LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
csytri.f
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1 *> \brief \b CSYTRI
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CSYTRI( 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 A( LDA, * ), WORK( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> CSYTRI computes the inverse of a complex symmetric indefinite matrix
39 *> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
40 *> CSYTRF.
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**T;
52 *> = 'L': Lower triangular, form is A = L*D*L**T.
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 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 CSYTRF.
66 *>
67 *> On exit, if INFO = 0, the (symmetric) 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 CSYTRF.
86 *> \endverbatim
87 *>
88 *> \param[out] WORK
89 *> \verbatim
90 *> WORK is COMPLEX array, dimension (2*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 December 2016
111 *
112 *> \ingroup complexSYcomputational
113 *
114 * =====================================================================
115  SUBROUTINE csytri( UPLO, N, A, LDA, IPIV, WORK, INFO )
116 *
117 * -- LAPACK computational routine (version 3.7.0) --
118 * -- LAPACK is a software package provided by Univ. of Tennessee, --
119 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
120 * December 2016
121 *
122 * .. Scalar Arguments ..
123  CHARACTER UPLO
124  INTEGER INFO, LDA, N
125 * ..
126 * .. Array Arguments ..
127  INTEGER IPIV( * )
128  COMPLEX A( lda, * ), WORK( * )
129 * ..
130 *
131 * =====================================================================
132 *
133 * .. Parameters ..
134  COMPLEX ONE, ZERO
135  parameter( one = ( 1.0e+0, 0.0e+0 ),
136  \$ zero = ( 0.0e+0, 0.0e+0 ) )
137 * ..
138 * .. Local Scalars ..
139  LOGICAL UPPER
140  INTEGER K, KP, KSTEP
141  COMPLEX AK, AKKP1, AKP1, D, T, TEMP
142 * ..
143 * .. External Functions ..
144  LOGICAL LSAME
145  COMPLEX CDOTU
146  EXTERNAL lsame, cdotu
147 * ..
148 * .. External Subroutines ..
149  EXTERNAL ccopy, cswap, csymv, xerbla
150 * ..
151 * .. Intrinsic Functions ..
152  INTRINSIC abs, max
153 * ..
154 * .. Executable Statements ..
155 *
156 * Test the input parameters.
157 *
158  info = 0
159  upper = lsame( uplo, 'U' )
160  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
161  info = -1
162  ELSE IF( n.LT.0 ) THEN
163  info = -2
164  ELSE IF( lda.LT.max( 1, n ) ) THEN
165  info = -4
166  END IF
167  IF( info.NE.0 ) THEN
168  CALL xerbla( 'CSYTRI', -info )
169  RETURN
170  END IF
171 *
172 * Quick return if possible
173 *
174  IF( n.EQ.0 )
175  \$ RETURN
176 *
177 * Check that the diagonal matrix D is nonsingular.
178 *
179  IF( upper ) THEN
180 *
181 * Upper triangular storage: examine D from bottom to top
182 *
183  DO 10 info = n, 1, -1
184  IF( ipiv( info ).GT.0 .AND. a( info, info ).EQ.zero )
185  \$ RETURN
186  10 CONTINUE
187  ELSE
188 *
189 * Lower triangular storage: examine D from top to bottom.
190 *
191  DO 20 info = 1, n
192  IF( ipiv( info ).GT.0 .AND. a( info, info ).EQ.zero )
193  \$ RETURN
194  20 CONTINUE
195  END IF
196  info = 0
197 *
198  IF( upper ) THEN
199 *
200 * Compute inv(A) from the factorization A = U*D*U**T.
201 *
202 * K is the main loop index, increasing from 1 to N in steps of
203 * 1 or 2, depending on the size of the diagonal blocks.
204 *
205  k = 1
206  30 CONTINUE
207 *
208 * If K > N, exit from loop.
209 *
210  IF( k.GT.n )
211  \$ GO TO 40
212 *
213  IF( ipiv( k ).GT.0 ) THEN
214 *
215 * 1 x 1 diagonal block
216 *
217 * Invert the diagonal block.
218 *
219  a( k, k ) = one / a( k, k )
220 *
221 * Compute column K of the inverse.
222 *
223  IF( k.GT.1 ) THEN
224  CALL ccopy( k-1, a( 1, k ), 1, work, 1 )
225  CALL csymv( uplo, k-1, -one, a, lda, work, 1, zero,
226  \$ a( 1, k ), 1 )
227  a( k, k ) = a( k, k ) - cdotu( k-1, work, 1, a( 1, k ),
228  \$ 1 )
229  END IF
230  kstep = 1
231  ELSE
232 *
233 * 2 x 2 diagonal block
234 *
235 * Invert the diagonal block.
236 *
237  t = a( k, k+1 )
238  ak = a( k, k ) / t
239  akp1 = a( k+1, k+1 ) / t
240  akkp1 = a( k, k+1 ) / t
241  d = t*( ak*akp1-one )
242  a( k, k ) = akp1 / d
243  a( k+1, k+1 ) = ak / d
244  a( k, k+1 ) = -akkp1 / d
245 *
246 * Compute columns K and K+1 of the inverse.
247 *
248  IF( k.GT.1 ) THEN
249  CALL ccopy( k-1, a( 1, k ), 1, work, 1 )
250  CALL csymv( uplo, k-1, -one, a, lda, work, 1, zero,
251  \$ a( 1, k ), 1 )
252  a( k, k ) = a( k, k ) - cdotu( k-1, work, 1, a( 1, k ),
253  \$ 1 )
254  a( k, k+1 ) = a( k, k+1 ) -
255  \$ cdotu( k-1, a( 1, k ), 1, a( 1, k+1 ), 1 )
256  CALL ccopy( k-1, a( 1, k+1 ), 1, work, 1 )
257  CALL csymv( uplo, k-1, -one, a, lda, work, 1, zero,
258  \$ a( 1, k+1 ), 1 )
259  a( k+1, k+1 ) = a( k+1, k+1 ) -
260  \$ cdotu( k-1, work, 1, a( 1, k+1 ), 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 cswap( kp-1, a( 1, k ), 1, a( 1, kp ), 1 )
272  CALL cswap( k-kp-1, a( kp+1, k ), 1, a( kp, kp+1 ), lda )
273  temp = a( k, k )
274  a( k, k ) = a( kp, kp )
275  a( kp, kp ) = temp
276  IF( kstep.EQ.2 ) THEN
277  temp = a( k, k+1 )
278  a( k, k+1 ) = a( kp, k+1 )
279  a( kp, k+1 ) = temp
280  END IF
281  END IF
282 *
283  k = k + kstep
284  GO TO 30
285  40 CONTINUE
286 *
287  ELSE
288 *
289 * Compute inv(A) from the factorization A = L*D*L**T.
290 *
291 * K is the main loop index, increasing from 1 to N in steps of
292 * 1 or 2, depending on the size of the diagonal blocks.
293 *
294  k = n
295  50 CONTINUE
296 *
297 * If K < 1, exit from loop.
298 *
299  IF( k.LT.1 )
300  \$ GO TO 60
301 *
302  IF( ipiv( k ).GT.0 ) THEN
303 *
304 * 1 x 1 diagonal block
305 *
306 * Invert the diagonal block.
307 *
308  a( k, k ) = one / a( k, k )
309 *
310 * Compute column K of the inverse.
311 *
312  IF( k.LT.n ) THEN
313  CALL ccopy( n-k, a( k+1, k ), 1, work, 1 )
314  CALL csymv( uplo, n-k, -one, a( k+1, k+1 ), lda, work, 1,
315  \$ zero, a( k+1, k ), 1 )
316  a( k, k ) = a( k, k ) - cdotu( n-k, work, 1, a( k+1, k ),
317  \$ 1 )
318  END IF
319  kstep = 1
320  ELSE
321 *
322 * 2 x 2 diagonal block
323 *
324 * Invert the diagonal block.
325 *
326  t = a( k, k-1 )
327  ak = a( k-1, k-1 ) / t
328  akp1 = a( k, k ) / t
329  akkp1 = a( k, k-1 ) / t
330  d = t*( ak*akp1-one )
331  a( k-1, k-1 ) = akp1 / d
332  a( k, k ) = ak / d
333  a( k, k-1 ) = -akkp1 / d
334 *
335 * Compute columns K-1 and K of the inverse.
336 *
337  IF( k.LT.n ) THEN
338  CALL ccopy( n-k, a( k+1, k ), 1, work, 1 )
339  CALL csymv( uplo, n-k, -one, a( k+1, k+1 ), lda, work, 1,
340  \$ zero, a( k+1, k ), 1 )
341  a( k, k ) = a( k, k ) - cdotu( n-k, work, 1, a( k+1, k ),
342  \$ 1 )
343  a( k, k-1 ) = a( k, k-1 ) -
344  \$ cdotu( n-k, a( k+1, k ), 1, a( k+1, k-1 ),
345  \$ 1 )
346  CALL ccopy( n-k, a( k+1, k-1 ), 1, work, 1 )
347  CALL csymv( uplo, n-k, -one, a( k+1, k+1 ), lda, work, 1,
348  \$ zero, a( k+1, k-1 ), 1 )
349  a( k-1, k-1 ) = a( k-1, k-1 ) -
350  \$ cdotu( n-k, work, 1, a( k+1, k-1 ), 1 )
351  END IF
352  kstep = 2
353  END IF
354 *
355  kp = abs( ipiv( k ) )
356  IF( kp.NE.k ) THEN
357 *
358 * Interchange rows and columns K and KP in the trailing
359 * submatrix A(k-1:n,k-1:n)
360 *
361  IF( kp.LT.n )
362  \$ CALL cswap( n-kp, a( kp+1, k ), 1, a( kp+1, kp ), 1 )
363  CALL cswap( kp-k-1, a( k+1, k ), 1, a( kp, k+1 ), lda )
364  temp = a( k, k )
365  a( k, k ) = a( kp, kp )
366  a( kp, kp ) = temp
367  IF( kstep.EQ.2 ) THEN
368  temp = a( k, k-1 )
369  a( k, k-1 ) = a( kp, k-1 )
370  a( kp, k-1 ) = temp
371  END IF
372  END IF
373 *
374  k = k - kstep
375  GO TO 50
376  60 CONTINUE
377  END IF
378 *
379  RETURN
380 *
381 * End of CSYTRI
382 *
383  END
subroutine ccopy(N, CX, INCX, CY, INCY)
CCOPY
Definition: ccopy.f:83
subroutine csytri(UPLO, N, A, LDA, IPIV, WORK, INFO)
CSYTRI
Definition: csytri.f:116
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine cswap(N, CX, INCX, CY, INCY)
CSWAP
Definition: cswap.f:83
subroutine csymv(UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CSYMV computes a matrix-vector product for a complex symmetric matrix.
Definition: csymv.f:159