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: *> \date December 2016
110: *
111: *> \ingroup complex16OTHERcomputational
112: *
113: * =====================================================================
114: SUBROUTINE ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )
115: *
116: * -- LAPACK computational routine (version 3.7.0) --
117: * -- LAPACK is a software package provided by Univ. of Tennessee, --
118: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119: * December 2016
120: *
121: * .. Scalar Arguments ..
122: CHARACTER UPLO
123: INTEGER INFO, ITYPE, N
124: * ..
125: * .. Array Arguments ..
126: COMPLEX*16 AP( * ), BP( * )
127: * ..
128: *
129: * =====================================================================
130: *
131: * .. Parameters ..
132: DOUBLE PRECISION ONE, HALF
133: PARAMETER ( ONE = 1.0D+0, HALF = 0.5D+0 )
134: COMPLEX*16 CONE
135: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
136: * ..
137: * .. Local Scalars ..
138: LOGICAL UPPER
139: INTEGER J, J1, J1J1, JJ, K, K1, K1K1, KK
140: DOUBLE PRECISION AJJ, AKK, BJJ, BKK
141: COMPLEX*16 CT
142: * ..
143: * .. External Subroutines ..
144: EXTERNAL XERBLA, ZAXPY, ZDSCAL, ZHPMV, ZHPR2, ZTPMV,
145: $ ZTPSV
146: * ..
147: * .. Intrinsic Functions ..
148: INTRINSIC DBLE
149: * ..
150: * .. External Functions ..
151: LOGICAL LSAME
152: COMPLEX*16 ZDOTC
153: EXTERNAL LSAME, ZDOTC
154: * ..
155: * .. Executable Statements ..
156: *
157: * Test the input parameters.
158: *
159: INFO = 0
160: UPPER = LSAME( UPLO, 'U' )
161: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
162: INFO = -1
163: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
164: INFO = -2
165: ELSE IF( N.LT.0 ) THEN
166: INFO = -3
167: END IF
168: IF( INFO.NE.0 ) THEN
169: CALL XERBLA( 'ZHPGST', -INFO )
170: RETURN
171: END IF
172: *
173: IF( ITYPE.EQ.1 ) THEN
174: IF( UPPER ) THEN
175: *
176: * Compute inv(U**H)*A*inv(U)
177: *
178: * J1 and JJ are the indices of A(1,j) and A(j,j)
179: *
180: JJ = 0
181: DO 10 J = 1, N
182: J1 = JJ + 1
183: JJ = JJ + J
184: *
185: * Compute the j-th column of the upper triangle of A
186: *
187: AP( JJ ) = DBLE( AP( JJ ) )
188: BJJ = BP( JJ )
189: CALL ZTPSV( UPLO, 'Conjugate transpose', 'Non-unit', J,
190: $ BP, AP( J1 ), 1 )
191: CALL ZHPMV( UPLO, J-1, -CONE, AP, BP( J1 ), 1, CONE,
192: $ AP( J1 ), 1 )
193: CALL ZDSCAL( J-1, ONE / BJJ, AP( J1 ), 1 )
194: AP( JJ ) = ( AP( JJ )-ZDOTC( J-1, AP( J1 ), 1, BP( J1 ),
195: $ 1 ) ) / BJJ
196: 10 CONTINUE
197: ELSE
198: *
199: * Compute inv(L)*A*inv(L**H)
200: *
201: * KK and K1K1 are the indices of A(k,k) and A(k+1,k+1)
202: *
203: KK = 1
204: DO 20 K = 1, N
205: K1K1 = KK + N - K + 1
206: *
207: * Update the lower triangle of A(k:n,k:n)
208: *
209: AKK = AP( KK )
210: BKK = BP( KK )
211: AKK = AKK / BKK**2
212: AP( KK ) = AKK
213: IF( K.LT.N ) THEN
214: CALL ZDSCAL( N-K, ONE / BKK, AP( KK+1 ), 1 )
215: CT = -HALF*AKK
216: CALL ZAXPY( N-K, CT, BP( KK+1 ), 1, AP( KK+1 ), 1 )
217: CALL ZHPR2( UPLO, N-K, -CONE, AP( KK+1 ), 1,
218: $ BP( KK+1 ), 1, AP( K1K1 ) )
219: CALL ZAXPY( N-K, CT, BP( KK+1 ), 1, AP( KK+1 ), 1 )
220: CALL ZTPSV( UPLO, 'No transpose', 'Non-unit', N-K,
221: $ BP( K1K1 ), AP( KK+1 ), 1 )
222: END IF
223: KK = K1K1
224: 20 CONTINUE
225: END IF
226: ELSE
227: IF( UPPER ) THEN
228: *
229: * Compute U*A*U**H
230: *
231: * K1 and KK are the indices of A(1,k) and A(k,k)
232: *
233: KK = 0
234: DO 30 K = 1, N
235: K1 = KK + 1
236: KK = KK + K
237: *
238: * Update the upper triangle of A(1:k,1:k)
239: *
240: AKK = AP( KK )
241: BKK = BP( KK )
242: CALL ZTPMV( UPLO, 'No transpose', 'Non-unit', K-1, BP,
243: $ AP( K1 ), 1 )
244: CT = HALF*AKK
245: CALL ZAXPY( K-1, CT, BP( K1 ), 1, AP( K1 ), 1 )
246: CALL ZHPR2( UPLO, K-1, CONE, AP( K1 ), 1, BP( K1 ), 1,
247: $ AP )
248: CALL ZAXPY( K-1, CT, BP( K1 ), 1, AP( K1 ), 1 )
249: CALL ZDSCAL( K-1, BKK, AP( K1 ), 1 )
250: AP( KK ) = AKK*BKK**2
251: 30 CONTINUE
252: ELSE
253: *
254: * Compute L**H *A*L
255: *
256: * JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1)
257: *
258: JJ = 1
259: DO 40 J = 1, N
260: J1J1 = JJ + N - J + 1
261: *
262: * Compute the j-th column of the lower triangle of A
263: *
264: AJJ = AP( JJ )
265: BJJ = BP( JJ )
266: AP( JJ ) = AJJ*BJJ + ZDOTC( N-J, AP( JJ+1 ), 1,
267: $ BP( JJ+1 ), 1 )
268: CALL ZDSCAL( N-J, BJJ, AP( JJ+1 ), 1 )
269: CALL ZHPMV( UPLO, N-J, CONE, AP( J1J1 ), BP( JJ+1 ), 1,
270: $ CONE, AP( JJ+1 ), 1 )
271: CALL ZTPMV( UPLO, 'Conjugate transpose', 'Non-unit',
272: $ N-J+1, BP( JJ ), AP( JJ ), 1 )
273: JJ = J1J1
274: 40 CONTINUE
275: END IF
276: END IF
277: RETURN
278: *
279: * End of ZHPGST
280: *
281: END
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