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1.1 bertrand 1: SUBROUTINE ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
2: *
3: * -- LAPACK routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: CHARACTER UPLO
10: INTEGER INFO, ITYPE, LDA, LDB, N
11: * ..
12: * .. Array Arguments ..
13: COMPLEX*16 A( LDA, * ), B( LDB, * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * ZHEGST reduces a complex Hermitian-definite generalized
20: * eigenproblem to standard form.
21: *
22: * If ITYPE = 1, the problem is A*x = lambda*B*x,
23: * and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)
24: *
25: * If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
26: * B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L.
27: *
28: * B must have been previously factorized as U**H*U or L*L**H by ZPOTRF.
29: *
30: * Arguments
31: * =========
32: *
33: * ITYPE (input) INTEGER
34: * = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H);
35: * = 2 or 3: compute U*A*U**H or L**H*A*L.
36: *
37: * UPLO (input) CHARACTER*1
38: * = 'U': Upper triangle of A is stored and B is factored as
39: * U**H*U;
40: * = 'L': Lower triangle of A is stored and B is factored as
41: * L*L**H.
42: *
43: * N (input) INTEGER
44: * The order of the matrices A and B. N >= 0.
45: *
46: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
47: * On entry, the Hermitian matrix A. If UPLO = 'U', the leading
48: * N-by-N upper triangular part of A contains the upper
49: * triangular part of the matrix A, and the strictly lower
50: * triangular part of A is not referenced. If UPLO = 'L', the
51: * leading N-by-N lower triangular part of A contains the lower
52: * triangular part of the matrix A, and the strictly upper
53: * triangular part of A is not referenced.
54: *
55: * On exit, if INFO = 0, the transformed matrix, stored in the
56: * same format as A.
57: *
58: * LDA (input) INTEGER
59: * The leading dimension of the array A. LDA >= max(1,N).
60: *
61: * B (input) COMPLEX*16 array, dimension (LDB,N)
62: * The triangular factor from the Cholesky factorization of B,
63: * as returned by ZPOTRF.
64: *
65: * LDB (input) INTEGER
66: * The leading dimension of the array B. LDB >= max(1,N).
67: *
68: * INFO (output) INTEGER
69: * = 0: successful exit
70: * < 0: if INFO = -i, the i-th argument had an illegal value
71: *
72: * =====================================================================
73: *
74: * .. Parameters ..
75: DOUBLE PRECISION ONE
76: PARAMETER ( ONE = 1.0D+0 )
77: COMPLEX*16 CONE, HALF
78: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ),
79: $ HALF = ( 0.5D+0, 0.0D+0 ) )
80: * ..
81: * .. Local Scalars ..
82: LOGICAL UPPER
83: INTEGER K, KB, NB
84: * ..
85: * .. External Subroutines ..
86: EXTERNAL XERBLA, ZHEGS2, ZHEMM, ZHER2K, ZTRMM, ZTRSM
87: * ..
88: * .. Intrinsic Functions ..
89: INTRINSIC MAX, MIN
90: * ..
91: * .. External Functions ..
92: LOGICAL LSAME
93: INTEGER ILAENV
94: EXTERNAL LSAME, ILAENV
95: * ..
96: * .. Executable Statements ..
97: *
98: * Test the input parameters.
99: *
100: INFO = 0
101: UPPER = LSAME( UPLO, 'U' )
102: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
103: INFO = -1
104: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
105: INFO = -2
106: ELSE IF( N.LT.0 ) THEN
107: INFO = -3
108: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
109: INFO = -5
110: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
111: INFO = -7
112: END IF
113: IF( INFO.NE.0 ) THEN
114: CALL XERBLA( 'ZHEGST', -INFO )
115: RETURN
116: END IF
117: *
118: * Quick return if possible
119: *
120: IF( N.EQ.0 )
121: $ RETURN
122: *
123: * Determine the block size for this environment.
124: *
125: NB = ILAENV( 1, 'ZHEGST', UPLO, N, -1, -1, -1 )
126: *
127: IF( NB.LE.1 .OR. NB.GE.N ) THEN
128: *
129: * Use unblocked code
130: *
131: CALL ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
132: ELSE
133: *
134: * Use blocked code
135: *
136: IF( ITYPE.EQ.1 ) THEN
137: IF( UPPER ) THEN
138: *
139: * Compute inv(U')*A*inv(U)
140: *
141: DO 10 K = 1, N, NB
142: KB = MIN( N-K+1, NB )
143: *
144: * Update the upper triangle of A(k:n,k:n)
145: *
146: CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
147: $ B( K, K ), LDB, INFO )
148: IF( K+KB.LE.N ) THEN
149: CALL ZTRSM( 'Left', UPLO, 'Conjugate transpose',
150: $ 'Non-unit', KB, N-K-KB+1, CONE,
151: $ B( K, K ), LDB, A( K, K+KB ), LDA )
152: CALL ZHEMM( 'Left', UPLO, KB, N-K-KB+1, -HALF,
153: $ A( K, K ), LDA, B( K, K+KB ), LDB,
154: $ CONE, A( K, K+KB ), LDA )
155: CALL ZHER2K( UPLO, 'Conjugate transpose', N-K-KB+1,
156: $ KB, -CONE, A( K, K+KB ), LDA,
157: $ B( K, K+KB ), LDB, ONE,
158: $ A( K+KB, K+KB ), LDA )
159: CALL ZHEMM( 'Left', UPLO, KB, N-K-KB+1, -HALF,
160: $ A( K, K ), LDA, B( K, K+KB ), LDB,
161: $ CONE, A( K, K+KB ), LDA )
162: CALL ZTRSM( 'Right', UPLO, 'No transpose',
163: $ 'Non-unit', KB, N-K-KB+1, CONE,
164: $ B( K+KB, K+KB ), LDB, A( K, K+KB ),
165: $ LDA )
166: END IF
167: 10 CONTINUE
168: ELSE
169: *
170: * Compute inv(L)*A*inv(L')
171: *
172: DO 20 K = 1, N, NB
173: KB = MIN( N-K+1, NB )
174: *
175: * Update the lower triangle of A(k:n,k:n)
176: *
177: CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
178: $ B( K, K ), LDB, INFO )
179: IF( K+KB.LE.N ) THEN
180: CALL ZTRSM( 'Right', UPLO, 'Conjugate transpose',
181: $ 'Non-unit', N-K-KB+1, KB, CONE,
182: $ B( K, K ), LDB, A( K+KB, K ), LDA )
183: CALL ZHEMM( 'Right', UPLO, N-K-KB+1, KB, -HALF,
184: $ A( K, K ), LDA, B( K+KB, K ), LDB,
185: $ CONE, A( K+KB, K ), LDA )
186: CALL ZHER2K( UPLO, 'No transpose', N-K-KB+1, KB,
187: $ -CONE, A( K+KB, K ), LDA,
188: $ B( K+KB, K ), LDB, ONE,
189: $ A( K+KB, K+KB ), LDA )
190: CALL ZHEMM( 'Right', UPLO, N-K-KB+1, KB, -HALF,
191: $ A( K, K ), LDA, B( K+KB, K ), LDB,
192: $ CONE, A( K+KB, K ), LDA )
193: CALL ZTRSM( 'Left', UPLO, 'No transpose',
194: $ 'Non-unit', N-K-KB+1, KB, CONE,
195: $ B( K+KB, K+KB ), LDB, A( K+KB, K ),
196: $ LDA )
197: END IF
198: 20 CONTINUE
199: END IF
200: ELSE
201: IF( UPPER ) THEN
202: *
203: * Compute U*A*U'
204: *
205: DO 30 K = 1, N, NB
206: KB = MIN( N-K+1, NB )
207: *
208: * Update the upper triangle of A(1:k+kb-1,1:k+kb-1)
209: *
210: CALL ZTRMM( 'Left', UPLO, 'No transpose', 'Non-unit',
211: $ K-1, KB, CONE, B, LDB, A( 1, K ), LDA )
212: CALL ZHEMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ),
213: $ LDA, B( 1, K ), LDB, CONE, A( 1, K ),
214: $ LDA )
215: CALL ZHER2K( UPLO, 'No transpose', K-1, KB, CONE,
216: $ A( 1, K ), LDA, B( 1, K ), LDB, ONE, A,
217: $ LDA )
218: CALL ZHEMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ),
219: $ LDA, B( 1, K ), LDB, CONE, A( 1, K ),
220: $ LDA )
221: CALL ZTRMM( 'Right', UPLO, 'Conjugate transpose',
222: $ 'Non-unit', K-1, KB, CONE, B( K, K ), LDB,
223: $ A( 1, K ), LDA )
224: CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
225: $ B( K, K ), LDB, INFO )
226: 30 CONTINUE
227: ELSE
228: *
229: * Compute L'*A*L
230: *
231: DO 40 K = 1, N, NB
232: KB = MIN( N-K+1, NB )
233: *
234: * Update the lower triangle of A(1:k+kb-1,1:k+kb-1)
235: *
236: CALL ZTRMM( 'Right', UPLO, 'No transpose', 'Non-unit',
237: $ KB, K-1, CONE, B, LDB, A( K, 1 ), LDA )
238: CALL ZHEMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ),
239: $ LDA, B( K, 1 ), LDB, CONE, A( K, 1 ),
240: $ LDA )
241: CALL ZHER2K( UPLO, 'Conjugate transpose', K-1, KB,
242: $ CONE, A( K, 1 ), LDA, B( K, 1 ), LDB,
243: $ ONE, A, LDA )
244: CALL ZHEMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ),
245: $ LDA, B( K, 1 ), LDB, CONE, A( K, 1 ),
246: $ LDA )
247: CALL ZTRMM( 'Left', UPLO, 'Conjugate transpose',
248: $ 'Non-unit', KB, K-1, CONE, B( K, K ), LDB,
249: $ A( K, 1 ), LDA )
250: CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
251: $ B( K, K ), LDB, INFO )
252: 40 CONTINUE
253: END IF
254: END IF
255: END IF
256: RETURN
257: *
258: * End of ZHEGST
259: *
260: END