LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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zhetri.f
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1*> \brief \b ZHETRI
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetri.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZHETRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
22*
23* .. Scalar Arguments ..
24* CHARACTER UPLO
25* INTEGER INFO, LDA, N
26* ..
27* .. Array Arguments ..
28* INTEGER IPIV( * )
29* COMPLEX*16 A( LDA, * ), WORK( * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> ZHETRI computes the inverse of a complex Hermitian indefinite matrix
39*> A using the factorization A = U*D*U**H or A = L*D*L**H computed by
40*> ZHETRF.
41*> \endverbatim
42*
43* Arguments:
44* ==========
45*
46*> \param[in] UPLO
47*> \verbatim
48*> UPLO is CHARACTER*1
49*> Specifies whether the details of the factorization are stored
50*> as an upper or lower triangular matrix.
51*> = 'U': Upper triangular, form is A = U*D*U**H;
52*> = 'L': Lower triangular, form is A = L*D*L**H.
53*> \endverbatim
54*>
55*> \param[in] N
56*> \verbatim
57*> N is INTEGER
58*> The order of the matrix A. N >= 0.
59*> \endverbatim
60*>
61*> \param[in,out] A
62*> \verbatim
63*> A is COMPLEX*16 array, dimension (LDA,N)
64*> On entry, the block diagonal matrix D and the multipliers
65*> used to obtain the factor U or L as computed by ZHETRF.
66*>
67*> On exit, if INFO = 0, the (Hermitian) inverse of the original
68*> matrix. If UPLO = 'U', the upper triangular part of the
69*> inverse is formed and the part of A below the diagonal is not
70*> referenced; if UPLO = 'L' the lower triangular part of the
71*> inverse is formed and the part of A above the diagonal is
72*> not referenced.
73*> \endverbatim
74*>
75*> \param[in] LDA
76*> \verbatim
77*> LDA is INTEGER
78*> The leading dimension of the array A. LDA >= max(1,N).
79*> \endverbatim
80*>
81*> \param[in] IPIV
82*> \verbatim
83*> IPIV is INTEGER array, dimension (N)
84*> Details of the interchanges and the block structure of D
85*> as determined by ZHETRF.
86*> \endverbatim
87*>
88*> \param[out] WORK
89*> \verbatim
90*> WORK is COMPLEX*16 array, dimension (N)
91*> \endverbatim
92*>
93*> \param[out] INFO
94*> \verbatim
95*> INFO is INTEGER
96*> = 0: successful exit
97*> < 0: if INFO = -i, the i-th argument had an illegal value
98*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
99*> inverse could not be computed.
100*> \endverbatim
101*
102* Authors:
103* ========
104*
105*> \author Univ. of Tennessee
106*> \author Univ. of California Berkeley
107*> \author Univ. of Colorado Denver
108*> \author NAG Ltd.
109*
110*> \ingroup complex16HEcomputational
111*
112* =====================================================================
113 SUBROUTINE zhetri( UPLO, N, A, LDA, IPIV, WORK, INFO )
114*
115* -- LAPACK computational routine --
116* -- LAPACK is a software package provided by Univ. of Tennessee, --
117* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118*
119* .. Scalar Arguments ..
120 CHARACTER UPLO
121 INTEGER INFO, LDA, N
122* ..
123* .. Array Arguments ..
124 INTEGER IPIV( * )
125 COMPLEX*16 A( LDA, * ), WORK( * )
126* ..
127*
128* =====================================================================
129*
130* .. Parameters ..
131 DOUBLE PRECISION ONE
132 COMPLEX*16 CONE, ZERO
133 parameter( one = 1.0d+0, cone = ( 1.0d+0, 0.0d+0 ),
134 \$ zero = ( 0.0d+0, 0.0d+0 ) )
135* ..
136* .. Local Scalars ..
137 LOGICAL UPPER
138 INTEGER J, K, KP, KSTEP
139 DOUBLE PRECISION AK, AKP1, D, T
140 COMPLEX*16 AKKP1, TEMP
141* ..
142* .. External Functions ..
143 LOGICAL LSAME
144 COMPLEX*16 ZDOTC
145 EXTERNAL lsame, zdotc
146* ..
147* .. External Subroutines ..
148 EXTERNAL xerbla, zcopy, zhemv, zswap
149* ..
150* .. Intrinsic Functions ..
151 INTRINSIC abs, dble, dconjg, max
152* ..
153* .. Executable Statements ..
154*
155* Test the input parameters.
156*
157 info = 0
158 upper = lsame( uplo, 'U' )
159 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
160 info = -1
161 ELSE IF( n.LT.0 ) THEN
162 info = -2
163 ELSE IF( lda.LT.max( 1, n ) ) THEN
164 info = -4
165 END IF
166 IF( info.NE.0 ) THEN
167 CALL xerbla( 'ZHETRI', -info )
168 RETURN
169 END IF
170*
171* Quick return if possible
172*
173 IF( n.EQ.0 )
174 \$ RETURN
175*
176* Check that the diagonal matrix D is nonsingular.
177*
178 IF( upper ) THEN
179*
180* Upper triangular storage: examine D from bottom to top
181*
182 DO 10 info = n, 1, -1
183 IF( ipiv( info ).GT.0 .AND. a( info, info ).EQ.zero )
184 \$ RETURN
185 10 CONTINUE
186 ELSE
187*
188* Lower triangular storage: examine D from top to bottom.
189*
190 DO 20 info = 1, n
191 IF( ipiv( info ).GT.0 .AND. a( info, info ).EQ.zero )
192 \$ RETURN
193 20 CONTINUE
194 END IF
195 info = 0
196*
197 IF( upper ) THEN
198*
199* Compute inv(A) from the factorization A = U*D*U**H.
200*
201* K is the main loop index, increasing from 1 to N in steps of
202* 1 or 2, depending on the size of the diagonal blocks.
203*
204 k = 1
205 30 CONTINUE
206*
207* If K > N, exit from loop.
208*
209 IF( k.GT.n )
210 \$ GO TO 50
211*
212 IF( ipiv( k ).GT.0 ) THEN
213*
214* 1 x 1 diagonal block
215*
216* Invert the diagonal block.
217*
218 a( k, k ) = one / dble( a( k, k ) )
219*
220* Compute column K of the inverse.
221*
222 IF( k.GT.1 ) THEN
223 CALL zcopy( k-1, a( 1, k ), 1, work, 1 )
224 CALL zhemv( uplo, k-1, -cone, a, lda, work, 1, zero,
225 \$ a( 1, k ), 1 )
226 a( k, k ) = a( k, k ) - dble( zdotc( k-1, work, 1, a( 1,
227 \$ k ), 1 ) )
228 END IF
229 kstep = 1
230 ELSE
231*
232* 2 x 2 diagonal block
233*
234* Invert the diagonal block.
235*
236 t = abs( a( k, k+1 ) )
237 ak = dble( a( k, k ) ) / t
238 akp1 = dble( a( k+1, k+1 ) ) / t
239 akkp1 = a( k, k+1 ) / t
240 d = t*( ak*akp1-one )
241 a( k, k ) = akp1 / d
242 a( k+1, k+1 ) = ak / d
243 a( k, k+1 ) = -akkp1 / d
244*
245* Compute columns K and K+1 of the inverse.
246*
247 IF( k.GT.1 ) THEN
248 CALL zcopy( k-1, a( 1, k ), 1, work, 1 )
249 CALL zhemv( uplo, k-1, -cone, a, lda, work, 1, zero,
250 \$ a( 1, k ), 1 )
251 a( k, k ) = a( k, k ) - dble( zdotc( k-1, work, 1, a( 1,
252 \$ k ), 1 ) )
253 a( k, k+1 ) = a( k, k+1 ) -
254 \$ zdotc( k-1, a( 1, k ), 1, a( 1, k+1 ), 1 )
255 CALL zcopy( k-1, a( 1, k+1 ), 1, work, 1 )
256 CALL zhemv( uplo, k-1, -cone, a, lda, work, 1, zero,
257 \$ a( 1, k+1 ), 1 )
258 a( k+1, k+1 ) = a( k+1, k+1 ) -
259 \$ dble( zdotc( k-1, work, 1, a( 1, k+1 ),
260 \$ 1 ) )
261 END IF
262 kstep = 2
263 END IF
264*
265 kp = abs( ipiv( k ) )
266 IF( kp.NE.k ) THEN
267*
268* Interchange rows and columns K and KP in the leading
269* submatrix A(1:k+1,1:k+1)
270*
271 CALL zswap( kp-1, a( 1, k ), 1, a( 1, kp ), 1 )
272 DO 40 j = kp + 1, k - 1
273 temp = dconjg( a( j, k ) )
274 a( j, k ) = dconjg( a( kp, j ) )
275 a( kp, j ) = temp
276 40 CONTINUE
277 a( kp, k ) = dconjg( a( kp, k ) )
278 temp = a( k, k )
279 a( k, k ) = a( kp, kp )
280 a( kp, kp ) = temp
281 IF( kstep.EQ.2 ) THEN
282 temp = a( k, k+1 )
283 a( k, k+1 ) = a( kp, k+1 )
284 a( kp, k+1 ) = temp
285 END IF
286 END IF
287*
288 k = k + kstep
289 GO TO 30
290 50 CONTINUE
291*
292 ELSE
293*
294* Compute inv(A) from the factorization A = L*D*L**H.
295*
296* K is the main loop index, increasing from 1 to N in steps of
297* 1 or 2, depending on the size of the diagonal blocks.
298*
299 k = n
300 60 CONTINUE
301*
302* If K < 1, exit from loop.
303*
304 IF( k.LT.1 )
305 \$ GO TO 80
306*
307 IF( ipiv( k ).GT.0 ) THEN
308*
309* 1 x 1 diagonal block
310*
311* Invert the diagonal block.
312*
313 a( k, k ) = one / dble( a( k, k ) )
314*
315* Compute column K of the inverse.
316*
317 IF( k.LT.n ) THEN
318 CALL zcopy( n-k, a( k+1, k ), 1, work, 1 )
319 CALL zhemv( uplo, n-k, -cone, a( k+1, k+1 ), lda, work,
320 \$ 1, zero, a( k+1, k ), 1 )
321 a( k, k ) = a( k, k ) - dble( zdotc( n-k, work, 1,
322 \$ a( k+1, k ), 1 ) )
323 END IF
324 kstep = 1
325 ELSE
326*
327* 2 x 2 diagonal block
328*
329* Invert the diagonal block.
330*
331 t = abs( a( k, k-1 ) )
332 ak = dble( a( k-1, k-1 ) ) / t
333 akp1 = dble( a( k, k ) ) / t
334 akkp1 = a( k, k-1 ) / t
335 d = t*( ak*akp1-one )
336 a( k-1, k-1 ) = akp1 / d
337 a( k, k ) = ak / d
338 a( k, k-1 ) = -akkp1 / d
339*
340* Compute columns K-1 and K of the inverse.
341*
342 IF( k.LT.n ) THEN
343 CALL zcopy( n-k, a( k+1, k ), 1, work, 1 )
344 CALL zhemv( uplo, n-k, -cone, a( k+1, k+1 ), lda, work,
345 \$ 1, zero, a( k+1, k ), 1 )
346 a( k, k ) = a( k, k ) - dble( zdotc( n-k, work, 1,
347 \$ a( k+1, k ), 1 ) )
348 a( k, k-1 ) = a( k, k-1 ) -
349 \$ zdotc( n-k, a( k+1, k ), 1, a( k+1, k-1 ),
350 \$ 1 )
351 CALL zcopy( n-k, a( k+1, k-1 ), 1, work, 1 )
352 CALL zhemv( uplo, n-k, -cone, a( k+1, k+1 ), lda, work,
353 \$ 1, zero, a( k+1, k-1 ), 1 )
354 a( k-1, k-1 ) = a( k-1, k-1 ) -
355 \$ dble( zdotc( n-k, work, 1, a( k+1, k-1 ),
356 \$ 1 ) )
357 END IF
358 kstep = 2
359 END IF
360*
361 kp = abs( ipiv( k ) )
362 IF( kp.NE.k ) THEN
363*
364* Interchange rows and columns K and KP in the trailing
365* submatrix A(k-1:n,k-1:n)
366*
367 IF( kp.LT.n )
368 \$ CALL zswap( n-kp, a( kp+1, k ), 1, a( kp+1, kp ), 1 )
369 DO 70 j = k + 1, kp - 1
370 temp = dconjg( a( j, k ) )
371 a( j, k ) = dconjg( a( kp, j ) )
372 a( kp, j ) = temp
373 70 CONTINUE
374 a( kp, k ) = dconjg( a( kp, k ) )
375 temp = a( k, k )
376 a( k, k ) = a( kp, kp )
377 a( kp, kp ) = temp
378 IF( kstep.EQ.2 ) THEN
379 temp = a( k, k-1 )
380 a( k, k-1 ) = a( kp, k-1 )
381 a( kp, k-1 ) = temp
382 END IF
383 END IF
384*
385 k = k - kstep
386 GO TO 60
387 80 CONTINUE
388 END IF
389*
390 RETURN
391*
392* End of ZHETRI
393*
394 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:81
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
subroutine zhetri(UPLO, N, A, LDA, IPIV, WORK, INFO)
ZHETRI
Definition: zhetri.f:114