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diff --git a/ml/dlib/dlib/matrix/lapack/syevr.h b/ml/dlib/dlib/matrix/lapack/syevr.h new file mode 100644 index 000000000..65190b3d8 --- /dev/null +++ b/ml/dlib/dlib/matrix/lapack/syevr.h @@ -0,0 +1,445 @@ +// Copyright (C) 2010 Davis E. King (davis@dlib.net) +// License: Boost Software License See LICENSE.txt for the full license. +#ifndef DLIB_LAPACk_EVR_Hh_ +#define DLIB_LAPACk_EVR_Hh_ + +#include "fortran_id.h" +#include "../matrix.h" + +namespace dlib +{ + namespace lapack + { + namespace binding + { + extern "C" + { + void DLIB_FORTRAN_ID(dsyevr) (char *jobz, char *range, char *uplo, integer *n, + double *a, integer *lda, double *vl, double *vu, integer * il, + integer *iu, double *abstol, integer *m, double *w, + double *z_, integer *ldz, integer *isuppz, double *work, + integer *lwork, integer *iwork, integer *liwork, integer *info); + + void DLIB_FORTRAN_ID(ssyevr) (char *jobz, char *range, char *uplo, integer *n, + float *a, integer *lda, float *vl, float *vu, integer * il, + integer *iu, float *abstol, integer *m, float *w, + float *z_, integer *ldz, integer *isuppz, float *work, + integer *lwork, integer *iwork, integer *liwork, integer *info); + } + + inline int syevr (char jobz, char range, char uplo, integer n, + double* a, integer lda, double vl, double vu, integer il, + integer iu, double abstol, integer *m, double *w, + double *z, integer ldz, integer *isuppz, double *work, + integer lwork, integer *iwork, integer liwork) + { + integer info = 0; + DLIB_FORTRAN_ID(dsyevr)(&jobz, &range, &uplo, &n, + a, &lda, &vl, &vu, &il, + &iu, &abstol, m, w, + z, &ldz, isuppz, work, + &lwork, iwork, &liwork, &info); + return info; + } + + inline int syevr (char jobz, char range, char uplo, integer n, + float* a, integer lda, float vl, float vu, integer il, + integer iu, float abstol, integer *m, float *w, + float *z, integer ldz, integer *isuppz, float *work, + integer lwork, integer *iwork, integer liwork) + { + integer info = 0; + DLIB_FORTRAN_ID(ssyevr)(&jobz, &range, &uplo, &n, + a, &lda, &vl, &vu, &il, + &iu, &abstol, m, w, + z, &ldz, isuppz, work, + &lwork, iwork, &liwork, &info); + return info; + } + + } + + // ------------------------------------------------------------------------------------ + + /* + +* -- LAPACK driver routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER JOBZ, RANGE, UPLO + INTEGER IL, INFO, IU, LDA, LDZ, LIWORK, LWORK, M, N + DOUBLE PRECISION ABSTOL, VL, VU +* .. +* .. Array Arguments .. + INTEGER ISUPPZ( * ), IWORK( * ) + DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * ) +* .. +* +* Purpose +* ======= +* +* DSYEVR computes selected eigenvalues and, optionally, eigenvectors +* of a real symmetric matrix A. Eigenvalues and eigenvectors can be +* selected by specifying either a range of values or a range of +* indices for the desired eigenvalues. +* +* DSYEVR first reduces the matrix A to tridiagonal form T with a call +* to DSYTRD. Then, whenever possible, DSYEVR calls DSTEMR to compute +* the eigenspectrum using Relatively Robust Representations. DSTEMR +* computes eigenvalues by the dqds algorithm, while orthogonal +* eigenvectors are computed from various "good" L D L^T representations +* (also known as Relatively Robust Representations). Gram-Schmidt +* orthogonalization is avoided as far as possible. More specifically, +* the various steps of the algorithm are as follows. +* +* For each unreduced block (submatrix) of T, +* (a) Compute T - sigma I = L D L^T, so that L and D +* define all the wanted eigenvalues to high relative accuracy. +* This means that small relative changes in the entries of D and L +* cause only small relative changes in the eigenvalues and +* eigenvectors. The standard (unfactored) representation of the +* tridiagonal matrix T does not have this property in general. +* (b) Compute the eigenvalues to suitable accuracy. +* If the eigenvectors are desired, the algorithm attains full +* accuracy of the computed eigenvalues only right before +* the corresponding vectors have to be computed, see steps c) and d). +* (c) For each cluster of close eigenvalues, select a new +* shift close to the cluster, find a new factorization, and refine +* the shifted eigenvalues to suitable accuracy. +* (d) For each eigenvalue with a large enough relative separation compute +* the corresponding eigenvector by forming a rank revealing twisted +* factorization. Go back to (c) for any clusters that remain. +* +* The desired accuracy of the output can be specified by the input +* parameter ABSTOL. +* +* For more details, see DSTEMR's documentation and: +* - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations +* to compute orthogonal eigenvectors of symmetric tridiagonal matrices," +* Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004. +* - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and +* Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25, +* 2004. Also LAPACK Working Note 154. +* - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric +* tridiagonal eigenvalue/eigenvector problem", +* Computer Science Division Technical Report No. UCB/CSD-97-971, +* UC Berkeley, May 1997. +* +* +* Note 1 : DSYEVR calls DSTEMR when the full spectrum is requested +* on machines which conform to the ieee-754 floating point standard. +* DSYEVR calls DSTEBZ and SSTEIN on non-ieee machines and +* when partial spectrum requests are made. +* +* Normal execution of DSTEMR may create NaNs and infinities and +* hence may abort due to a floating point exception in environments +* which do not handle NaNs and infinities in the ieee standard default +* manner. +* +* Arguments +* ========= +* +* JOBZ (input) CHARACTER*1 +* = 'N': Compute eigenvalues only; +* = 'V': Compute eigenvalues and eigenvectors. +* +* RANGE (input) CHARACTER*1 +* = 'A': all eigenvalues will be found. +* = 'V': all eigenvalues in the half-open interval (VL,VU] +* will be found. +* = 'I': the IL-th through IU-th eigenvalues will be found. +********** For RANGE = 'V' or 'I' and IU - IL < N - 1, DSTEBZ and +********** DSTEIN are called +* +* UPLO (input) CHARACTER*1 +* = 'U': Upper triangle of A is stored; +* = 'L': Lower triangle of A is stored. +* +* N (input) INTEGER +* The order of the matrix A. N >= 0. +* +* A (input/output) DOUBLE PRECISION array, dimension (LDA, N) +* On entry, the symmetric matrix A. If UPLO = 'U', the +* leading N-by-N upper triangular part of A contains the +* upper triangular part of the matrix A. If UPLO = 'L', +* the leading N-by-N lower triangular part of A contains +* the lower triangular part of the matrix A. +* On exit, the lower triangle (if UPLO='L') or the upper +* triangle (if UPLO='U') of A, including the diagonal, is +* destroyed. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* VL (input) DOUBLE PRECISION +* VU (input) DOUBLE PRECISION +* If RANGE='V', the lower and upper bounds of the interval to +* be searched for eigenvalues. VL < VU. +* Not referenced if RANGE = 'A' or 'I'. +* +* IL (input) INTEGER +* IU (input) INTEGER +* If RANGE='I', the indices (in ascending order) of the +* smallest and largest eigenvalues to be returned. +* 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. +* Not referenced if RANGE = 'A' or 'V'. +* +* ABSTOL (input) DOUBLE PRECISION +* The absolute error tolerance for the eigenvalues. +* An approximate eigenvalue is accepted as converged +* when it is determined to lie in an interval [a,b] +* of width less than or equal to +* +* ABSTOL + EPS * max( |a|,|b| ) , +* +* where EPS is the machine precision. If ABSTOL is less than +* or equal to zero, then EPS*|T| will be used in its place, +* where |T| is the 1-norm of the tridiagonal matrix obtained +* by reducing A to tridiagonal form. +* +* See "Computing Small Singular Values of Bidiagonal Matrices +* with Guaranteed High Relative Accuracy," by Demmel and +* Kahan, LAPACK Working Note #3. +* +* If high relative accuracy is important, set ABSTOL to +* DLAMCH( 'Safe minimum' ). Doing so will guarantee that +* eigenvalues are computed to high relative accuracy when +* possible in future releases. The current code does not +* make any guarantees about high relative accuracy, but +* future releases will. See J. Barlow and J. Demmel, +* "Computing Accurate Eigensystems of Scaled Diagonally +* Dominant Matrices", LAPACK Working Note #7, for a discussion +* of which matrices define their eigenvalues to high relative +* accuracy. +* +* M (output) INTEGER +* The total number of eigenvalues found. 0 <= M <= N. +* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. +* +* W (output) DOUBLE PRECISION array, dimension (N) +* The first M elements contain the selected eigenvalues in +* ascending order. +* +* Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M)) +* If JOBZ = 'V', then if INFO = 0, the first M columns of Z +* contain the orthonormal eigenvectors of the matrix A +* corresponding to the selected eigenvalues, with the i-th +* column of Z holding the eigenvector associated with W(i). +* If JOBZ = 'N', then Z is not referenced. +* Note: the user must ensure that at least max(1,M) columns are +* supplied in the array Z; if RANGE = 'V', the exact value of M +* is not known in advance and an upper bound must be used. +* Supplying N columns is always safe. +* +* LDZ (input) INTEGER +* The leading dimension of the array Z. LDZ >= 1, and if +* JOBZ = 'V', LDZ >= max(1,N). +* +* ISUPPZ (output) INTEGER array, dimension ( 2*max(1,M) ) +* The support of the eigenvectors in Z, i.e., the indices +* indicating the nonzero elements in Z. The i-th eigenvector +* is nonzero only in elements ISUPPZ( 2*i-1 ) through +* ISUPPZ( 2*i ). +********** Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1 +* +* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) +* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +* +* LWORK (input) INTEGER +* The dimension of the array WORK. LWORK >= max(1,26*N). +* For optimal efficiency, LWORK >= (NB+6)*N, +* where NB is the max of the blocksize for DSYTRD and DORMTR +* returned by ILAENV. +* +* If LWORK = -1, then a workspace query is assumed; the routine +* only calculates the optimal size of the WORK array, returns +* this value as the first entry of the WORK array, and no error +* message related to LWORK is issued by XERBLA. +* +* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) +* On exit, if INFO = 0, IWORK(1) returns the optimal LWORK. +* +* LIWORK (input) INTEGER +* The dimension of the array IWORK. LIWORK >= max(1,10*N). +* +* If LIWORK = -1, then a workspace query is assumed; the +* routine only calculates the optimal size of the IWORK array, +* returns this value as the first entry of the IWORK array, and +* no error message related to LIWORK is issued by XERBLA. +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* > 0: Internal error +* +* Further Details +* =============== +* +* Based on contributions by +* Inderjit Dhillon, IBM Almaden, USA +* Osni Marques, LBNL/NERSC, USA +* Ken Stanley, Computer Science Division, University of +* California at Berkeley, USA +* Jason Riedy, Computer Science Division, University of +* California at Berkeley, USA +* +* ===================================================================== + + */ + + // ------------------------------------------------------------------------------------ + + template < + typename T, + long NR1, long NR2, long NR3, long NR4, + long NC1, long NC2, long NC3, long NC4, + typename MM + > + int syevr ( + const char jobz, + const char range, + const char uplo, + matrix<T,NR1,NC1,MM,column_major_layout>& a, + const double vl, + const double vu, + const integer il, + const integer iu, + const double abstol, + integer& num_eigenvalues_found, + matrix<T,NR2,NC2,MM,column_major_layout>& w, + matrix<T,NR3,NC3,MM,column_major_layout>& z, + matrix<integer,NR4,NC4,MM,column_major_layout>& isuppz + ) + { + matrix<T,0,1,MM,column_major_layout> work; + matrix<integer,0,1,MM,column_major_layout> iwork; + + const long n = a.nr(); + + w.set_size(n,1); + + isuppz.set_size(2*n, 1); + + if (jobz == 'V') + { + z.set_size(n,n); + } + else + { + z.set_size(NR3?NR3:1, NC3?NC3:1); + } + + // figure out how big the workspace needs to be. + T work_size = 1; + integer iwork_size = 1; + int info = binding::syevr(jobz, range, uplo, n, &a(0,0), + a.nr(), vl, vu, il, iu, abstol, &num_eigenvalues_found, + &w(0,0), &z(0,0), z.nr(), &isuppz(0,0), &work_size, -1, + &iwork_size, -1); + + if (info != 0) + return info; + + if (work.size() < work_size) + work.set_size(static_cast<long>(work_size), 1); + if (iwork.size() < iwork_size) + iwork.set_size(iwork_size, 1); + + // compute the actual decomposition + info = binding::syevr(jobz, range, uplo, n, &a(0,0), + a.nr(), vl, vu, il, iu, abstol, &num_eigenvalues_found, + &w(0,0), &z(0,0), z.nr(), &isuppz(0,0), &work(0,0), work.size(), + &iwork(0,0), iwork.size()); + + + return info; + } + + // ------------------------------------------------------------------------------------ + + template < + typename T, + long NR1, long NR2, long NR3, long NR4, + long NC1, long NC2, long NC3, long NC4, + typename MM + > + int syevr ( + const char jobz, + const char range, + char uplo, + matrix<T,NR1,NC1,MM,row_major_layout>& a, + const double vl, + const double vu, + const integer il, + const integer iu, + const double abstol, + integer& num_eigenvalues_found, + matrix<T,NR2,NC2,MM,row_major_layout>& w, + matrix<T,NR3,NC3,MM,row_major_layout>& z, + matrix<integer,NR4,NC4,MM,row_major_layout>& isuppz + ) + { + matrix<T,0,1,MM,row_major_layout> work; + matrix<integer,0,1,MM,row_major_layout> iwork; + + if (uplo == 'L') + uplo = 'U'; + else + uplo = 'L'; + + const long n = a.nr(); + + w.set_size(n,1); + + isuppz.set_size(2*n, 1); + + if (jobz == 'V') + { + z.set_size(n,n); + } + else + { + z.set_size(NR3?NR3:1, NC3?NC3:1); + } + + // figure out how big the workspace needs to be. + T work_size = 1; + integer iwork_size = 1; + int info = binding::syevr(jobz, range, uplo, n, &a(0,0), + a.nc(), vl, vu, il, iu, abstol, &num_eigenvalues_found, + &w(0,0), &z(0,0), z.nc(), &isuppz(0,0), &work_size, -1, + &iwork_size, -1); + + if (info != 0) + return info; + + if (work.size() < work_size) + work.set_size(static_cast<long>(work_size), 1); + if (iwork.size() < iwork_size) + iwork.set_size(iwork_size, 1); + + // compute the actual decomposition + info = binding::syevr(jobz, range, uplo, n, &a(0,0), + a.nc(), vl, vu, il, iu, abstol, &num_eigenvalues_found, + &w(0,0), &z(0,0), z.nc(), &isuppz(0,0), &work(0,0), work.size(), + &iwork(0,0), iwork.size()); + + z = trans(z); + + return info; + } + + // ------------------------------------------------------------------------------------ + + } + +} + +// ---------------------------------------------------------------------------------------- + +#endif // DLIB_LAPACk_EVR_Hh_ + + + |