LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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zhpgst.f
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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
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 hpgst
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
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zaxpy(n, za, zx, incx, zy, incy)
ZAXPY
Definition zaxpy.f:88
subroutine zhpgst(itype, uplo, n, ap, bp, info)
ZHPGST
Definition zhpgst.f:113
subroutine zhpmv(uplo, n, alpha, ap, x, incx, beta, y, incy)
ZHPMV
Definition zhpmv.f:149
subroutine zhpr2(uplo, n, alpha, x, incx, y, incy, ap)
ZHPR2
Definition zhpr2.f:145
subroutine zdscal(n, da, zx, incx)
ZDSCAL
Definition zdscal.f:78
subroutine ztpmv(uplo, trans, diag, n, ap, x, incx)
ZTPMV
Definition ztpmv.f:142
subroutine ztpsv(uplo, trans, diag, n, ap, x, incx)
ZTPSV
Definition ztpsv.f:144