Annotation of rpl/lapack/lapack/dspgvd.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 DSPGVD + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspgvd.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspgvd.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspgvd.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
! 22: * LWORK, IWORK, LIWORK, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER JOBZ, UPLO
! 26: * INTEGER INFO, ITYPE, LDZ, LIWORK, LWORK, N
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * INTEGER IWORK( * )
! 30: * DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
! 31: * $ Z( LDZ, * )
! 32: * ..
! 33: *
! 34: *
! 35: *> \par Purpose:
! 36: * =============
! 37: *>
! 38: *> \verbatim
! 39: *>
! 40: *> DSPGVD computes all the eigenvalues, and optionally, the eigenvectors
! 41: *> of a real generalized symmetric-definite eigenproblem, of the form
! 42: *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
! 43: *> B are assumed to be symmetric, stored in packed format, and B is also
! 44: *> positive definite.
! 45: *> If eigenvectors are desired, it uses a divide and conquer algorithm.
! 46: *>
! 47: *> The divide and conquer algorithm makes very mild assumptions about
! 48: *> floating point arithmetic. It will work on machines with a guard
! 49: *> digit in add/subtract, or on those binary machines without guard
! 50: *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
! 51: *> Cray-2. It could conceivably fail on hexadecimal or decimal machines
! 52: *> without guard digits, but we know of none.
! 53: *> \endverbatim
! 54: *
! 55: * Arguments:
! 56: * ==========
! 57: *
! 58: *> \param[in] ITYPE
! 59: *> \verbatim
! 60: *> ITYPE is INTEGER
! 61: *> Specifies the problem type to be solved:
! 62: *> = 1: A*x = (lambda)*B*x
! 63: *> = 2: A*B*x = (lambda)*x
! 64: *> = 3: B*A*x = (lambda)*x
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[in] JOBZ
! 68: *> \verbatim
! 69: *> JOBZ is CHARACTER*1
! 70: *> = 'N': Compute eigenvalues only;
! 71: *> = 'V': Compute eigenvalues and eigenvectors.
! 72: *> \endverbatim
! 73: *>
! 74: *> \param[in] UPLO
! 75: *> \verbatim
! 76: *> UPLO is CHARACTER*1
! 77: *> = 'U': Upper triangles of A and B are stored;
! 78: *> = 'L': Lower triangles of A and B are stored.
! 79: *> \endverbatim
! 80: *>
! 81: *> \param[in] N
! 82: *> \verbatim
! 83: *> N is INTEGER
! 84: *> The order of the matrices A and B. N >= 0.
! 85: *> \endverbatim
! 86: *>
! 87: *> \param[in,out] AP
! 88: *> \verbatim
! 89: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
! 90: *> On entry, the upper or lower triangle of the symmetric matrix
! 91: *> A, packed columnwise in a linear array. The j-th column of A
! 92: *> is stored in the array AP as follows:
! 93: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 94: *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
! 95: *>
! 96: *> On exit, the contents of AP are destroyed.
! 97: *> \endverbatim
! 98: *>
! 99: *> \param[in,out] BP
! 100: *> \verbatim
! 101: *> BP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
! 102: *> On entry, the upper or lower triangle of the symmetric matrix
! 103: *> B, packed columnwise in a linear array. The j-th column of B
! 104: *> is stored in the array BP as follows:
! 105: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
! 106: *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
! 107: *>
! 108: *> On exit, the triangular factor U or L from the Cholesky
! 109: *> factorization B = U**T*U or B = L*L**T, in the same storage
! 110: *> format as B.
! 111: *> \endverbatim
! 112: *>
! 113: *> \param[out] W
! 114: *> \verbatim
! 115: *> W is DOUBLE PRECISION array, dimension (N)
! 116: *> If INFO = 0, the eigenvalues in ascending order.
! 117: *> \endverbatim
! 118: *>
! 119: *> \param[out] Z
! 120: *> \verbatim
! 121: *> Z is DOUBLE PRECISION array, dimension (LDZ, N)
! 122: *> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
! 123: *> eigenvectors. The eigenvectors are normalized as follows:
! 124: *> if ITYPE = 1 or 2, Z**T*B*Z = I;
! 125: *> if ITYPE = 3, Z**T*inv(B)*Z = I.
! 126: *> If JOBZ = 'N', then Z is not referenced.
! 127: *> \endverbatim
! 128: *>
! 129: *> \param[in] LDZ
! 130: *> \verbatim
! 131: *> LDZ is INTEGER
! 132: *> The leading dimension of the array Z. LDZ >= 1, and if
! 133: *> JOBZ = 'V', LDZ >= max(1,N).
! 134: *> \endverbatim
! 135: *>
! 136: *> \param[out] WORK
! 137: *> \verbatim
! 138: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 139: *> On exit, if INFO = 0, WORK(1) returns the required LWORK.
! 140: *> \endverbatim
! 141: *>
! 142: *> \param[in] LWORK
! 143: *> \verbatim
! 144: *> LWORK is INTEGER
! 145: *> The dimension of the array WORK.
! 146: *> If N <= 1, LWORK >= 1.
! 147: *> If JOBZ = 'N' and N > 1, LWORK >= 2*N.
! 148: *> If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
! 149: *>
! 150: *> If LWORK = -1, then a workspace query is assumed; the routine
! 151: *> only calculates the required sizes of the WORK and IWORK
! 152: *> arrays, returns these values as the first entries of the WORK
! 153: *> and IWORK arrays, and no error message related to LWORK or
! 154: *> LIWORK is issued by XERBLA.
! 155: *> \endverbatim
! 156: *>
! 157: *> \param[out] IWORK
! 158: *> \verbatim
! 159: *> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
! 160: *> On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
! 161: *> \endverbatim
! 162: *>
! 163: *> \param[in] LIWORK
! 164: *> \verbatim
! 165: *> LIWORK is INTEGER
! 166: *> The dimension of the array IWORK.
! 167: *> If JOBZ = 'N' or N <= 1, LIWORK >= 1.
! 168: *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
! 169: *>
! 170: *> If LIWORK = -1, then a workspace query is assumed; the
! 171: *> routine only calculates the required sizes of the WORK and
! 172: *> IWORK arrays, returns these values as the first entries of
! 173: *> the WORK and IWORK arrays, and no error message related to
! 174: *> LWORK or LIWORK is issued by XERBLA.
! 175: *> \endverbatim
! 176: *>
! 177: *> \param[out] INFO
! 178: *> \verbatim
! 179: *> INFO is INTEGER
! 180: *> = 0: successful exit
! 181: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 182: *> > 0: DPPTRF or DSPEVD returned an error code:
! 183: *> <= N: if INFO = i, DSPEVD failed to converge;
! 184: *> i off-diagonal elements of an intermediate
! 185: *> tridiagonal form did not converge to zero;
! 186: *> > N: if INFO = N + i, for 1 <= i <= N, then the leading
! 187: *> minor of order i of B is not positive definite.
! 188: *> The factorization of B could not be completed and
! 189: *> no eigenvalues or eigenvectors were computed.
! 190: *> \endverbatim
! 191: *
! 192: * Authors:
! 193: * ========
! 194: *
! 195: *> \author Univ. of Tennessee
! 196: *> \author Univ. of California Berkeley
! 197: *> \author Univ. of Colorado Denver
! 198: *> \author NAG Ltd.
! 199: *
! 200: *> \date November 2011
! 201: *
! 202: *> \ingroup doubleOTHEReigen
! 203: *
! 204: *> \par Contributors:
! 205: * ==================
! 206: *>
! 207: *> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
! 208: *
! 209: * =====================================================================
1.1 bertrand 210: SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
211: $ LWORK, IWORK, LIWORK, INFO )
212: *
1.9 ! bertrand 213: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 214: * -- LAPACK is a software package provided by Univ. of Tennessee, --
215: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 216: * November 2011
1.1 bertrand 217: *
218: * .. Scalar Arguments ..
219: CHARACTER JOBZ, UPLO
220: INTEGER INFO, ITYPE, LDZ, LIWORK, LWORK, N
221: * ..
222: * .. Array Arguments ..
223: INTEGER IWORK( * )
224: DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
225: $ Z( LDZ, * )
226: * ..
227: *
228: * =====================================================================
229: *
230: * .. Parameters ..
231: DOUBLE PRECISION TWO
232: PARAMETER ( TWO = 2.0D+0 )
233: * ..
234: * .. Local Scalars ..
235: LOGICAL LQUERY, UPPER, WANTZ
236: CHARACTER TRANS
237: INTEGER J, LIWMIN, LWMIN, NEIG
238: * ..
239: * .. External Functions ..
240: LOGICAL LSAME
241: EXTERNAL LSAME
242: * ..
243: * .. External Subroutines ..
244: EXTERNAL DPPTRF, DSPEVD, DSPGST, DTPMV, DTPSV, XERBLA
245: * ..
246: * .. Intrinsic Functions ..
247: INTRINSIC DBLE, MAX
248: * ..
249: * .. Executable Statements ..
250: *
251: * Test the input parameters.
252: *
253: WANTZ = LSAME( JOBZ, 'V' )
254: UPPER = LSAME( UPLO, 'U' )
255: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
256: *
257: INFO = 0
258: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
259: INFO = -1
260: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
261: INFO = -2
262: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
263: INFO = -3
264: ELSE IF( N.LT.0 ) THEN
265: INFO = -4
266: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
267: INFO = -9
268: END IF
269: *
270: IF( INFO.EQ.0 ) THEN
271: IF( N.LE.1 ) THEN
272: LIWMIN = 1
273: LWMIN = 1
274: ELSE
275: IF( WANTZ ) THEN
276: LIWMIN = 3 + 5*N
277: LWMIN = 1 + 6*N + 2*N**2
278: ELSE
279: LIWMIN = 1
280: LWMIN = 2*N
281: END IF
282: END IF
283: WORK( 1 ) = LWMIN
284: IWORK( 1 ) = LIWMIN
285: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
286: INFO = -11
287: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
288: INFO = -13
289: END IF
290: END IF
291: *
292: IF( INFO.NE.0 ) THEN
293: CALL XERBLA( 'DSPGVD', -INFO )
294: RETURN
295: ELSE IF( LQUERY ) THEN
296: RETURN
297: END IF
298: *
299: * Quick return if possible
300: *
301: IF( N.EQ.0 )
302: $ RETURN
303: *
304: * Form a Cholesky factorization of BP.
305: *
306: CALL DPPTRF( UPLO, N, BP, INFO )
307: IF( INFO.NE.0 ) THEN
308: INFO = N + INFO
309: RETURN
310: END IF
311: *
312: * Transform problem to standard eigenvalue problem and solve.
313: *
314: CALL DSPGST( ITYPE, UPLO, N, AP, BP, INFO )
315: CALL DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK,
316: $ LIWORK, INFO )
317: LWMIN = MAX( DBLE( LWMIN ), DBLE( WORK( 1 ) ) )
318: LIWMIN = MAX( DBLE( LIWMIN ), DBLE( IWORK( 1 ) ) )
319: *
320: IF( WANTZ ) THEN
321: *
322: * Backtransform eigenvectors to the original problem.
323: *
324: NEIG = N
325: IF( INFO.GT.0 )
326: $ NEIG = INFO - 1
327: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
328: *
329: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
1.8 bertrand 330: * backtransform eigenvectors: x = inv(L)**T *y or inv(U)*y
1.1 bertrand 331: *
332: IF( UPPER ) THEN
333: TRANS = 'N'
334: ELSE
335: TRANS = 'T'
336: END IF
337: *
338: DO 10 J = 1, NEIG
339: CALL DTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
340: $ 1 )
341: 10 CONTINUE
342: *
343: ELSE IF( ITYPE.EQ.3 ) THEN
344: *
345: * For B*A*x=(lambda)*x;
1.8 bertrand 346: * backtransform eigenvectors: x = L*y or U**T *y
1.1 bertrand 347: *
348: IF( UPPER ) THEN
349: TRANS = 'T'
350: ELSE
351: TRANS = 'N'
352: END IF
353: *
354: DO 20 J = 1, NEIG
355: CALL DTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
356: $ 1 )
357: 20 CONTINUE
358: END IF
359: END IF
360: *
361: WORK( 1 ) = LWMIN
362: IWORK( 1 ) = LIWMIN
363: *
364: RETURN
365: *
366: * End of DSPGVD
367: *
368: END
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