eigensolvers.h

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/* ------------------------------------------------------------
   This is the file "eigensolvers.h" of the H2Lib package.
   All rights reserved, Steffen Boerm 2009
   ------------------------------------------------------------ */

#ifndef EIGENSOLVERS_H
#define EIGENSOLVERS_H

typedef struct _tridiag tridiag;

typedef tridiag *ptridiag;

typedef const tridiag *pctridiag;

#include "amatrix.h"
#include "realavector.h"
#include "settings.h"

struct _tridiag {
  preal d;

  preal l;
  
  preal u;

  uint size;

  ptridiag owner;
};

/* ------------------------------------------------------------
   Constructors and destructors
   ------------------------------------------------------------ */

HEADER_PREFIX ptridiag
init_tridiag(ptridiag T, uint size);

HEADER_PREFIX ptridiag
init_sub_tridiag(ptridiag T, ptridiag src, uint size, uint off);

HEADER_PREFIX ptridiag
init_vec_tridiag(ptridiag T, prealavector src, uint size);

HEADER_PREFIX void
uninit_tridiag(ptridiag T);

HEADER_PREFIX ptridiag
new_tridiag(uint size);

HEADER_PREFIX void
del_tridiag(ptridiag T);

/* ------------------------------------------------------------
   Simple utility functions
   ------------------------------------------------------------ */

HEADER_PREFIX void
copy_tridiag(pctridiag T, ptridiag Tcopy);

HEADER_PREFIX real
check_tridiag(pctridiag T, pcamatrix Ts);

HEADER_PREFIX real
check_lower_tridiag(pctridiag T, pcamatrix Ts);

HEADER_PREFIX void
diageval_tridiag_amatrix(field alpha,
       bool atrans, pctridiag a,
       bool xtrans, pamatrix x);

HEADER_PREFIX void
lowereval_tridiag_amatrix(field alpha,
        bool atrans, pctridiag a,
        bool xtrans, pamatrix x);

/* ------------------------------------------------------------
   Compute eigenvalues and eigenvectors,
   only for self-adjoint tridiagonal matrices
   ------------------------------------------------------------ */

HEADER_PREFIX void
qrstep_tridiag(ptridiag T, field shift, pamatrix Q);

HEADER_PREFIX uint
sb_muleig_tridiag(ptridiag T, pamatrix Q, uint maxiter);

HEADER_PREFIX uint
muleig_tridiag(ptridiag T, pamatrix Q);

HEADER_PREFIX uint
eig_tridiag(ptridiag T, pamatrix Q);

HEADER_PREFIX void
sb_tridiagonalize_amatrix(pamatrix A,
        ptridiag T, pamatrix Q);

HEADER_PREFIX void
tridiagonalize_amatrix(pamatrix A,
           ptridiag T, pamatrix Q);

HEADER_PREFIX uint
sb_eig_amatrix(pamatrix A, prealavector lambda, pamatrix Q, uint maxiter);

HEADER_PREFIX uint
eig_amatrix(pamatrix A, prealavector lambda, pamatrix Q);

HEADER_PREFIX uint
geig_amatrix(pamatrix A, pamatrix M, prealavector lambda, pamatrix Q);

/* ------------------------------------------------------------
   Singular value decomposition of a sub-bidiagonal matrix
   ------------------------------------------------------------ */

HEADER_PREFIX void
svdstep_tridiag(ptridiag T, field shift, pamatrix U, pamatrix Vt);

HEADER_PREFIX uint
sb_mulsvd_tridiag(ptridiag T, pamatrix U, pamatrix Vt, uint maxiter);

HEADER_PREFIX uint
mulsvd_tridiag(ptridiag T, pamatrix U, pamatrix Vt);

HEADER_PREFIX uint
svd_tridiag(ptridiag T, pamatrix U, pamatrix Vt);

HEADER_PREFIX void
sb_bidiagonalize_amatrix(pamatrix A,
       ptridiag T, pamatrix U, pamatrix Vt);

HEADER_PREFIX void
bidiagonalize_amatrix(pamatrix A,
          ptridiag T, pamatrix U, pamatrix Vt);

HEADER_PREFIX uint
sb_svd_amatrix(pamatrix A,
         prealavector sigma, pamatrix U, pamatrix Vt, uint maxiter);

HEADER_PREFIX uint
svd_amatrix(pamatrix A, prealavector sigma, pamatrix U, pamatrix Vt);

#endif