Annotation of rpl/lapack/lapack/zhetri_3.f, revision 1.5
1.1 bertrand 1: *> \brief \b ZHETRI_3
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZHETRI_3 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetri_3.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhetri_3.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetri_3.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHETRI_3( UPLO, N, A, LDA, E, IPIV, WORK, LWORK,
22: * INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER UPLO
26: * INTEGER INFO, LDA, LWORK, N
27: * ..
28: * .. Array Arguments ..
29: * INTEGER IPIV( * )
30: * COMPLEX*16 A( LDA, * ), E( * ), WORK( * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *> ZHETRI_3 computes the inverse of a complex Hermitian indefinite
39: *> matrix A using the factorization computed by ZHETRF_RK or ZHETRF_BK:
40: *>
41: *> A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),
42: *>
43: *> where U (or L) is unit upper (or lower) triangular matrix,
44: *> U**H (or L**H) is the conjugate of U (or L), P is a permutation
45: *> matrix, P**T is the transpose of P, and D is Hermitian and block
46: *> diagonal with 1-by-1 and 2-by-2 diagonal blocks.
47: *>
48: *> ZHETRI_3 sets the leading dimension of the workspace before calling
49: *> ZHETRI_3X that actually computes the inverse. This is the blocked
50: *> version of the algorithm, calling Level 3 BLAS.
51: *> \endverbatim
52: *
53: * Arguments:
54: * ==========
55: *
56: *> \param[in] UPLO
57: *> \verbatim
58: *> UPLO is CHARACTER*1
59: *> Specifies whether the details of the factorization are
60: *> stored as an upper or lower triangular matrix.
61: *> = 'U': Upper triangle of A is stored;
62: *> = 'L': Lower triangle of A is stored.
63: *> \endverbatim
64: *>
65: *> \param[in] N
66: *> \verbatim
67: *> N is INTEGER
68: *> The order of the matrix A. N >= 0.
69: *> \endverbatim
70: *>
71: *> \param[in,out] A
72: *> \verbatim
73: *> A is COMPLEX*16 array, dimension (LDA,N)
74: *> On entry, diagonal of the block diagonal matrix D and
75: *> factors U or L as computed by ZHETRF_RK and ZHETRF_BK:
76: *> a) ONLY diagonal elements of the Hermitian block diagonal
77: *> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
78: *> (superdiagonal (or subdiagonal) elements of D
79: *> should be provided on entry in array E), and
80: *> b) If UPLO = 'U': factor U in the superdiagonal part of A.
81: *> If UPLO = 'L': factor L in the subdiagonal part of A.
82: *>
83: *> On exit, if INFO = 0, the Hermitian inverse of the original
84: *> matrix.
85: *> If UPLO = 'U': the upper triangular part of the inverse
86: *> is formed and the part of A below the diagonal is not
87: *> referenced;
88: *> If UPLO = 'L': the lower triangular part of the inverse
89: *> is formed and the part of A above the diagonal is not
90: *> referenced.
91: *> \endverbatim
92: *>
93: *> \param[in] LDA
94: *> \verbatim
95: *> LDA is INTEGER
96: *> The leading dimension of the array A. LDA >= max(1,N).
97: *> \endverbatim
98: *>
99: *> \param[in] E
100: *> \verbatim
101: *> E is COMPLEX*16 array, dimension (N)
102: *> On entry, contains the superdiagonal (or subdiagonal)
103: *> elements of the Hermitian block diagonal matrix D
104: *> with 1-by-1 or 2-by-2 diagonal blocks, where
1.3 bertrand 105: *> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
1.1 bertrand 106: *> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
107: *>
108: *> NOTE: For 1-by-1 diagonal block D(k), where
109: *> 1 <= k <= N, the element E(k) is not referenced in both
110: *> UPLO = 'U' or UPLO = 'L' cases.
111: *> \endverbatim
112: *>
113: *> \param[in] IPIV
114: *> \verbatim
115: *> IPIV is INTEGER array, dimension (N)
116: *> Details of the interchanges and the block structure of D
117: *> as determined by ZHETRF_RK or ZHETRF_BK.
118: *> \endverbatim
119: *>
120: *> \param[out] WORK
121: *> \verbatim
122: *> WORK is COMPLEX*16 array, dimension (N+NB+1)*(NB+3).
123: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
124: *> \endverbatim
125: *>
126: *> \param[in] LWORK
127: *> \verbatim
128: *> LWORK is INTEGER
129: *> The length of WORK. LWORK >= (N+NB+1)*(NB+3).
130: *>
131: *> If LDWORK = -1, then a workspace query is assumed;
132: *> the routine only calculates the optimal size of the optimal
133: *> size of the WORK array, returns this value as the first
134: *> entry of the WORK array, and no error message related to
135: *> LWORK is issued by XERBLA.
136: *> \endverbatim
137: *>
138: *> \param[out] INFO
139: *> \verbatim
140: *> INFO is INTEGER
141: *> = 0: successful exit
142: *> < 0: if INFO = -i, the i-th argument had an illegal value
143: *> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
144: *> inverse could not be computed.
145: *> \endverbatim
146: *
147: * Authors:
148: * ========
149: *
150: *> \author Univ. of Tennessee
151: *> \author Univ. of California Berkeley
152: *> \author Univ. of Colorado Denver
153: *> \author NAG Ltd.
154: *
155: *> \ingroup complex16HEcomputational
156: *
157: *> \par Contributors:
158: * ==================
159: *> \verbatim
160: *>
1.3 bertrand 161: *> November 2017, Igor Kozachenko,
1.1 bertrand 162: *> Computer Science Division,
163: *> University of California, Berkeley
164: *>
165: *> \endverbatim
166: *
167: * =====================================================================
168: SUBROUTINE ZHETRI_3( UPLO, N, A, LDA, E, IPIV, WORK, LWORK,
169: $ INFO )
170: *
1.5 ! bertrand 171: * -- LAPACK computational routine --
1.1 bertrand 172: * -- LAPACK is a software package provided by Univ. of Tennessee, --
173: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
174: *
175: * .. Scalar Arguments ..
176: CHARACTER UPLO
177: INTEGER INFO, LDA, LWORK, N
178: * ..
179: * .. Array Arguments ..
180: INTEGER IPIV( * )
181: COMPLEX*16 A( LDA, * ), E( * ), WORK( * )
182: * ..
183: *
184: * =====================================================================
185: *
186: * .. Local Scalars ..
187: LOGICAL UPPER, LQUERY
188: INTEGER LWKOPT, NB
189: * ..
190: * .. External Functions ..
191: LOGICAL LSAME
192: INTEGER ILAENV
193: EXTERNAL LSAME, ILAENV
194: * ..
195: * .. External Subroutines ..
1.3 bertrand 196: EXTERNAL ZHETRI_3X, XERBLA
1.1 bertrand 197: * ..
198: * .. Intrinsic Functions ..
199: INTRINSIC MAX
200: * ..
201: * .. Executable Statements ..
202: *
203: * Test the input parameters.
204: *
205: INFO = 0
206: UPPER = LSAME( UPLO, 'U' )
207: LQUERY = ( LWORK.EQ.-1 )
208: *
209: * Determine the block size
210: *
211: NB = MAX( 1, ILAENV( 1, 'ZHETRI_3', UPLO, N, -1, -1, -1 ) )
212: LWKOPT = ( N+NB+1 ) * ( NB+3 )
213: *
214: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
215: INFO = -1
216: ELSE IF( N.LT.0 ) THEN
217: INFO = -2
218: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
219: INFO = -4
220: ELSE IF ( LWORK .LT. LWKOPT .AND. .NOT.LQUERY ) THEN
221: INFO = -8
222: END IF
223: *
224: IF( INFO.NE.0 ) THEN
225: CALL XERBLA( 'ZHETRI_3', -INFO )
226: RETURN
227: ELSE IF( LQUERY ) THEN
228: WORK( 1 ) = LWKOPT
229: RETURN
230: END IF
231: *
232: * Quick return if possible
233: *
234: IF( N.EQ.0 )
235: $ RETURN
236: *
237: CALL ZHETRI_3X( UPLO, N, A, LDA, E, IPIV, WORK, NB, INFO )
238: *
239: WORK( 1 ) = LWKOPT
240: *
241: RETURN
242: *
243: * End of ZHETRI_3
244: *
245: END
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