LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

◆ zhetri_rook()

 subroutine zhetri_rook ( character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex*16, dimension( * ) WORK, integer INFO )

ZHETRI_ROOK computes the inverse of HE matrix using the factorization obtained with the bounded Bunch-Kaufman ("rook") diagonal pivoting method.

Purpose:
``` ZHETRI_ROOK computes the inverse of a complex Hermitian indefinite matrix
A using the factorization A = U*D*U**H or A = L*D*L**H computed by
ZHETRF_ROOK.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**H; = 'L': Lower triangular, form is A = L*D*L**H.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in,out] A ``` A is COMPLEX*16 array, dimension (LDA,N) On entry, the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZHETRF_ROOK. On exit, if INFO = 0, the (Hermitian) inverse of the original matrix. If UPLO = 'U', the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced; if UPLO = 'L' the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.``` [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 ZHETRF_ROOK.``` [out] WORK ` WORK is COMPLEX*16 array, dimension (N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed.```
Contributors:
```  November 2013,  Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester```

Definition at line 127 of file zhetri_rook.f.

128 *
129 * -- LAPACK computational routine --
130 * -- LAPACK is a software package provided by Univ. of Tennessee, --
131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132 *
133 * .. Scalar Arguments ..
134  CHARACTER UPLO
135  INTEGER INFO, LDA, N
136 * ..
137 * .. Array Arguments ..
138  INTEGER IPIV( * )
139  COMPLEX*16 A( LDA, * ), WORK( * )
140 * ..
141 *
142 * =====================================================================
143 *
144 * .. Parameters ..
145  DOUBLE PRECISION ONE
146  COMPLEX*16 CONE, CZERO
147  parameter( one = 1.0d+0, cone = ( 1.0d+0, 0.0d+0 ),
148  \$ czero = ( 0.0d+0, 0.0d+0 ) )
149 * ..
150 * .. Local Scalars ..
151  LOGICAL UPPER
152  INTEGER J, K, KP, KSTEP
153  DOUBLE PRECISION AK, AKP1, D, T
154  COMPLEX*16 AKKP1, TEMP
155 * ..
156 * .. External Functions ..
157  LOGICAL LSAME
158  COMPLEX*16 ZDOTC
159  EXTERNAL lsame, zdotc
160 * ..
161 * .. External Subroutines ..
162  EXTERNAL zcopy, zhemv, zswap, xerbla
163 * ..
164 * .. Intrinsic Functions ..
165  INTRINSIC abs, dconjg, max, dble
166 * ..
167 * .. Executable Statements ..
168 *
169 * Test the input parameters.
170 *
171  info = 0
172  upper = lsame( uplo, 'U' )
173  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
174  info = -1
175  ELSE IF( n.LT.0 ) THEN
176  info = -2
177  ELSE IF( lda.LT.max( 1, n ) ) THEN
178  info = -4
179  END IF
180  IF( info.NE.0 ) THEN
181  CALL xerbla( 'ZHETRI_ROOK', -info )
182  RETURN
183  END IF
184 *
185 * Quick return if possible
186 *
187  IF( n.EQ.0 )
188  \$ RETURN
189 *
190 * Check that the diagonal matrix D is nonsingular.
191 *
192  IF( upper ) THEN
193 *
194 * Upper triangular storage: examine D from bottom to top
195 *
196  DO 10 info = n, 1, -1
197  IF( ipiv( info ).GT.0 .AND. a( info, info ).EQ.czero )
198  \$ RETURN
199  10 CONTINUE
200  ELSE
201 *
202 * Lower triangular storage: examine D from top to bottom.
203 *
204  DO 20 info = 1, n
205  IF( ipiv( info ).GT.0 .AND. a( info, info ).EQ.czero )
206  \$ RETURN
207  20 CONTINUE
208  END IF
209  info = 0
210 *
211  IF( upper ) THEN
212 *
213 * Compute inv(A) from the factorization A = U*D*U**H.
214 *
215 * K is the main loop index, increasing from 1 to N in steps of
216 * 1 or 2, depending on the size of the diagonal blocks.
217 *
218  k = 1
219  30 CONTINUE
220 *
221 * If K > N, exit from loop.
222 *
223  IF( k.GT.n )
224  \$ GO TO 70
225 *
226  IF( ipiv( k ).GT.0 ) THEN
227 *
228 * 1 x 1 diagonal block
229 *
230 * Invert the diagonal block.
231 *
232  a( k, k ) = one / dble( a( k, k ) )
233 *
234 * Compute column K of the inverse.
235 *
236  IF( k.GT.1 ) THEN
237  CALL zcopy( k-1, a( 1, k ), 1, work, 1 )
238  CALL zhemv( uplo, k-1, -cone, a, lda, work, 1, czero,
239  \$ a( 1, k ), 1 )
240  a( k, k ) = a( k, k ) - dble( zdotc( k-1, work, 1, a( 1,
241  \$ k ), 1 ) )
242  END IF
243  kstep = 1
244  ELSE
245 *
246 * 2 x 2 diagonal block
247 *
248 * Invert the diagonal block.
249 *
250  t = abs( a( k, k+1 ) )
251  ak = dble( a( k, k ) ) / t
252  akp1 = dble( a( k+1, k+1 ) ) / t
253  akkp1 = a( k, k+1 ) / t
254  d = t*( ak*akp1-one )
255  a( k, k ) = akp1 / d
256  a( k+1, k+1 ) = ak / d
257  a( k, k+1 ) = -akkp1 / d
258 *
259 * Compute columns K and K+1 of the inverse.
260 *
261  IF( k.GT.1 ) THEN
262  CALL zcopy( k-1, a( 1, k ), 1, work, 1 )
263  CALL zhemv( uplo, k-1, -cone, a, lda, work, 1, czero,
264  \$ a( 1, k ), 1 )
265  a( k, k ) = a( k, k ) - dble( zdotc( k-1, work, 1, a( 1,
266  \$ k ), 1 ) )
267  a( k, k+1 ) = a( k, k+1 ) -
268  \$ zdotc( k-1, a( 1, k ), 1, a( 1, k+1 ), 1 )
269  CALL zcopy( k-1, a( 1, k+1 ), 1, work, 1 )
270  CALL zhemv( uplo, k-1, -cone, a, lda, work, 1, czero,
271  \$ a( 1, k+1 ), 1 )
272  a( k+1, k+1 ) = a( k+1, k+1 ) -
273  \$ dble( zdotc( k-1, work, 1, a( 1, k+1 ),
274  \$ 1 ) )
275  END IF
276  kstep = 2
277  END IF
278 *
279  IF( kstep.EQ.1 ) THEN
280 *
281 * Interchange rows and columns K and IPIV(K) in the leading
282 * submatrix A(1:k,1:k)
283 *
284  kp = ipiv( k )
285  IF( kp.NE.k ) THEN
286 *
287  IF( kp.GT.1 )
288  \$ CALL zswap( kp-1, a( 1, k ), 1, a( 1, kp ), 1 )
289 *
290  DO 40 j = kp + 1, k - 1
291  temp = dconjg( a( j, k ) )
292  a( j, k ) = dconjg( a( kp, j ) )
293  a( kp, j ) = temp
294  40 CONTINUE
295 *
296  a( kp, k ) = dconjg( a( kp, k ) )
297 *
298  temp = a( k, k )
299  a( k, k ) = a( kp, kp )
300  a( kp, kp ) = temp
301  END IF
302  ELSE
303 *
304 * Interchange rows and columns K and K+1 with -IPIV(K) and
305 * -IPIV(K+1) in the leading submatrix A(k+1:n,k+1:n)
306 *
307 * (1) Interchange rows and columns K and -IPIV(K)
308 *
309  kp = -ipiv( k )
310  IF( kp.NE.k ) THEN
311 *
312  IF( kp.GT.1 )
313  \$ CALL zswap( kp-1, a( 1, k ), 1, a( 1, kp ), 1 )
314 *
315  DO 50 j = kp + 1, k - 1
316  temp = dconjg( a( j, k ) )
317  a( j, k ) = dconjg( a( kp, j ) )
318  a( kp, j ) = temp
319  50 CONTINUE
320 *
321  a( kp, k ) = dconjg( a( kp, k ) )
322 *
323  temp = a( k, k )
324  a( k, k ) = a( kp, kp )
325  a( kp, kp ) = temp
326 *
327  temp = a( k, k+1 )
328  a( k, k+1 ) = a( kp, k+1 )
329  a( kp, k+1 ) = temp
330  END IF
331 *
332 * (2) Interchange rows and columns K+1 and -IPIV(K+1)
333 *
334  k = k + 1
335  kp = -ipiv( k )
336  IF( kp.NE.k ) THEN
337 *
338  IF( kp.GT.1 )
339  \$ CALL zswap( kp-1, a( 1, k ), 1, a( 1, kp ), 1 )
340 *
341  DO 60 j = kp + 1, k - 1
342  temp = dconjg( a( j, k ) )
343  a( j, k ) = dconjg( a( kp, j ) )
344  a( kp, j ) = temp
345  60 CONTINUE
346 *
347  a( kp, k ) = dconjg( a( kp, k ) )
348 *
349  temp = a( k, k )
350  a( k, k ) = a( kp, kp )
351  a( kp, kp ) = temp
352  END IF
353  END IF
354 *
355  k = k + 1
356  GO TO 30
357  70 CONTINUE
358 *
359  ELSE
360 *
361 * Compute inv(A) from the factorization A = L*D*L**H.
362 *
363 * K is the main loop index, decreasing from N to 1 in steps of
364 * 1 or 2, depending on the size of the diagonal blocks.
365 *
366  k = n
367  80 CONTINUE
368 *
369 * If K < 1, exit from loop.
370 *
371  IF( k.LT.1 )
372  \$ GO TO 120
373 *
374  IF( ipiv( k ).GT.0 ) THEN
375 *
376 * 1 x 1 diagonal block
377 *
378 * Invert the diagonal block.
379 *
380  a( k, k ) = one / dble( a( k, k ) )
381 *
382 * Compute column K of the inverse.
383 *
384  IF( k.LT.n ) THEN
385  CALL zcopy( n-k, a( k+1, k ), 1, work, 1 )
386  CALL zhemv( uplo, n-k, -cone, a( k+1, k+1 ), lda, work,
387  \$ 1, czero, a( k+1, k ), 1 )
388  a( k, k ) = a( k, k ) - dble( zdotc( n-k, work, 1,
389  \$ a( k+1, k ), 1 ) )
390  END IF
391  kstep = 1
392  ELSE
393 *
394 * 2 x 2 diagonal block
395 *
396 * Invert the diagonal block.
397 *
398  t = abs( a( k, k-1 ) )
399  ak = dble( a( k-1, k-1 ) ) / t
400  akp1 = dble( a( k, k ) ) / t
401  akkp1 = a( k, k-1 ) / t
402  d = t*( ak*akp1-one )
403  a( k-1, k-1 ) = akp1 / d
404  a( k, k ) = ak / d
405  a( k, k-1 ) = -akkp1 / d
406 *
407 * Compute columns K-1 and K of the inverse.
408 *
409  IF( k.LT.n ) THEN
410  CALL zcopy( n-k, a( k+1, k ), 1, work, 1 )
411  CALL zhemv( uplo, n-k, -cone, a( k+1, k+1 ), lda, work,
412  \$ 1, czero, a( k+1, k ), 1 )
413  a( k, k ) = a( k, k ) - dble( zdotc( n-k, work, 1,
414  \$ a( k+1, k ), 1 ) )
415  a( k, k-1 ) = a( k, k-1 ) -
416  \$ zdotc( n-k, a( k+1, k ), 1, a( k+1, k-1 ),
417  \$ 1 )
418  CALL zcopy( n-k, a( k+1, k-1 ), 1, work, 1 )
419  CALL zhemv( uplo, n-k, -cone, a( k+1, k+1 ), lda, work,
420  \$ 1, czero, a( k+1, k-1 ), 1 )
421  a( k-1, k-1 ) = a( k-1, k-1 ) -
422  \$ dble( zdotc( n-k, work, 1, a( k+1, k-1 ),
423  \$ 1 ) )
424  END IF
425  kstep = 2
426  END IF
427 *
428  IF( kstep.EQ.1 ) THEN
429 *
430 * Interchange rows and columns K and IPIV(K) in the trailing
431 * submatrix A(k:n,k:n)
432 *
433  kp = ipiv( k )
434  IF( kp.NE.k ) THEN
435 *
436  IF( kp.LT.n )
437  \$ CALL zswap( n-kp, a( kp+1, k ), 1, a( kp+1, kp ), 1 )
438 *
439  DO 90 j = k + 1, kp - 1
440  temp = dconjg( a( j, k ) )
441  a( j, k ) = dconjg( a( kp, j ) )
442  a( kp, j ) = temp
443  90 CONTINUE
444 *
445  a( kp, k ) = dconjg( a( kp, k ) )
446 *
447  temp = a( k, k )
448  a( k, k ) = a( kp, kp )
449  a( kp, kp ) = temp
450  END IF
451  ELSE
452 *
453 * Interchange rows and columns K and K-1 with -IPIV(K) and
454 * -IPIV(K-1) in the trailing submatrix A(k-1:n,k-1:n)
455 *
456 * (1) Interchange rows and columns K and -IPIV(K)
457 *
458  kp = -ipiv( k )
459  IF( kp.NE.k ) THEN
460 *
461  IF( kp.LT.n )
462  \$ CALL zswap( n-kp, a( kp+1, k ), 1, a( kp+1, kp ), 1 )
463 *
464  DO 100 j = k + 1, kp - 1
465  temp = dconjg( a( j, k ) )
466  a( j, k ) = dconjg( a( kp, j ) )
467  a( kp, j ) = temp
468  100 CONTINUE
469 *
470  a( kp, k ) = dconjg( a( kp, k ) )
471 *
472  temp = a( k, k )
473  a( k, k ) = a( kp, kp )
474  a( kp, kp ) = temp
475 *
476  temp = a( k, k-1 )
477  a( k, k-1 ) = a( kp, k-1 )
478  a( kp, k-1 ) = temp
479  END IF
480 *
481 * (2) Interchange rows and columns K-1 and -IPIV(K-1)
482 *
483  k = k - 1
484  kp = -ipiv( k )
485  IF( kp.NE.k ) THEN
486 *
487  IF( kp.LT.n )
488  \$ CALL zswap( n-kp, a( kp+1, k ), 1, a( kp+1, kp ), 1 )
489 *
490  DO 110 j = k + 1, kp - 1
491  temp = dconjg( a( j, k ) )
492  a( j, k ) = dconjg( a( kp, j ) )
493  a( kp, j ) = temp
494  110 CONTINUE
495 *
496  a( kp, k ) = dconjg( a( kp, k ) )
497 *
498  temp = a( k, k )
499  a( k, k ) = a( kp, kp )
500  a( kp, kp ) = temp
501  END IF
502  END IF
503 *
504  k = k - 1
505  GO TO 80
506  120 CONTINUE
507  END IF
508 *
509  RETURN
510 *
511 * End of ZHETRI_ROOK
512 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:81
complex *16 function zdotc(N, ZX, INCX, ZY, INCY)
ZDOTC
Definition: zdotc.f:83
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:81
subroutine zhemv(UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZHEMV
Definition: zhemv.f:154
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