LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
chpgst.f
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1 *> \brief \b CHPGST
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CHPGST( ITYPE, UPLO, N, AP, BP, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, ITYPE, N
26 * ..
27 * .. Array Arguments ..
28 * COMPLEX AP( * ), BP( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> CHPGST 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 CPPTRF.
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 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 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 CPPTRF.
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 complexOTHERcomputational
112 *
113 * =====================================================================
114  SUBROUTINE chpgst( 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 AP( * ), BP( * )
127 * ..
128 *
129 * =====================================================================
130 *
131 * .. Parameters ..
132  REAL ONE, HALF
133  parameter( one = 1.0e+0, half = 0.5e+0 )
134  COMPLEX CONE
135  parameter( cone = ( 1.0e+0, 0.0e+0 ) )
136 * ..
137 * .. Local Scalars ..
138  LOGICAL UPPER
139  INTEGER J, J1, J1J1, JJ, K, K1, K1K1, KK
140  REAL AJJ, AKK, BJJ, BKK
141  COMPLEX CT
142 * ..
143 * .. External Subroutines ..
144  EXTERNAL caxpy, chpmv, chpr2, csscal, ctpmv, ctpsv,
145  \$ xerbla
146 * ..
147 * .. Intrinsic Functions ..
148  INTRINSIC real
149 * ..
150 * .. External Functions ..
151  LOGICAL LSAME
152  COMPLEX CDOTC
153  EXTERNAL lsame, cdotc
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( 'CHPGST', -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 ) = REAL( AP( JJ ) )
188  bjj = bp( jj )
189  CALL ctpsv( uplo, 'Conjugate transpose', 'Non-unit', j,
190  \$ bp, ap( j1 ), 1 )
191  CALL chpmv( uplo, j-1, -cone, ap, bp( j1 ), 1, cone,
192  \$ ap( j1 ), 1 )
193  CALL csscal( j-1, one / bjj, ap( j1 ), 1 )
194  ap( jj ) = ( ap( jj )-cdotc( 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 csscal( n-k, one / bkk, ap( kk+1 ), 1 )
215  ct = -half*akk
216  CALL caxpy( n-k, ct, bp( kk+1 ), 1, ap( kk+1 ), 1 )
217  CALL chpr2( uplo, n-k, -cone, ap( kk+1 ), 1,
218  \$ bp( kk+1 ), 1, ap( k1k1 ) )
219  CALL caxpy( n-k, ct, bp( kk+1 ), 1, ap( kk+1 ), 1 )
220  CALL ctpsv( 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 ctpmv( uplo, 'No transpose', 'Non-unit', k-1, bp,
243  \$ ap( k1 ), 1 )
244  ct = half*akk
245  CALL caxpy( k-1, ct, bp( k1 ), 1, ap( k1 ), 1 )
246  CALL chpr2( uplo, k-1, cone, ap( k1 ), 1, bp( k1 ), 1,
247  \$ ap )
248  CALL caxpy( k-1, ct, bp( k1 ), 1, ap( k1 ), 1 )
249  CALL csscal( 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 + cdotc( n-j, ap( jj+1 ), 1,
267  \$ bp( jj+1 ), 1 )
268  CALL csscal( n-j, bjj, ap( jj+1 ), 1 )
269  CALL chpmv( uplo, n-j, cone, ap( j1j1 ), bp( jj+1 ), 1,
270  \$ cone, ap( jj+1 ), 1 )
271  CALL ctpmv( 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 CHPGST
280 *
281  END
subroutine ctpsv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPSV
Definition: ctpsv.f:146
subroutine chpr2(UPLO, N, ALPHA, X, INCX, Y, INCY, AP)
CHPR2
Definition: chpr2.f:147
subroutine caxpy(N, CA, CX, INCX, CY, INCY)
CAXPY
Definition: caxpy.f:90
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.f:80
subroutine chpmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
CHPMV
Definition: chpmv.f:151
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine chpgst(ITYPE, UPLO, N, AP, BP, INFO)
CHPGST
Definition: chpgst.f:115
subroutine ctpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPMV
Definition: ctpmv.f:144