Annotation of rpl/lapack/lapack/zhpgv.f, revision 1.9
1.9 ! bertrand 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 ZHPGV + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhpgv.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhpgv.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhpgv.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
! 22: * RWORK, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER JOBZ, UPLO
! 26: * INTEGER INFO, ITYPE, LDZ, N
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * DOUBLE PRECISION RWORK( * ), W( * )
! 30: * COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *>
! 39: *> ZHPGV computes all the eigenvalues and, optionally, the eigenvectors
! 40: *> of a complex generalized Hermitian-definite eigenproblem, of the form
! 41: *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
! 42: *> Here A and B are assumed to be Hermitian, stored in packed format,
! 43: *> and B is also positive definite.
! 44: *> \endverbatim
! 45: *
! 46: * Arguments:
! 47: * ==========
! 48: *
! 49: *> \param[in] ITYPE
! 50: *> \verbatim
! 51: *> ITYPE is INTEGER
! 52: *> Specifies the problem type to be solved:
! 53: *> = 1: A*x = (lambda)*B*x
! 54: *> = 2: A*B*x = (lambda)*x
! 55: *> = 3: B*A*x = (lambda)*x
! 56: *> \endverbatim
! 57: *>
! 58: *> \param[in] JOBZ
! 59: *> \verbatim
! 60: *> JOBZ is CHARACTER*1
! 61: *> = 'N': Compute eigenvalues only;
! 62: *> = 'V': Compute eigenvalues and eigenvectors.
! 63: *> \endverbatim
! 64: *>
! 65: *> \param[in] UPLO
! 66: *> \verbatim
! 67: *> UPLO is CHARACTER*1
! 68: *> = 'U': Upper triangles of A and B are stored;
! 69: *> = 'L': Lower triangles of A and B are stored.
! 70: *> \endverbatim
! 71: *>
! 72: *> \param[in] N
! 73: *> \verbatim
! 74: *> N is INTEGER
! 75: *> The order of the matrices A and B. N >= 0.
! 76: *> \endverbatim
! 77: *>
! 78: *> \param[in,out] AP
! 79: *> \verbatim
! 80: *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
! 81: *> On entry, the upper or lower triangle of the Hermitian matrix
! 82: *> A, packed columnwise in a linear array. The j-th column of A
! 83: *> is stored in the array AP as follows:
! 84: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 85: *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
! 86: *>
! 87: *> On exit, the contents of AP are destroyed.
! 88: *> \endverbatim
! 89: *>
! 90: *> \param[in,out] BP
! 91: *> \verbatim
! 92: *> BP is COMPLEX*16 array, dimension (N*(N+1)/2)
! 93: *> On entry, the upper or lower triangle of the Hermitian matrix
! 94: *> B, packed columnwise in a linear array. The j-th column of B
! 95: *> is stored in the array BP as follows:
! 96: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
! 97: *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
! 98: *>
! 99: *> On exit, the triangular factor U or L from the Cholesky
! 100: *> factorization B = U**H*U or B = L*L**H, in the same storage
! 101: *> format as B.
! 102: *> \endverbatim
! 103: *>
! 104: *> \param[out] W
! 105: *> \verbatim
! 106: *> W is DOUBLE PRECISION array, dimension (N)
! 107: *> If INFO = 0, the eigenvalues in ascending order.
! 108: *> \endverbatim
! 109: *>
! 110: *> \param[out] Z
! 111: *> \verbatim
! 112: *> Z is COMPLEX*16 array, dimension (LDZ, N)
! 113: *> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
! 114: *> eigenvectors. The eigenvectors are normalized as follows:
! 115: *> if ITYPE = 1 or 2, Z**H*B*Z = I;
! 116: *> if ITYPE = 3, Z**H*inv(B)*Z = I.
! 117: *> If JOBZ = 'N', then Z is not referenced.
! 118: *> \endverbatim
! 119: *>
! 120: *> \param[in] LDZ
! 121: *> \verbatim
! 122: *> LDZ is INTEGER
! 123: *> The leading dimension of the array Z. LDZ >= 1, and if
! 124: *> JOBZ = 'V', LDZ >= max(1,N).
! 125: *> \endverbatim
! 126: *>
! 127: *> \param[out] WORK
! 128: *> \verbatim
! 129: *> WORK is COMPLEX*16 array, dimension (max(1, 2*N-1))
! 130: *> \endverbatim
! 131: *>
! 132: *> \param[out] RWORK
! 133: *> \verbatim
! 134: *> RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2))
! 135: *> \endverbatim
! 136: *>
! 137: *> \param[out] INFO
! 138: *> \verbatim
! 139: *> INFO is INTEGER
! 140: *> = 0: successful exit
! 141: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 142: *> > 0: ZPPTRF or ZHPEV returned an error code:
! 143: *> <= N: if INFO = i, ZHPEV failed to converge;
! 144: *> i off-diagonal elements of an intermediate
! 145: *> tridiagonal form did not convergeto zero;
! 146: *> > N: if INFO = N + i, for 1 <= i <= n, then the leading
! 147: *> minor of order i of B is not positive definite.
! 148: *> The factorization of B could not be completed and
! 149: *> no eigenvalues or eigenvectors were computed.
! 150: *> \endverbatim
! 151: *
! 152: * Authors:
! 153: * ========
! 154: *
! 155: *> \author Univ. of Tennessee
! 156: *> \author Univ. of California Berkeley
! 157: *> \author Univ. of Colorado Denver
! 158: *> \author NAG Ltd.
! 159: *
! 160: *> \date November 2011
! 161: *
! 162: *> \ingroup complex16OTHEReigen
! 163: *
! 164: * =====================================================================
1.1 bertrand 165: SUBROUTINE ZHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
166: $ RWORK, INFO )
167: *
1.9 ! bertrand 168: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 169: * -- LAPACK is a software package provided by Univ. of Tennessee, --
170: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 171: * November 2011
1.1 bertrand 172: *
173: * .. Scalar Arguments ..
174: CHARACTER JOBZ, UPLO
175: INTEGER INFO, ITYPE, LDZ, N
176: * ..
177: * .. Array Arguments ..
178: DOUBLE PRECISION RWORK( * ), W( * )
179: COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
180: * ..
181: *
182: * =====================================================================
183: *
184: * .. Local Scalars ..
185: LOGICAL UPPER, WANTZ
186: CHARACTER TRANS
187: INTEGER J, NEIG
188: * ..
189: * .. External Functions ..
190: LOGICAL LSAME
191: EXTERNAL LSAME
192: * ..
193: * .. External Subroutines ..
194: EXTERNAL XERBLA, ZHPEV, ZHPGST, ZPPTRF, ZTPMV, ZTPSV
195: * ..
196: * .. Executable Statements ..
197: *
198: * Test the input parameters.
199: *
200: WANTZ = LSAME( JOBZ, 'V' )
201: UPPER = LSAME( UPLO, 'U' )
202: *
203: INFO = 0
204: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
205: INFO = -1
206: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
207: INFO = -2
208: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
209: INFO = -3
210: ELSE IF( N.LT.0 ) THEN
211: INFO = -4
212: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
213: INFO = -9
214: END IF
215: IF( INFO.NE.0 ) THEN
216: CALL XERBLA( 'ZHPGV ', -INFO )
217: RETURN
218: END IF
219: *
220: * Quick return if possible
221: *
222: IF( N.EQ.0 )
223: $ RETURN
224: *
225: * Form a Cholesky factorization of B.
226: *
227: CALL ZPPTRF( UPLO, N, BP, INFO )
228: IF( INFO.NE.0 ) THEN
229: INFO = N + INFO
230: RETURN
231: END IF
232: *
233: * Transform problem to standard eigenvalue problem and solve.
234: *
235: CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )
236: CALL ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK, INFO )
237: *
238: IF( WANTZ ) THEN
239: *
240: * Backtransform eigenvectors to the original problem.
241: *
242: NEIG = N
243: IF( INFO.GT.0 )
244: $ NEIG = INFO - 1
245: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
246: *
247: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
1.8 bertrand 248: * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
1.1 bertrand 249: *
250: IF( UPPER ) THEN
251: TRANS = 'N'
252: ELSE
253: TRANS = 'C'
254: END IF
255: *
256: DO 10 J = 1, NEIG
257: CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
258: $ 1 )
259: 10 CONTINUE
260: *
261: ELSE IF( ITYPE.EQ.3 ) THEN
262: *
263: * For B*A*x=(lambda)*x;
1.8 bertrand 264: * backtransform eigenvectors: x = L*y or U**H *y
1.1 bertrand 265: *
266: IF( UPPER ) THEN
267: TRANS = 'C'
268: ELSE
269: TRANS = 'N'
270: END IF
271: *
272: DO 20 J = 1, NEIG
273: CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
274: $ 1 )
275: 20 CONTINUE
276: END IF
277: END IF
278: RETURN
279: *
280: * End of ZHPGV
281: *
282: END
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