1: *> \brief \b ZHEGST
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZHEGST + dependencies
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11: *> [TGZ]</a>
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15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, ITYPE, LDA, LDB, N
26: * ..
27: * .. Array Arguments ..
28: * COMPLEX*16 A( LDA, * ), B( LDB, * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZHEGST reduces a complex Hermitian-definite generalized
38: *> eigenproblem to standard form.
39: *>
40: *> If ITYPE = 1, the problem is A*x = lambda*B*x,
41: *> and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)
42: *>
43: *> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
44: *> B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L.
45: *>
46: *> B must have been previously factorized as U**H*U or L*L**H by ZPOTRF.
47: *> \endverbatim
48: *
49: * Arguments:
50: * ==========
51: *
52: *> \param[in] ITYPE
53: *> \verbatim
54: *> ITYPE is INTEGER
55: *> = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H);
56: *> = 2 or 3: compute U*A*U**H or L**H*A*L.
57: *> \endverbatim
58: *>
59: *> \param[in] UPLO
60: *> \verbatim
61: *> UPLO is CHARACTER*1
62: *> = 'U': Upper triangle of A is stored and B is factored as
63: *> U**H*U;
64: *> = 'L': Lower triangle of A is stored and B is factored as
65: *> L*L**H.
66: *> \endverbatim
67: *>
68: *> \param[in] N
69: *> \verbatim
70: *> N is INTEGER
71: *> The order of the matrices A and B. N >= 0.
72: *> \endverbatim
73: *>
74: *> \param[in,out] A
75: *> \verbatim
76: *> A is COMPLEX*16 array, dimension (LDA,N)
77: *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading
78: *> N-by-N upper triangular part of A contains the upper
79: *> triangular part of the matrix A, and the strictly lower
80: *> triangular part of A is not referenced. If UPLO = 'L', the
81: *> leading N-by-N lower triangular part of A contains the lower
82: *> triangular part of the matrix A, and the strictly upper
83: *> triangular part of A is not referenced.
84: *>
85: *> On exit, if INFO = 0, the transformed matrix, stored in the
86: *> same format as A.
87: *> \endverbatim
88: *>
89: *> \param[in] LDA
90: *> \verbatim
91: *> LDA is INTEGER
92: *> The leading dimension of the array A. LDA >= max(1,N).
93: *> \endverbatim
94: *>
95: *> \param[in,out] B
96: *> \verbatim
97: *> B is COMPLEX*16 array, dimension (LDB,N)
98: *> The triangular factor from the Cholesky factorization of B,
99: *> as returned by ZPOTRF.
100: *> B is modified by the routine but restored on exit.
101: *> \endverbatim
102: *>
103: *> \param[in] LDB
104: *> \verbatim
105: *> LDB is INTEGER
106: *> The leading dimension of the array B. LDB >= max(1,N).
107: *> \endverbatim
108: *>
109: *> \param[out] INFO
110: *> \verbatim
111: *> INFO is INTEGER
112: *> = 0: successful exit
113: *> < 0: if INFO = -i, the i-th argument had an illegal value
114: *> \endverbatim
115: *
116: * Authors:
117: * ========
118: *
119: *> \author Univ. of Tennessee
120: *> \author Univ. of California Berkeley
121: *> \author Univ. of Colorado Denver
122: *> \author NAG Ltd.
123: *
124: *> \ingroup complex16HEcomputational
125: *
126: * =====================================================================
127: SUBROUTINE ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
128: *
129: * -- LAPACK computational routine --
130: * -- LAPACK is a software package provided by Univ. of Tennessee, --
131: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132: *
133: * .. Scalar Arguments ..
134: CHARACTER UPLO
135: INTEGER INFO, ITYPE, LDA, LDB, N
136: * ..
137: * .. Array Arguments ..
138: COMPLEX*16 A( LDA, * ), B( LDB, * )
139: * ..
140: *
141: * =====================================================================
142: *
143: * .. Parameters ..
144: DOUBLE PRECISION ONE
145: PARAMETER ( ONE = 1.0D+0 )
146: COMPLEX*16 CONE, HALF
147: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ),
148: $ HALF = ( 0.5D+0, 0.0D+0 ) )
149: * ..
150: * .. Local Scalars ..
151: LOGICAL UPPER
152: INTEGER K, KB, NB
153: * ..
154: * .. External Subroutines ..
155: EXTERNAL XERBLA, ZHEGS2, ZHEMM, ZHER2K, ZTRMM, ZTRSM
156: * ..
157: * .. Intrinsic Functions ..
158: INTRINSIC MAX, MIN
159: * ..
160: * .. External Functions ..
161: LOGICAL LSAME
162: INTEGER ILAENV
163: EXTERNAL LSAME, ILAENV
164: * ..
165: * .. Executable Statements ..
166: *
167: * Test the input parameters.
168: *
169: INFO = 0
170: UPPER = LSAME( UPLO, 'U' )
171: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
172: INFO = -1
173: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
174: INFO = -2
175: ELSE IF( N.LT.0 ) THEN
176: INFO = -3
177: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
178: INFO = -5
179: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
180: INFO = -7
181: END IF
182: IF( INFO.NE.0 ) THEN
183: CALL XERBLA( 'ZHEGST', -INFO )
184: RETURN
185: END IF
186: *
187: * Quick return if possible
188: *
189: IF( N.EQ.0 )
190: $ RETURN
191: *
192: * Determine the block size for this environment.
193: *
194: NB = ILAENV( 1, 'ZHEGST', UPLO, N, -1, -1, -1 )
195: *
196: IF( NB.LE.1 .OR. NB.GE.N ) THEN
197: *
198: * Use unblocked code
199: *
200: CALL ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
201: ELSE
202: *
203: * Use blocked code
204: *
205: IF( ITYPE.EQ.1 ) THEN
206: IF( UPPER ) THEN
207: *
208: * Compute inv(U**H)*A*inv(U)
209: *
210: DO 10 K = 1, N, NB
211: KB = MIN( N-K+1, NB )
212: *
213: * Update the upper triangle of A(k:n,k:n)
214: *
215: CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
216: $ B( K, K ), LDB, INFO )
217: IF( K+KB.LE.N ) THEN
218: CALL ZTRSM( 'Left', UPLO, 'Conjugate transpose',
219: $ 'Non-unit', KB, N-K-KB+1, CONE,
220: $ B( K, K ), LDB, A( K, K+KB ), LDA )
221: CALL ZHEMM( 'Left', UPLO, KB, N-K-KB+1, -HALF,
222: $ A( K, K ), LDA, B( K, K+KB ), LDB,
223: $ CONE, A( K, K+KB ), LDA )
224: CALL ZHER2K( UPLO, 'Conjugate transpose', N-K-KB+1,
225: $ KB, -CONE, A( K, K+KB ), LDA,
226: $ B( K, K+KB ), LDB, ONE,
227: $ A( K+KB, K+KB ), LDA )
228: CALL ZHEMM( 'Left', UPLO, KB, N-K-KB+1, -HALF,
229: $ A( K, K ), LDA, B( K, K+KB ), LDB,
230: $ CONE, A( K, K+KB ), LDA )
231: CALL ZTRSM( 'Right', UPLO, 'No transpose',
232: $ 'Non-unit', KB, N-K-KB+1, CONE,
233: $ B( K+KB, K+KB ), LDB, A( K, K+KB ),
234: $ LDA )
235: END IF
236: 10 CONTINUE
237: ELSE
238: *
239: * Compute inv(L)*A*inv(L**H)
240: *
241: DO 20 K = 1, N, NB
242: KB = MIN( N-K+1, NB )
243: *
244: * Update the lower triangle of A(k:n,k:n)
245: *
246: CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
247: $ B( K, K ), LDB, INFO )
248: IF( K+KB.LE.N ) THEN
249: CALL ZTRSM( 'Right', UPLO, 'Conjugate transpose',
250: $ 'Non-unit', N-K-KB+1, KB, CONE,
251: $ B( K, K ), LDB, A( K+KB, K ), LDA )
252: CALL ZHEMM( 'Right', UPLO, N-K-KB+1, KB, -HALF,
253: $ A( K, K ), LDA, B( K+KB, K ), LDB,
254: $ CONE, A( K+KB, K ), LDA )
255: CALL ZHER2K( UPLO, 'No transpose', N-K-KB+1, KB,
256: $ -CONE, A( K+KB, K ), LDA,
257: $ B( K+KB, K ), LDB, ONE,
258: $ A( K+KB, K+KB ), LDA )
259: CALL ZHEMM( 'Right', UPLO, N-K-KB+1, KB, -HALF,
260: $ A( K, K ), LDA, B( K+KB, K ), LDB,
261: $ CONE, A( K+KB, K ), LDA )
262: CALL ZTRSM( 'Left', UPLO, 'No transpose',
263: $ 'Non-unit', N-K-KB+1, KB, CONE,
264: $ B( K+KB, K+KB ), LDB, A( K+KB, K ),
265: $ LDA )
266: END IF
267: 20 CONTINUE
268: END IF
269: ELSE
270: IF( UPPER ) THEN
271: *
272: * Compute U*A*U**H
273: *
274: DO 30 K = 1, N, NB
275: KB = MIN( N-K+1, NB )
276: *
277: * Update the upper triangle of A(1:k+kb-1,1:k+kb-1)
278: *
279: CALL ZTRMM( 'Left', UPLO, 'No transpose', 'Non-unit',
280: $ K-1, KB, CONE, B, LDB, A( 1, K ), LDA )
281: CALL ZHEMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ),
282: $ LDA, B( 1, K ), LDB, CONE, A( 1, K ),
283: $ LDA )
284: CALL ZHER2K( UPLO, 'No transpose', K-1, KB, CONE,
285: $ A( 1, K ), LDA, B( 1, K ), LDB, ONE, A,
286: $ LDA )
287: CALL ZHEMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ),
288: $ LDA, B( 1, K ), LDB, CONE, A( 1, K ),
289: $ LDA )
290: CALL ZTRMM( 'Right', UPLO, 'Conjugate transpose',
291: $ 'Non-unit', K-1, KB, CONE, B( K, K ), LDB,
292: $ A( 1, K ), LDA )
293: CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
294: $ B( K, K ), LDB, INFO )
295: 30 CONTINUE
296: ELSE
297: *
298: * Compute L**H*A*L
299: *
300: DO 40 K = 1, N, NB
301: KB = MIN( N-K+1, NB )
302: *
303: * Update the lower triangle of A(1:k+kb-1,1:k+kb-1)
304: *
305: CALL ZTRMM( 'Right', UPLO, 'No transpose', 'Non-unit',
306: $ KB, K-1, CONE, B, LDB, A( K, 1 ), LDA )
307: CALL ZHEMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ),
308: $ LDA, B( K, 1 ), LDB, CONE, A( K, 1 ),
309: $ LDA )
310: CALL ZHER2K( UPLO, 'Conjugate transpose', K-1, KB,
311: $ CONE, A( K, 1 ), LDA, B( K, 1 ), LDB,
312: $ ONE, A, LDA )
313: CALL ZHEMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ),
314: $ LDA, B( K, 1 ), LDB, CONE, A( K, 1 ),
315: $ LDA )
316: CALL ZTRMM( 'Left', UPLO, 'Conjugate transpose',
317: $ 'Non-unit', KB, K-1, CONE, B( K, K ), LDB,
318: $ A( K, 1 ), LDA )
319: CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
320: $ B( K, K ), LDB, INFO )
321: 40 CONTINUE
322: END IF
323: END IF
324: END IF
325: RETURN
326: *
327: * End of ZHEGST
328: *
329: END
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