1: *> \brief \b ZHPGST
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZHPGST + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhpgst.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhpgst.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhpgst.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, ITYPE, N
26: * ..
27: * .. Array Arguments ..
28: * COMPLEX*16 AP( * ), BP( * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZHPGST reduces a complex Hermitian-definite generalized
38: *> eigenproblem to standard form, using packed storage.
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 ZPPTRF.
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] AP
75: *> \verbatim
76: *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
77: *> On entry, the upper or lower triangle of the Hermitian matrix
78: *> A, packed columnwise in a linear array. The j-th column of A
79: *> is stored in the array AP as follows:
80: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
81: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
82: *>
83: *> On exit, if INFO = 0, the transformed matrix, stored in the
84: *> same format as A.
85: *> \endverbatim
86: *>
87: *> \param[in] BP
88: *> \verbatim
89: *> BP is COMPLEX*16 array, dimension (N*(N+1)/2)
90: *> The triangular factor from the Cholesky factorization of B,
91: *> stored in the same format as A, as returned by ZPPTRF.
92: *> \endverbatim
93: *>
94: *> \param[out] INFO
95: *> \verbatim
96: *> INFO is INTEGER
97: *> = 0: successful exit
98: *> < 0: if INFO = -i, the i-th argument had an illegal value
99: *> \endverbatim
100: *
101: * Authors:
102: * ========
103: *
104: *> \author Univ. of Tennessee
105: *> \author Univ. of California Berkeley
106: *> \author Univ. of Colorado Denver
107: *> \author NAG Ltd.
108: *
109: *> \ingroup complex16OTHERcomputational
110: *
111: * =====================================================================
112: SUBROUTINE ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )
113: *
114: * -- LAPACK computational routine --
115: * -- LAPACK is a software package provided by Univ. of Tennessee, --
116: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117: *
118: * .. Scalar Arguments ..
119: CHARACTER UPLO
120: INTEGER INFO, ITYPE, N
121: * ..
122: * .. Array Arguments ..
123: COMPLEX*16 AP( * ), BP( * )
124: * ..
125: *
126: * =====================================================================
127: *
128: * .. Parameters ..
129: DOUBLE PRECISION ONE, HALF
130: PARAMETER ( ONE = 1.0D+0, HALF = 0.5D+0 )
131: COMPLEX*16 CONE
132: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
133: * ..
134: * .. Local Scalars ..
135: LOGICAL UPPER
136: INTEGER J, J1, J1J1, JJ, K, K1, K1K1, KK
137: DOUBLE PRECISION AJJ, AKK, BJJ, BKK
138: COMPLEX*16 CT
139: * ..
140: * .. External Subroutines ..
141: EXTERNAL XERBLA, ZAXPY, ZDSCAL, ZHPMV, ZHPR2, ZTPMV,
142: $ ZTPSV
143: * ..
144: * .. Intrinsic Functions ..
145: INTRINSIC DBLE
146: * ..
147: * .. External Functions ..
148: LOGICAL LSAME
149: COMPLEX*16 ZDOTC
150: EXTERNAL LSAME, ZDOTC
151: * ..
152: * .. Executable Statements ..
153: *
154: * Test the input parameters.
155: *
156: INFO = 0
157: UPPER = LSAME( UPLO, 'U' )
158: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
159: INFO = -1
160: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
161: INFO = -2
162: ELSE IF( N.LT.0 ) THEN
163: INFO = -3
164: END IF
165: IF( INFO.NE.0 ) THEN
166: CALL XERBLA( 'ZHPGST', -INFO )
167: RETURN
168: END IF
169: *
170: IF( ITYPE.EQ.1 ) THEN
171: IF( UPPER ) THEN
172: *
173: * Compute inv(U**H)*A*inv(U)
174: *
175: * J1 and JJ are the indices of A(1,j) and A(j,j)
176: *
177: JJ = 0
178: DO 10 J = 1, N
179: J1 = JJ + 1
180: JJ = JJ + J
181: *
182: * Compute the j-th column of the upper triangle of A
183: *
184: AP( JJ ) = DBLE( AP( JJ ) )
185: BJJ = DBLE( BP( JJ ) )
186: CALL ZTPSV( UPLO, 'Conjugate transpose', 'Non-unit', J,
187: $ BP, AP( J1 ), 1 )
188: CALL ZHPMV( UPLO, J-1, -CONE, AP, BP( J1 ), 1, CONE,
189: $ AP( J1 ), 1 )
190: CALL ZDSCAL( J-1, ONE / BJJ, AP( J1 ), 1 )
191: AP( JJ ) = ( AP( JJ )-ZDOTC( J-1, AP( J1 ), 1, BP( J1 ),
192: $ 1 ) ) / BJJ
193: 10 CONTINUE
194: ELSE
195: *
196: * Compute inv(L)*A*inv(L**H)
197: *
198: * KK and K1K1 are the indices of A(k,k) and A(k+1,k+1)
199: *
200: KK = 1
201: DO 20 K = 1, N
202: K1K1 = KK + N - K + 1
203: *
204: * Update the lower triangle of A(k:n,k:n)
205: *
206: AKK = DBLE( AP( KK ) )
207: BKK = DBLE( BP( KK ) )
208: AKK = AKK / BKK**2
209: AP( KK ) = AKK
210: IF( K.LT.N ) THEN
211: CALL ZDSCAL( N-K, ONE / BKK, AP( KK+1 ), 1 )
212: CT = -HALF*AKK
213: CALL ZAXPY( N-K, CT, BP( KK+1 ), 1, AP( KK+1 ), 1 )
214: CALL ZHPR2( UPLO, N-K, -CONE, AP( KK+1 ), 1,
215: $ BP( KK+1 ), 1, AP( K1K1 ) )
216: CALL ZAXPY( N-K, CT, BP( KK+1 ), 1, AP( KK+1 ), 1 )
217: CALL ZTPSV( UPLO, 'No transpose', 'Non-unit', N-K,
218: $ BP( K1K1 ), AP( KK+1 ), 1 )
219: END IF
220: KK = K1K1
221: 20 CONTINUE
222: END IF
223: ELSE
224: IF( UPPER ) THEN
225: *
226: * Compute U*A*U**H
227: *
228: * K1 and KK are the indices of A(1,k) and A(k,k)
229: *
230: KK = 0
231: DO 30 K = 1, N
232: K1 = KK + 1
233: KK = KK + K
234: *
235: * Update the upper triangle of A(1:k,1:k)
236: *
237: AKK = DBLE( AP( KK ) )
238: BKK = DBLE( BP( KK ) )
239: CALL ZTPMV( UPLO, 'No transpose', 'Non-unit', K-1, BP,
240: $ AP( K1 ), 1 )
241: CT = HALF*AKK
242: CALL ZAXPY( K-1, CT, BP( K1 ), 1, AP( K1 ), 1 )
243: CALL ZHPR2( UPLO, K-1, CONE, AP( K1 ), 1, BP( K1 ), 1,
244: $ AP )
245: CALL ZAXPY( K-1, CT, BP( K1 ), 1, AP( K1 ), 1 )
246: CALL ZDSCAL( K-1, BKK, AP( K1 ), 1 )
247: AP( KK ) = AKK*BKK**2
248: 30 CONTINUE
249: ELSE
250: *
251: * Compute L**H *A*L
252: *
253: * JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1)
254: *
255: JJ = 1
256: DO 40 J = 1, N
257: J1J1 = JJ + N - J + 1
258: *
259: * Compute the j-th column of the lower triangle of A
260: *
261: AJJ = DBLE( AP( JJ ) )
262: BJJ = DBLE( BP( JJ ) )
263: AP( JJ ) = AJJ*BJJ + ZDOTC( N-J, AP( JJ+1 ), 1,
264: $ BP( JJ+1 ), 1 )
265: CALL ZDSCAL( N-J, BJJ, AP( JJ+1 ), 1 )
266: CALL ZHPMV( UPLO, N-J, CONE, AP( J1J1 ), BP( JJ+1 ), 1,
267: $ CONE, AP( JJ+1 ), 1 )
268: CALL ZTPMV( UPLO, 'Conjugate transpose', 'Non-unit',
269: $ N-J+1, BP( JJ ), AP( JJ ), 1 )
270: JJ = J1J1
271: 40 CONTINUE
272: END IF
273: END IF
274: RETURN
275: *
276: * End of ZHPGST
277: *
278: END
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