LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
csptri.f
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1 *> \brief \b CSPTRI
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/csptri.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CSPTRI( UPLO, N, AP, IPIV, WORK, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, N
26 * ..
27 * .. Array Arguments ..
28 * INTEGER IPIV( * )
29 * COMPLEX AP( * ), WORK( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> CSPTRI computes the inverse of a complex symmetric indefinite matrix
39 *> A in packed storage using the factorization A = U*D*U**T or
40 *> A = L*D*L**T computed by CSPTRF.
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] AP
62 *> \verbatim
63 *> AP is COMPLEX array, dimension (N*(N+1)/2)
64 *> On entry, the block diagonal matrix D and the multipliers
65 *> used to obtain the factor U or L as computed by CSPTRF,
66 *> stored as a packed triangular matrix.
67 *>
68 *> On exit, if INFO = 0, the (symmetric) inverse of the original
69 *> matrix, stored as a packed triangular matrix. The j-th column
70 *> of inv(A) is stored in the array AP as follows:
71 *> if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
72 *> if UPLO = 'L',
73 *> AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
74 *> \endverbatim
75 *>
76 *> \param[in] IPIV
77 *> \verbatim
78 *> IPIV is INTEGER array, dimension (N)
79 *> Details of the interchanges and the block structure of D
80 *> as determined by CSPTRF.
81 *> \endverbatim
82 *>
83 *> \param[out] WORK
84 *> \verbatim
85 *> WORK is COMPLEX array, dimension (N)
86 *> \endverbatim
87 *>
88 *> \param[out] INFO
89 *> \verbatim
90 *> INFO is INTEGER
91 *> = 0: successful exit
92 *> < 0: if INFO = -i, the i-th argument had an illegal value
93 *> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
94 *> inverse could not be computed.
95 *> \endverbatim
96 *
97 * Authors:
98 * ========
99 *
100 *> \author Univ. of Tennessee
101 *> \author Univ. of California Berkeley
102 *> \author Univ. of Colorado Denver
103 *> \author NAG Ltd.
104 *
105 *> \ingroup complexOTHERcomputational
106 *
107 * =====================================================================
108  SUBROUTINE csptri( UPLO, N, AP, IPIV, WORK, INFO )
109 *
110 * -- LAPACK computational routine --
111 * -- LAPACK is a software package provided by Univ. of Tennessee, --
112 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
113 *
114 * .. Scalar Arguments ..
115  CHARACTER UPLO
116  INTEGER INFO, N
117 * ..
118 * .. Array Arguments ..
119  INTEGER IPIV( * )
120  COMPLEX AP( * ), WORK( * )
121 * ..
122 *
123 * =====================================================================
124 *
125 * .. Parameters ..
126  COMPLEX ONE, ZERO
127  parameter( one = ( 1.0e+0, 0.0e+0 ),
128  $ zero = ( 0.0e+0, 0.0e+0 ) )
129 * ..
130 * .. Local Scalars ..
131  LOGICAL UPPER
132  INTEGER J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP
133  COMPLEX AK, AKKP1, AKP1, D, T, TEMP
134 * ..
135 * .. External Functions ..
136  LOGICAL LSAME
137  COMPLEX CDOTU
138  EXTERNAL lsame, cdotu
139 * ..
140 * .. External Subroutines ..
141  EXTERNAL ccopy, cspmv, cswap, xerbla
142 * ..
143 * .. Intrinsic Functions ..
144  INTRINSIC abs
145 * ..
146 * .. Executable Statements ..
147 *
148 * Test the input parameters.
149 *
150  info = 0
151  upper = lsame( uplo, 'U' )
152  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
153  info = -1
154  ELSE IF( n.LT.0 ) THEN
155  info = -2
156  END IF
157  IF( info.NE.0 ) THEN
158  CALL xerbla( 'CSPTRI', -info )
159  RETURN
160  END IF
161 *
162 * Quick return if possible
163 *
164  IF( n.EQ.0 )
165  $ RETURN
166 *
167 * Check that the diagonal matrix D is nonsingular.
168 *
169  IF( upper ) THEN
170 *
171 * Upper triangular storage: examine D from bottom to top
172 *
173  kp = n*( n+1 ) / 2
174  DO 10 info = n, 1, -1
175  IF( ipiv( info ).GT.0 .AND. ap( kp ).EQ.zero )
176  $ RETURN
177  kp = kp - info
178  10 CONTINUE
179  ELSE
180 *
181 * Lower triangular storage: examine D from top to bottom.
182 *
183  kp = 1
184  DO 20 info = 1, n
185  IF( ipiv( info ).GT.0 .AND. ap( kp ).EQ.zero )
186  $ RETURN
187  kp = kp + n - info + 1
188  20 CONTINUE
189  END IF
190  info = 0
191 *
192  IF( upper ) THEN
193 *
194 * Compute inv(A) from the factorization A = U*D*U**T.
195 *
196 * K is the main loop index, increasing from 1 to N in steps of
197 * 1 or 2, depending on the size of the diagonal blocks.
198 *
199  k = 1
200  kc = 1
201  30 CONTINUE
202 *
203 * If K > N, exit from loop.
204 *
205  IF( k.GT.n )
206  $ GO TO 50
207 *
208  kcnext = kc + k
209  IF( ipiv( k ).GT.0 ) THEN
210 *
211 * 1 x 1 diagonal block
212 *
213 * Invert the diagonal block.
214 *
215  ap( kc+k-1 ) = one / ap( kc+k-1 )
216 *
217 * Compute column K of the inverse.
218 *
219  IF( k.GT.1 ) THEN
220  CALL ccopy( k-1, ap( kc ), 1, work, 1 )
221  CALL cspmv( uplo, k-1, -one, ap, work, 1, zero, ap( kc ),
222  $ 1 )
223  ap( kc+k-1 ) = ap( kc+k-1 ) -
224  $ cdotu( k-1, work, 1, ap( kc ), 1 )
225  END IF
226  kstep = 1
227  ELSE
228 *
229 * 2 x 2 diagonal block
230 *
231 * Invert the diagonal block.
232 *
233  t = ap( kcnext+k-1 )
234  ak = ap( kc+k-1 ) / t
235  akp1 = ap( kcnext+k ) / t
236  akkp1 = ap( kcnext+k-1 ) / t
237  d = t*( ak*akp1-one )
238  ap( kc+k-1 ) = akp1 / d
239  ap( kcnext+k ) = ak / d
240  ap( kcnext+k-1 ) = -akkp1 / d
241 *
242 * Compute columns K and K+1 of the inverse.
243 *
244  IF( k.GT.1 ) THEN
245  CALL ccopy( k-1, ap( kc ), 1, work, 1 )
246  CALL cspmv( uplo, k-1, -one, ap, work, 1, zero, ap( kc ),
247  $ 1 )
248  ap( kc+k-1 ) = ap( kc+k-1 ) -
249  $ cdotu( k-1, work, 1, ap( kc ), 1 )
250  ap( kcnext+k-1 ) = ap( kcnext+k-1 ) -
251  $ cdotu( k-1, ap( kc ), 1, ap( kcnext ),
252  $ 1 )
253  CALL ccopy( k-1, ap( kcnext ), 1, work, 1 )
254  CALL cspmv( uplo, k-1, -one, ap, work, 1, zero,
255  $ ap( kcnext ), 1 )
256  ap( kcnext+k ) = ap( kcnext+k ) -
257  $ cdotu( k-1, work, 1, ap( kcnext ), 1 )
258  END IF
259  kstep = 2
260  kcnext = kcnext + k + 1
261  END IF
262 *
263  kp = abs( ipiv( k ) )
264  IF( kp.NE.k ) THEN
265 *
266 * Interchange rows and columns K and KP in the leading
267 * submatrix A(1:k+1,1:k+1)
268 *
269  kpc = ( kp-1 )*kp / 2 + 1
270  CALL cswap( kp-1, ap( kc ), 1, ap( kpc ), 1 )
271  kx = kpc + kp - 1
272  DO 40 j = kp + 1, k - 1
273  kx = kx + j - 1
274  temp = ap( kc+j-1 )
275  ap( kc+j-1 ) = ap( kx )
276  ap( kx ) = temp
277  40 CONTINUE
278  temp = ap( kc+k-1 )
279  ap( kc+k-1 ) = ap( kpc+kp-1 )
280  ap( kpc+kp-1 ) = temp
281  IF( kstep.EQ.2 ) THEN
282  temp = ap( kc+k+k-1 )
283  ap( kc+k+k-1 ) = ap( kc+k+kp-1 )
284  ap( kc+k+kp-1 ) = temp
285  END IF
286  END IF
287 *
288  k = k + kstep
289  kc = kcnext
290  GO TO 30
291  50 CONTINUE
292 *
293  ELSE
294 *
295 * Compute inv(A) from the factorization A = L*D*L**T.
296 *
297 * K is the main loop index, increasing from 1 to N in steps of
298 * 1 or 2, depending on the size of the diagonal blocks.
299 *
300  npp = n*( n+1 ) / 2
301  k = n
302  kc = npp
303  60 CONTINUE
304 *
305 * If K < 1, exit from loop.
306 *
307  IF( k.LT.1 )
308  $ GO TO 80
309 *
310  kcnext = kc - ( n-k+2 )
311  IF( ipiv( k ).GT.0 ) THEN
312 *
313 * 1 x 1 diagonal block
314 *
315 * Invert the diagonal block.
316 *
317  ap( kc ) = one / ap( kc )
318 *
319 * Compute column K of the inverse.
320 *
321  IF( k.LT.n ) THEN
322  CALL ccopy( n-k, ap( kc+1 ), 1, work, 1 )
323  CALL cspmv( uplo, n-k, -one, ap( kc+n-k+1 ), work, 1,
324  $ zero, ap( kc+1 ), 1 )
325  ap( kc ) = ap( kc ) - cdotu( n-k, work, 1, ap( kc+1 ),
326  $ 1 )
327  END IF
328  kstep = 1
329  ELSE
330 *
331 * 2 x 2 diagonal block
332 *
333 * Invert the diagonal block.
334 *
335  t = ap( kcnext+1 )
336  ak = ap( kcnext ) / t
337  akp1 = ap( kc ) / t
338  akkp1 = ap( kcnext+1 ) / t
339  d = t*( ak*akp1-one )
340  ap( kcnext ) = akp1 / d
341  ap( kc ) = ak / d
342  ap( kcnext+1 ) = -akkp1 / d
343 *
344 * Compute columns K-1 and K of the inverse.
345 *
346  IF( k.LT.n ) THEN
347  CALL ccopy( n-k, ap( kc+1 ), 1, work, 1 )
348  CALL cspmv( uplo, n-k, -one, ap( kc+( n-k+1 ) ), work, 1,
349  $ zero, ap( kc+1 ), 1 )
350  ap( kc ) = ap( kc ) - cdotu( n-k, work, 1, ap( kc+1 ),
351  $ 1 )
352  ap( kcnext+1 ) = ap( kcnext+1 ) -
353  $ cdotu( n-k, ap( kc+1 ), 1,
354  $ ap( kcnext+2 ), 1 )
355  CALL ccopy( n-k, ap( kcnext+2 ), 1, work, 1 )
356  CALL cspmv( uplo, n-k, -one, ap( kc+( n-k+1 ) ), work, 1,
357  $ zero, ap( kcnext+2 ), 1 )
358  ap( kcnext ) = ap( kcnext ) -
359  $ cdotu( n-k, work, 1, ap( kcnext+2 ), 1 )
360  END IF
361  kstep = 2
362  kcnext = kcnext - ( n-k+3 )
363  END IF
364 *
365  kp = abs( ipiv( k ) )
366  IF( kp.NE.k ) THEN
367 *
368 * Interchange rows and columns K and KP in the trailing
369 * submatrix A(k-1:n,k-1:n)
370 *
371  kpc = npp - ( n-kp+1 )*( n-kp+2 ) / 2 + 1
372  IF( kp.LT.n )
373  $ CALL cswap( n-kp, ap( kc+kp-k+1 ), 1, ap( kpc+1 ), 1 )
374  kx = kc + kp - k
375  DO 70 j = k + 1, kp - 1
376  kx = kx + n - j + 1
377  temp = ap( kc+j-k )
378  ap( kc+j-k ) = ap( kx )
379  ap( kx ) = temp
380  70 CONTINUE
381  temp = ap( kc )
382  ap( kc ) = ap( kpc )
383  ap( kpc ) = temp
384  IF( kstep.EQ.2 ) THEN
385  temp = ap( kc-n+k-1 )
386  ap( kc-n+k-1 ) = ap( kc-n+kp-1 )
387  ap( kc-n+kp-1 ) = temp
388  END IF
389  END IF
390 *
391  k = k - kstep
392  kc = kcnext
393  GO TO 60
394  80 CONTINUE
395  END IF
396 *
397  RETURN
398 *
399 * End of CSPTRI
400 *
401  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ccopy(N, CX, INCX, CY, INCY)
CCOPY
Definition: ccopy.f:81
subroutine cswap(N, CX, INCX, CY, INCY)
CSWAP
Definition: cswap.f:81
subroutine cspmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
CSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix
Definition: cspmv.f:151
subroutine csptri(UPLO, N, AP, IPIV, WORK, INFO)
CSPTRI
Definition: csptri.f:109