *
452  ELSE
453  IF( k.GT.2 ) THEN
454 *
455 * Swap the second of pair with Pth
456 *
457  kp = abs( ipiv( k ) )
458  IF( kp.NE.k )
459  \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
460 *
461 * Now swap the first of pair with IMAX(r)th
462 *
463  kp = abs( ipiv( k-1 ) )
464  IF( kp.NE.k-1 )
465  \$ CALL sswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ),
466  \$ ldb )
467 *
468 * Apply the transformations
469 *
470  CALL sgemv( 'Transpose', k-2, nrhs, one, b, ldb,
471  \$ a( 1, k ), 1, one, b( k, 1 ), ldb )
472  CALL sgemv( 'Transpose', k-2, nrhs, one, b, ldb,
473  \$ a( 1, k-1 ), 1, one, b( k-1, 1 ), ldb )
474  END IF
475 *
476 * Multiply by the diagonal block if non-unit.
477 *
478  IF( nounit ) THEN
479  d11 = a( k-1, k-1 )
480  d22 = a( k, k )
481  d12 = a( k-1, k )
482  d21 = d12
483  DO 80 j = 1, nrhs
484  t1 = b( k-1, j )
485  t2 = b( k, j )
486  b( k-1, j ) = d11*t1 + d12*t2
487  b( k, j ) = d21*t1 + d22*t2
488  80 CONTINUE
489  END IF
490  k = k - 2
491  END IF
492  GO TO 70
493  90 CONTINUE
494 *
495 * Form B := L'*B
496 * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m))
497 * and L' = inv(L'(m))*P(m)* ... *inv(L'(1))*P(1)
498 *
499  ELSE
500 *
501 * Loop forward applying the L-transformations.
502 *
503  k = 1
504  100 CONTINUE
505  IF( k.GT.n )
506  \$ GO TO 120
507 *
508 * 1 x 1 pivot block
509 *
510  IF( ipiv( k ).GT.0 ) THEN
511  IF( k.LT.n ) THEN
512 *
513 * Interchange if P(K) .ne. I.
514 *
515  kp = ipiv( k )
516  IF( kp.NE.k )
517  \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
518 *
519 * Apply the transformation
520 *
521  CALL sgemv( 'Transpose', n-k, nrhs, one, b( k+1, 1 ),
522  \$ ldb, a( k+1, k ), 1, one, b( k, 1 ), ldb )
523  END IF
524  IF( nounit )
525  \$ CALL sscal( nrhs, a( k, k ), b( k, 1 ), ldb )
526  k = k + 1
527 *
528 * 2 x 2 pivot block.
529 *
530  ELSE
531  IF( k.LT.n-1 ) THEN
532 *
533 * Swap the first of pair with Pth
534 *
535  kp = abs( ipiv( k ) )
536  IF( kp.NE.k )
537  \$ CALL sswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
538 *
539 * Now swap the second of pair with IMAX(r)th
540 *
541  kp = abs( ipiv( k+1 ) )
542  IF( kp.NE.k+1 )
543  \$ CALL sswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ),
544  \$ ldb )
545 *
546 * Apply the transformation
547 *
548  CALL sgemv( 'Transpose', n-k-1, nrhs, one,
549  \$ b( k+2, 1 ), ldb, a( k+2, k+1 ), 1, one,
550  \$ b( k+1, 1 ), ldb )
551  CALL sgemv( 'Transpose', n-k-1, nrhs, one,
552  \$ b( k+2, 1 ), ldb, a( k+2, k ), 1, one,
553  \$ b( k, 1 ), ldb )
554  END IF
555 *
556 * Multiply by the diagonal block if non-unit.
557 *
558  IF( nounit ) THEN
559  d11 = a( k, k )
560  d22 = a( k+1, k+1 )
561  d21 = a( k+1, k )
562  d12 = d21
563  DO 110 j = 1, nrhs
564  t1 = b( k, j )
565  t2 = b( k+1, j )
566  b( k, j ) = d11*t1 + d12*t2
567  b( k+1, j ) = d21*t1 + d22*t2
568  110 CONTINUE
569  END IF
570  k = k + 2
571  END IF
572  GO TO 100
573  120 CONTINUE
574  END IF
575 *
576  END IF
577  RETURN
578 *
579 * End of SLAVSY_ROOK
580 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine sswap(N, SX, INCX, SY, INCY)
SSWAP
Definition: sswap.f:82
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
subroutine sger(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
SGER
Definition: sger.f:130
subroutine sgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGEMV
Definition: sgemv.f:156
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