Annotation of rpl/lapack/lapack/zhpgvd.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 ZHPGVD + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhpgvd.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhpgvd.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhpgvd.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
! 22: * LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER JOBZ, UPLO
! 26: * INTEGER INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * INTEGER IWORK( * )
! 30: * DOUBLE PRECISION RWORK( * ), W( * )
! 31: * COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
! 32: * ..
! 33: *
! 34: *
! 35: *> \par Purpose:
! 36: * =============
! 37: *>
! 38: *> \verbatim
! 39: *>
! 40: *> ZHPGVD computes all the eigenvalues and, optionally, the eigenvectors
! 41: *> of a complex generalized Hermitian-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 Hermitian, 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 COMPLEX*16 array, dimension (N*(N+1)/2)
! 90: *> On entry, the upper or lower triangle of the Hermitian 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 COMPLEX*16 array, dimension (N*(N+1)/2)
! 102: *> On entry, the upper or lower triangle of the Hermitian 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**H*U or B = L*L**H, 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 COMPLEX*16 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**H*B*Z = I;
! 125: *> if ITYPE = 3, Z**H*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 COMPLEX*16 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 >= N.
! 148: *> If JOBZ = 'V' and N > 1, LWORK >= 2*N.
! 149: *>
! 150: *> If LWORK = -1, then a workspace query is assumed; the routine
! 151: *> only calculates the required sizes of the WORK, RWORK and
! 152: *> IWORK arrays, returns these values as the first entries of
! 153: *> the WORK, RWORK and IWORK arrays, and no error message
! 154: *> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 155: *> \endverbatim
! 156: *>
! 157: *> \param[out] RWORK
! 158: *> \verbatim
! 159: *> RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
! 160: *> On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
! 161: *> \endverbatim
! 162: *>
! 163: *> \param[in] LRWORK
! 164: *> \verbatim
! 165: *> LRWORK is INTEGER
! 166: *> The dimension of array RWORK.
! 167: *> If N <= 1, LRWORK >= 1.
! 168: *> If JOBZ = 'N' and N > 1, LRWORK >= N.
! 169: *> If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
! 170: *>
! 171: *> If LRWORK = -1, then a workspace query is assumed; the
! 172: *> routine only calculates the required sizes of the WORK, RWORK
! 173: *> and IWORK arrays, returns these values as the first entries
! 174: *> of the WORK, RWORK and IWORK arrays, and no error message
! 175: *> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 176: *> \endverbatim
! 177: *>
! 178: *> \param[out] IWORK
! 179: *> \verbatim
! 180: *> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
! 181: *> On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
! 182: *> \endverbatim
! 183: *>
! 184: *> \param[in] LIWORK
! 185: *> \verbatim
! 186: *> LIWORK is INTEGER
! 187: *> The dimension of array IWORK.
! 188: *> If JOBZ = 'N' or N <= 1, LIWORK >= 1.
! 189: *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
! 190: *>
! 191: *> If LIWORK = -1, then a workspace query is assumed; the
! 192: *> routine only calculates the required sizes of the WORK, RWORK
! 193: *> and IWORK arrays, returns these values as the first entries
! 194: *> of the WORK, RWORK and IWORK arrays, and no error message
! 195: *> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 196: *> \endverbatim
! 197: *>
! 198: *> \param[out] INFO
! 199: *> \verbatim
! 200: *> INFO is INTEGER
! 201: *> = 0: successful exit
! 202: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 203: *> > 0: ZPPTRF or ZHPEVD returned an error code:
! 204: *> <= N: if INFO = i, ZHPEVD failed to converge;
! 205: *> i off-diagonal elements of an intermediate
! 206: *> tridiagonal form did not convergeto zero;
! 207: *> > N: if INFO = N + i, for 1 <= i <= n, then the leading
! 208: *> minor of order i of B is not positive definite.
! 209: *> The factorization of B could not be completed and
! 210: *> no eigenvalues or eigenvectors were computed.
! 211: *> \endverbatim
! 212: *
! 213: * Authors:
! 214: * ========
! 215: *
! 216: *> \author Univ. of Tennessee
! 217: *> \author Univ. of California Berkeley
! 218: *> \author Univ. of Colorado Denver
! 219: *> \author NAG Ltd.
! 220: *
! 221: *> \date November 2011
! 222: *
! 223: *> \ingroup complex16OTHEReigen
! 224: *
! 225: *> \par Contributors:
! 226: * ==================
! 227: *>
! 228: *> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
! 229: *
! 230: * =====================================================================
1.1 bertrand 231: SUBROUTINE ZHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
232: $ LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
233: *
1.9 ! bertrand 234: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 235: * -- LAPACK is a software package provided by Univ. of Tennessee, --
236: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 237: * November 2011
1.1 bertrand 238: *
239: * .. Scalar Arguments ..
240: CHARACTER JOBZ, UPLO
241: INTEGER INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N
242: * ..
243: * .. Array Arguments ..
244: INTEGER IWORK( * )
245: DOUBLE PRECISION RWORK( * ), W( * )
246: COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
247: * ..
248: *
249: * =====================================================================
250: *
251: * .. Local Scalars ..
252: LOGICAL LQUERY, UPPER, WANTZ
253: CHARACTER TRANS
254: INTEGER J, LIWMIN, LRWMIN, LWMIN, NEIG
255: * ..
256: * .. External Functions ..
257: LOGICAL LSAME
258: EXTERNAL LSAME
259: * ..
260: * .. External Subroutines ..
261: EXTERNAL XERBLA, ZHPEVD, ZHPGST, ZPPTRF, ZTPMV, ZTPSV
262: * ..
263: * .. Intrinsic Functions ..
264: INTRINSIC DBLE, MAX
265: * ..
266: * .. Executable Statements ..
267: *
268: * Test the input parameters.
269: *
270: WANTZ = LSAME( JOBZ, 'V' )
271: UPPER = LSAME( UPLO, 'U' )
272: LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
273: *
274: INFO = 0
275: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
276: INFO = -1
277: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
278: INFO = -2
279: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
280: INFO = -3
281: ELSE IF( N.LT.0 ) THEN
282: INFO = -4
283: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
284: INFO = -9
285: END IF
286: *
287: IF( INFO.EQ.0 ) THEN
288: IF( N.LE.1 ) THEN
289: LWMIN = 1
290: LIWMIN = 1
291: LRWMIN = 1
292: ELSE
293: IF( WANTZ ) THEN
294: LWMIN = 2*N
295: LRWMIN = 1 + 5*N + 2*N**2
296: LIWMIN = 3 + 5*N
297: ELSE
298: LWMIN = N
299: LRWMIN = N
300: LIWMIN = 1
301: END IF
302: END IF
303: *
304: WORK( 1 ) = LWMIN
305: RWORK( 1 ) = LRWMIN
306: IWORK( 1 ) = LIWMIN
307: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
308: INFO = -11
309: ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
310: INFO = -13
311: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
312: INFO = -15
313: END IF
314: END IF
315: *
316: IF( INFO.NE.0 ) THEN
317: CALL XERBLA( 'ZHPGVD', -INFO )
318: RETURN
319: ELSE IF( LQUERY ) THEN
320: RETURN
321: END IF
322: *
323: * Quick return if possible
324: *
325: IF( N.EQ.0 )
326: $ RETURN
327: *
328: * Form a Cholesky factorization of B.
329: *
330: CALL ZPPTRF( UPLO, N, BP, INFO )
331: IF( INFO.NE.0 ) THEN
332: INFO = N + INFO
333: RETURN
334: END IF
335: *
336: * Transform problem to standard eigenvalue problem and solve.
337: *
338: CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )
339: CALL ZHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
340: $ LRWORK, IWORK, LIWORK, INFO )
341: LWMIN = MAX( DBLE( LWMIN ), DBLE( WORK( 1 ) ) )
342: LRWMIN = MAX( DBLE( LRWMIN ), DBLE( RWORK( 1 ) ) )
343: LIWMIN = MAX( DBLE( LIWMIN ), DBLE( IWORK( 1 ) ) )
344: *
345: IF( WANTZ ) THEN
346: *
347: * Backtransform eigenvectors to the original problem.
348: *
349: NEIG = N
350: IF( INFO.GT.0 )
351: $ NEIG = INFO - 1
352: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
353: *
354: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
1.8 bertrand 355: * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
1.1 bertrand 356: *
357: IF( UPPER ) THEN
358: TRANS = 'N'
359: ELSE
360: TRANS = 'C'
361: END IF
362: *
363: DO 10 J = 1, NEIG
364: CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
365: $ 1 )
366: 10 CONTINUE
367: *
368: ELSE IF( ITYPE.EQ.3 ) THEN
369: *
370: * For B*A*x=(lambda)*x;
1.8 bertrand 371: * backtransform eigenvectors: x = L*y or U**H *y
1.1 bertrand 372: *
373: IF( UPPER ) THEN
374: TRANS = 'C'
375: ELSE
376: TRANS = 'N'
377: END IF
378: *
379: DO 20 J = 1, NEIG
380: CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
381: $ 1 )
382: 20 CONTINUE
383: END IF
384: END IF
385: *
386: WORK( 1 ) = LWMIN
387: RWORK( 1 ) = LRWMIN
388: IWORK( 1 ) = LIWMIN
389: RETURN
390: *
391: * End of ZHPGVD
392: *
393: END
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