 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ chpgst()

 subroutine chpgst ( integer ITYPE, character UPLO, integer N, complex, dimension( * ) AP, complex, dimension( * ) BP, integer INFO )

CHPGST

Purpose:
``` CHPGST reduces a complex Hermitian-definite generalized
eigenproblem to standard form, using packed storage.

If ITYPE = 1, the problem is A*x = lambda*B*x,
and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)

If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L.

B must have been previously factorized as U**H*U or L*L**H by CPPTRF.```
Parameters
 [in] ITYPE ``` ITYPE is INTEGER = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H); = 2 or 3: compute U*A*U**H or L**H*A*L.``` [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored and B is factored as U**H*U; = 'L': Lower triangle of A is stored and B is factored as L*L**H.``` [in] N ``` N is INTEGER The order of the matrices A and B. N >= 0.``` [in,out] AP ``` AP is COMPLEX array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. On exit, if INFO = 0, the transformed matrix, stored in the same format as A.``` [in] BP ``` BP is COMPLEX array, dimension (N*(N+1)/2) The triangular factor from the Cholesky factorization of B, stored in the same format as A, as returned by CPPTRF.``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```

Definition at line 112 of file chpgst.f.

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 AP( * ), BP( * )
124 * ..
125 *
126 * =====================================================================
127 *
128 * .. Parameters ..
129  REAL ONE, HALF
130  parameter( one = 1.0e+0, half = 0.5e+0 )
131  COMPLEX CONE
132  parameter( cone = ( 1.0e+0, 0.0e+0 ) )
133 * ..
134 * .. Local Scalars ..
135  LOGICAL UPPER
136  INTEGER J, J1, J1J1, JJ, K, K1, K1K1, KK
137  REAL AJJ, AKK, BJJ, BKK
138  COMPLEX CT
139 * ..
140 * .. External Subroutines ..
141  EXTERNAL caxpy, chpmv, chpr2, csscal, ctpmv, ctpsv,
142  \$ xerbla
143 * ..
144 * .. Intrinsic Functions ..
145  INTRINSIC real
146 * ..
147 * .. External Functions ..
148  LOGICAL LSAME
149  COMPLEX CDOTC
150  EXTERNAL lsame, cdotc
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( 'CHPGST', -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 ) = real( ap( jj ) )
185  bjj = real( bp( jj ) )
186  CALL ctpsv( uplo, 'Conjugate transpose', 'Non-unit', j,
187  \$ bp, ap( j1 ), 1 )
188  CALL chpmv( uplo, j-1, -cone, ap, bp( j1 ), 1, cone,
189  \$ ap( j1 ), 1 )
190  CALL csscal( j-1, one / bjj, ap( j1 ), 1 )
191  ap( jj ) = ( ap( jj )-cdotc( 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 = real( ap( kk ) )
207  bkk = real( bp( kk ) )
208  akk = akk / bkk**2
209  ap( kk ) = akk
210  IF( k.LT.n ) THEN
211  CALL csscal( n-k, one / bkk, ap( kk+1 ), 1 )
212  ct = -half*akk
213  CALL caxpy( n-k, ct, bp( kk+1 ), 1, ap( kk+1 ), 1 )
214  CALL chpr2( uplo, n-k, -cone, ap( kk+1 ), 1,
215  \$ bp( kk+1 ), 1, ap( k1k1 ) )
216  CALL caxpy( n-k, ct, bp( kk+1 ), 1, ap( kk+1 ), 1 )
217  CALL ctpsv( 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 = real( ap( kk ) )
238  bkk = real( bp( kk ) )
239  CALL ctpmv( uplo, 'No transpose', 'Non-unit', k-1, bp,
240  \$ ap( k1 ), 1 )
241  ct = half*akk
242  CALL caxpy( k-1, ct, bp( k1 ), 1, ap( k1 ), 1 )
243  CALL chpr2( uplo, k-1, cone, ap( k1 ), 1, bp( k1 ), 1,
244  \$ ap )
245  CALL caxpy( k-1, ct, bp( k1 ), 1, ap( k1 ), 1 )
246  CALL csscal( 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 = real( ap( jj ) )
262  bjj = real( bp( jj ) )
263  ap( jj ) = ajj*bjj + cdotc( n-j, ap( jj+1 ), 1,
264  \$ bp( jj+1 ), 1 )
265  CALL csscal( n-j, bjj, ap( jj+1 ), 1 )
266  CALL chpmv( uplo, n-j, cone, ap( j1j1 ), bp( jj+1 ), 1,
267  \$ cone, ap( jj+1 ), 1 )
268  CALL ctpmv( 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 CHPGST
277 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
complex function cdotc(N, CX, INCX, CY, INCY)
CDOTC
Definition: cdotc.f:83
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.f:78
subroutine caxpy(N, CA, CX, INCX, CY, INCY)
CAXPY
Definition: caxpy.f:88
subroutine ctpsv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPSV
Definition: ctpsv.f:144
subroutine chpr2(UPLO, N, ALPHA, X, INCX, Y, INCY, AP)
CHPR2
Definition: chpr2.f:145
subroutine chpmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
CHPMV
Definition: chpmv.f:149
subroutine ctpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPMV
Definition: ctpmv.f:142
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