Annotation of rpl/lapack/lapack/dspgv.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DSPGST
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DSPGV + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspgv.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspgv.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspgv.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
! 22: * INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER JOBZ, UPLO
! 26: * INTEGER INFO, ITYPE, LDZ, N
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
! 30: * $ Z( LDZ, * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *>
! 39: *> DSPGV computes all the eigenvalues and, optionally, the eigenvectors
! 40: *> of a real generalized symmetric-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 symmetric, 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 DOUBLE PRECISION array, dimension
! 81: *> (N*(N+1)/2)
! 82: *> On entry, the upper or lower triangle of the symmetric matrix
! 83: *> A, packed columnwise in a linear array. The j-th column of A
! 84: *> is stored in the array AP as follows:
! 85: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 86: *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
! 87: *>
! 88: *> On exit, the contents of AP are destroyed.
! 89: *> \endverbatim
! 90: *>
! 91: *> \param[in,out] BP
! 92: *> \verbatim
! 93: *> BP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
! 94: *> On entry, the upper or lower triangle of the symmetric matrix
! 95: *> B, packed columnwise in a linear array. The j-th column of B
! 96: *> is stored in the array BP as follows:
! 97: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
! 98: *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
! 99: *>
! 100: *> On exit, the triangular factor U or L from the Cholesky
! 101: *> factorization B = U**T*U or B = L*L**T, in the same storage
! 102: *> format as B.
! 103: *> \endverbatim
! 104: *>
! 105: *> \param[out] W
! 106: *> \verbatim
! 107: *> W is DOUBLE PRECISION array, dimension (N)
! 108: *> If INFO = 0, the eigenvalues in ascending order.
! 109: *> \endverbatim
! 110: *>
! 111: *> \param[out] Z
! 112: *> \verbatim
! 113: *> Z is DOUBLE PRECISION array, dimension (LDZ, N)
! 114: *> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
! 115: *> eigenvectors. The eigenvectors are normalized as follows:
! 116: *> if ITYPE = 1 or 2, Z**T*B*Z = I;
! 117: *> if ITYPE = 3, Z**T*inv(B)*Z = I.
! 118: *> If JOBZ = 'N', then Z is not referenced.
! 119: *> \endverbatim
! 120: *>
! 121: *> \param[in] LDZ
! 122: *> \verbatim
! 123: *> LDZ is INTEGER
! 124: *> The leading dimension of the array Z. LDZ >= 1, and if
! 125: *> JOBZ = 'V', LDZ >= max(1,N).
! 126: *> \endverbatim
! 127: *>
! 128: *> \param[out] WORK
! 129: *> \verbatim
! 130: *> WORK is DOUBLE PRECISION array, dimension (3*N)
! 131: *> \endverbatim
! 132: *>
! 133: *> \param[out] INFO
! 134: *> \verbatim
! 135: *> INFO is INTEGER
! 136: *> = 0: successful exit
! 137: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 138: *> > 0: DPPTRF or DSPEV returned an error code:
! 139: *> <= N: if INFO = i, DSPEV failed to converge;
! 140: *> i off-diagonal elements of an intermediate
! 141: *> tridiagonal form did not converge to zero.
! 142: *> > N: if INFO = n + i, for 1 <= i <= n, then the leading
! 143: *> minor of order i of B is not positive definite.
! 144: *> The factorization of B could not be completed and
! 145: *> no eigenvalues or eigenvectors were computed.
! 146: *> \endverbatim
! 147: *
! 148: * Authors:
! 149: * ========
! 150: *
! 151: *> \author Univ. of Tennessee
! 152: *> \author Univ. of California Berkeley
! 153: *> \author Univ. of Colorado Denver
! 154: *> \author NAG Ltd.
! 155: *
! 156: *> \date November 2011
! 157: *
! 158: *> \ingroup doubleOTHEReigen
! 159: *
! 160: * =====================================================================
1.1 bertrand 161: SUBROUTINE DSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
162: $ INFO )
163: *
1.9 ! bertrand 164: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 165: * -- LAPACK is a software package provided by Univ. of Tennessee, --
166: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 167: * November 2011
1.1 bertrand 168: *
169: * .. Scalar Arguments ..
170: CHARACTER JOBZ, UPLO
171: INTEGER INFO, ITYPE, LDZ, N
172: * ..
173: * .. Array Arguments ..
174: DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
175: $ Z( LDZ, * )
176: * ..
177: *
178: * =====================================================================
179: *
180: * .. Local Scalars ..
181: LOGICAL UPPER, WANTZ
182: CHARACTER TRANS
183: INTEGER J, NEIG
184: * ..
185: * .. External Functions ..
186: LOGICAL LSAME
187: EXTERNAL LSAME
188: * ..
189: * .. External Subroutines ..
190: EXTERNAL DPPTRF, DSPEV, DSPGST, DTPMV, DTPSV, XERBLA
191: * ..
192: * .. Executable Statements ..
193: *
194: * Test the input parameters.
195: *
196: WANTZ = LSAME( JOBZ, 'V' )
197: UPPER = LSAME( UPLO, 'U' )
198: *
199: INFO = 0
200: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
201: INFO = -1
202: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
203: INFO = -2
204: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
205: INFO = -3
206: ELSE IF( N.LT.0 ) THEN
207: INFO = -4
208: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
209: INFO = -9
210: END IF
211: IF( INFO.NE.0 ) THEN
212: CALL XERBLA( 'DSPGV ', -INFO )
213: RETURN
214: END IF
215: *
216: * Quick return if possible
217: *
218: IF( N.EQ.0 )
219: $ RETURN
220: *
221: * Form a Cholesky factorization of B.
222: *
223: CALL DPPTRF( UPLO, N, BP, INFO )
224: IF( INFO.NE.0 ) THEN
225: INFO = N + INFO
226: RETURN
227: END IF
228: *
229: * Transform problem to standard eigenvalue problem and solve.
230: *
231: CALL DSPGST( ITYPE, UPLO, N, AP, BP, INFO )
232: CALL DSPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO )
233: *
234: IF( WANTZ ) THEN
235: *
236: * Backtransform eigenvectors to the original problem.
237: *
238: NEIG = N
239: IF( INFO.GT.0 )
240: $ NEIG = INFO - 1
241: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
242: *
243: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
1.8 bertrand 244: * backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
1.1 bertrand 245: *
246: IF( UPPER ) THEN
247: TRANS = 'N'
248: ELSE
249: TRANS = 'T'
250: END IF
251: *
252: DO 10 J = 1, NEIG
253: CALL DTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
254: $ 1 )
255: 10 CONTINUE
256: *
257: ELSE IF( ITYPE.EQ.3 ) THEN
258: *
259: * For B*A*x=(lambda)*x;
1.8 bertrand 260: * backtransform eigenvectors: x = L*y or U**T*y
1.1 bertrand 261: *
262: IF( UPPER ) THEN
263: TRANS = 'T'
264: ELSE
265: TRANS = 'N'
266: END IF
267: *
268: DO 20 J = 1, NEIG
269: CALL DTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
270: $ 1 )
271: 20 CONTINUE
272: END IF
273: END IF
274: RETURN
275: *
276: * End of DSPGV
277: *
278: END
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