LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
zhetri.f
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1 *> \brief \b ZHETRI
2 *
3 * =========== DOCUMENTATION ===========
4 *
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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 *> \date November 2011
111 *
112 *> \ingroup complex16HEcomputational
113 *
114 * =====================================================================
115  SUBROUTINE zhetri( UPLO, N, A, LDA, IPIV, WORK, INFO )
116 *
117 * -- LAPACK computational routine (version 3.4.0) --
118 * -- LAPACK is a software package provided by Univ. of Tennessee, --
119 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
120 * November 2011
121 *
122 * .. Scalar Arguments ..
123  CHARACTER UPLO
124  INTEGER INFO, LDA, N
125 * ..
126 * .. Array Arguments ..
127  INTEGER IPIV( * )
128  COMPLEX*16 A( lda, * ), WORK( * )
129 * ..
130 *
131 * =====================================================================
132 *
133 * .. Parameters ..
134  DOUBLE PRECISION ONE
135  COMPLEX*16 CONE, ZERO
136  parameter ( one = 1.0d+0, cone = ( 1.0d+0, 0.0d+0 ),
137  \$ zero = ( 0.0d+0, 0.0d+0 ) )
138 * ..
139 * .. Local Scalars ..
140  LOGICAL UPPER
141  INTEGER J, K, KP, KSTEP
142  DOUBLE PRECISION AK, AKP1, D, T
143  COMPLEX*16 AKKP1, TEMP
144 * ..
145 * .. External Functions ..
146  LOGICAL LSAME
147  COMPLEX*16 ZDOTC
148  EXTERNAL lsame, zdotc
149 * ..
150 * .. External Subroutines ..
151  EXTERNAL xerbla, zcopy, zhemv, zswap
152 * ..
153 * .. Intrinsic Functions ..
154  INTRINSIC abs, dble, dconjg, max
155 * ..
156 * .. Executable Statements ..
157 *
158 * Test the input parameters.
159 *
160  info = 0
161  upper = lsame( uplo, 'U' )
162  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
163  info = -1
164  ELSE IF( n.LT.0 ) THEN
165  info = -2
166  ELSE IF( lda.LT.max( 1, n ) ) THEN
167  info = -4
168  END IF
169  IF( info.NE.0 ) THEN
170  CALL xerbla( 'ZHETRI', -info )
171  RETURN
172  END IF
173 *
174 * Quick return if possible
175 *
176  IF( n.EQ.0 )
177  \$ RETURN
178 *
179 * Check that the diagonal matrix D is nonsingular.
180 *
181  IF( upper ) THEN
182 *
183 * Upper triangular storage: examine D from bottom to top
184 *
185  DO 10 info = n, 1, -1
186  IF( ipiv( info ).GT.0 .AND. a( info, info ).EQ.zero )
187  \$ RETURN
188  10 CONTINUE
189  ELSE
190 *
191 * Lower triangular storage: examine D from top to bottom.
192 *
193  DO 20 info = 1, n
194  IF( ipiv( info ).GT.0 .AND. a( info, info ).EQ.zero )
195  \$ RETURN
196  20 CONTINUE
197  END IF
198  info = 0
199 *
200  IF( upper ) THEN
201 *
202 * Compute inv(A) from the factorization A = U*D*U**H.
203 *
204 * K is the main loop index, increasing from 1 to N in steps of
205 * 1 or 2, depending on the size of the diagonal blocks.
206 *
207  k = 1
208  30 CONTINUE
209 *
210 * If K > N, exit from loop.
211 *
212  IF( k.GT.n )
213  \$ GO TO 50
214 *
215  IF( ipiv( k ).GT.0 ) THEN
216 *
217 * 1 x 1 diagonal block
218 *
219 * Invert the diagonal block.
220 *
221  a( k, k ) = one / dble( a( k, k ) )
222 *
223 * Compute column K of the inverse.
224 *
225  IF( k.GT.1 ) THEN
226  CALL zcopy( k-1, a( 1, k ), 1, work, 1 )
227  CALL zhemv( uplo, k-1, -cone, a, lda, work, 1, zero,
228  \$ a( 1, k ), 1 )
229  a( k, k ) = a( k, k ) - dble( zdotc( k-1, work, 1, a( 1,
230  \$ k ), 1 ) )
231  END IF
232  kstep = 1
233  ELSE
234 *
235 * 2 x 2 diagonal block
236 *
237 * Invert the diagonal block.
238 *
239  t = abs( a( k, k+1 ) )
240  ak = dble( a( k, k ) ) / t
241  akp1 = dble( a( k+1, k+1 ) ) / t
242  akkp1 = a( k, k+1 ) / t
243  d = t*( ak*akp1-one )
244  a( k, k ) = akp1 / d
245  a( k+1, k+1 ) = ak / d
246  a( k, k+1 ) = -akkp1 / d
247 *
248 * Compute columns K and K+1 of the inverse.
249 *
250  IF( k.GT.1 ) THEN
251  CALL zcopy( k-1, a( 1, k ), 1, work, 1 )
252  CALL zhemv( uplo, k-1, -cone, a, lda, work, 1, zero,
253  \$ a( 1, k ), 1 )
254  a( k, k ) = a( k, k ) - dble( zdotc( k-1, work, 1, a( 1,
255  \$ k ), 1 ) )
256  a( k, k+1 ) = a( k, k+1 ) -
257  \$ zdotc( k-1, a( 1, k ), 1, a( 1, k+1 ), 1 )
258  CALL zcopy( k-1, a( 1, k+1 ), 1, work, 1 )
259  CALL zhemv( uplo, k-1, -cone, a, lda, work, 1, zero,
260  \$ a( 1, k+1 ), 1 )
261  a( k+1, k+1 ) = a( k+1, k+1 ) -
262  \$ dble( zdotc( k-1, work, 1, a( 1, k+1 ),
263  \$ 1 ) )
264  END IF
265  kstep = 2
266  END IF
267 *
268  kp = abs( ipiv( k ) )
269  IF( kp.NE.k ) THEN
270 *
271 * Interchange rows and columns K and KP in the leading
272 * submatrix A(1:k+1,1:k+1)
273 *
274  CALL zswap( kp-1, a( 1, k ), 1, a( 1, kp ), 1 )
275  DO 40 j = kp + 1, k - 1
276  temp = dconjg( a( j, k ) )
277  a( j, k ) = dconjg( a( kp, j ) )
278  a( kp, j ) = temp
279  40 CONTINUE
280  a( kp, k ) = dconjg( a( kp, k ) )
281  temp = a( k, k )
282  a( k, k ) = a( kp, kp )
283  a( kp, kp ) = temp
284  IF( kstep.EQ.2 ) THEN
285  temp = a( k, k+1 )
286  a( k, k+1 ) = a( kp, k+1 )
287  a( kp, k+1 ) = temp
288  END IF
289  END IF
290 *
291  k = k + kstep
292  GO TO 30
293  50 CONTINUE
294 *
295  ELSE
296 *
297 * Compute inv(A) from the factorization A = L*D*L**H.
298 *
299 * K is the main loop index, increasing from 1 to N in steps of
300 * 1 or 2, depending on the size of the diagonal blocks.
301 *
302  k = n
303  60 CONTINUE
304 *
305 * If K < 1, exit from loop.
306 *
307  IF( k.LT.1 )
308  \$ GO TO 80
309 *
310  IF( ipiv( k ).GT.0 ) THEN
311 *
312 * 1 x 1 diagonal block
313 *
314 * Invert the diagonal block.
315 *
316  a( k, k ) = one / dble( a( k, k ) )
317 *
318 * Compute column K of the inverse.
319 *
320  IF( k.LT.n ) THEN
321  CALL zcopy( n-k, a( k+1, k ), 1, work, 1 )
322  CALL zhemv( uplo, n-k, -cone, a( k+1, k+1 ), lda, work,
323  \$ 1, zero, a( k+1, k ), 1 )
324  a( k, k ) = a( k, k ) - dble( zdotc( n-k, work, 1,
325  \$ a( k+1, k ), 1 ) )
326  END IF
327  kstep = 1
328  ELSE
329 *
330 * 2 x 2 diagonal block
331 *
332 * Invert the diagonal block.
333 *
334  t = abs( a( k, k-1 ) )
335  ak = dble( a( k-1, k-1 ) ) / t
336  akp1 = dble( a( k, k ) ) / t
337  akkp1 = a( k, k-1 ) / t
338  d = t*( ak*akp1-one )
339  a( k-1, k-1 ) = akp1 / d
340  a( k, k ) = ak / d
341  a( k, k-1 ) = -akkp1 / d
342 *
343 * Compute columns K-1 and K of the inverse.
344 *
345  IF( k.LT.n ) THEN
346  CALL zcopy( n-k, a( k+1, k ), 1, work, 1 )
347  CALL zhemv( uplo, n-k, -cone, a( k+1, k+1 ), lda, work,
348  \$ 1, zero, a( k+1, k ), 1 )
349  a( k, k ) = a( k, k ) - dble( zdotc( n-k, work, 1,
350  \$ a( k+1, k ), 1 ) )
351  a( k, k-1 ) = a( k, k-1 ) -
352  \$ zdotc( n-k, a( k+1, k ), 1, a( k+1, k-1 ),
353  \$ 1 )
354  CALL zcopy( n-k, a( k+1, k-1 ), 1, work, 1 )
355  CALL zhemv( uplo, n-k, -cone, a( k+1, k+1 ), lda, work,
356  \$ 1, zero, a( k+1, k-1 ), 1 )
357  a( k-1, k-1 ) = a( k-1, k-1 ) -
358  \$ dble( zdotc( n-k, work, 1, a( k+1, k-1 ),
359  \$ 1 ) )
360  END IF
361  kstep = 2
362  END IF
363 *
364  kp = abs( ipiv( k ) )
365  IF( kp.NE.k ) THEN
366 *
367 * Interchange rows and columns K and KP in the trailing
368 * submatrix A(k-1:n,k-1:n)
369 *
370  IF( kp.LT.n )
371  \$ CALL zswap( n-kp, a( kp+1, k ), 1, a( kp+1, kp ), 1 )
372  DO 70 j = k + 1, kp - 1
373  temp = dconjg( a( j, k ) )
374  a( j, k ) = dconjg( a( kp, j ) )
375  a( kp, j ) = temp
376  70 CONTINUE
377  a( kp, k ) = dconjg( a( kp, k ) )
378  temp = a( k, k )
379  a( k, k ) = a( kp, kp )
380  a( kp, kp ) = temp
381  IF( kstep.EQ.2 ) THEN
382  temp = a( k, k-1 )
383  a( k, k-1 ) = a( kp, k-1 )
384  a( kp, k-1 ) = temp
385  END IF
386  END IF
387 *
388  k = k - kstep
389  GO TO 60
390  80 CONTINUE
391  END IF
392 *
393  RETURN
394 *
395 * End of ZHETRI
396 *
397  END
subroutine zhemv(UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZHEMV
Definition: zhemv.f:156
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:52
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:52
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zhetri(UPLO, N, A, LDA, IPIV, WORK, INFO)
ZHETRI
Definition: zhetri.f:116