364 lines
9.7 KiB
C++
364 lines
9.7 KiB
C++
// SPDX-License-Identifier: Apache-2.0
|
|
//
|
|
// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
|
|
// Copyright 2008-2016 National ICT Australia (NICTA)
|
|
//
|
|
// Licensed under the Apache License, Version 2.0 (the "License");
|
|
// you may not use this file except in compliance with the License.
|
|
// You may obtain a copy of the License at
|
|
// http://www.apache.org/licenses/LICENSE-2.0
|
|
//
|
|
// Unless required by applicable law or agreed to in writing, software
|
|
// distributed under the License is distributed on an "AS IS" BASIS,
|
|
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
|
// See the License for the specific language governing permissions and
|
|
// limitations under the License.
|
|
// ------------------------------------------------------------------------
|
|
|
|
|
|
//! \addtogroup op_inv_spd
|
|
//! @{
|
|
|
|
|
|
|
|
template<typename T1>
|
|
inline
|
|
void
|
|
op_inv_spd_default::apply(Mat<typename T1::elem_type>& out, const Op<T1,op_inv_spd_default>& X)
|
|
{
|
|
arma_debug_sigprint();
|
|
|
|
const bool status = op_inv_spd_default::apply_direct(out, X.m);
|
|
|
|
if(status == false)
|
|
{
|
|
out.soft_reset();
|
|
arma_stop_runtime_error("inv_sympd(): matrix is singular or not positive definite");
|
|
}
|
|
}
|
|
|
|
|
|
|
|
template<typename T1>
|
|
inline
|
|
bool
|
|
op_inv_spd_default::apply_direct(Mat<typename T1::elem_type>& out, const Base<typename T1::elem_type,T1>& expr)
|
|
{
|
|
arma_debug_sigprint();
|
|
|
|
return op_inv_spd_full::apply_direct<T1,false>(out, expr, uword(0));
|
|
}
|
|
|
|
|
|
|
|
//
|
|
|
|
|
|
|
|
template<typename T1>
|
|
inline
|
|
void
|
|
op_inv_spd_full::apply(Mat<typename T1::elem_type>& out, const Op<T1,op_inv_spd_full>& X)
|
|
{
|
|
arma_debug_sigprint();
|
|
|
|
const uword flags = X.aux_uword_a;
|
|
|
|
const bool status = op_inv_spd_full::apply_direct(out, X.m, flags);
|
|
|
|
if(status == false)
|
|
{
|
|
out.soft_reset();
|
|
arma_stop_runtime_error("inv_sympd(): matrix is singular or not positive definite");
|
|
}
|
|
}
|
|
|
|
|
|
|
|
template<typename T1, const bool has_user_flags>
|
|
inline
|
|
bool
|
|
op_inv_spd_full::apply_direct(Mat<typename T1::elem_type>& out, const Base<typename T1::elem_type,T1>& expr, const uword flags)
|
|
{
|
|
arma_debug_sigprint();
|
|
|
|
typedef typename T1::elem_type eT;
|
|
typedef typename T1::pod_type T;
|
|
|
|
if(has_user_flags == true ) { arma_debug_print("op_inv_spd_full: has_user_flags = true"); }
|
|
if(has_user_flags == false) { arma_debug_print("op_inv_spd_full: has_user_flags = false"); }
|
|
|
|
const bool fast = has_user_flags && bool(flags & inv_opts::flag_fast );
|
|
const bool allow_approx = has_user_flags && bool(flags & inv_opts::flag_allow_approx);
|
|
const bool no_ugly = has_user_flags && bool(flags & inv_opts::flag_no_ugly );
|
|
|
|
if(has_user_flags)
|
|
{
|
|
arma_debug_print("op_inv_spd_full: enabled flags:");
|
|
|
|
if(fast ) { arma_debug_print("fast"); }
|
|
if(allow_approx) { arma_debug_print("allow_approx"); }
|
|
if(no_ugly ) { arma_debug_print("no_ugly"); }
|
|
|
|
arma_conform_check( (fast && allow_approx), "inv_sympd(): options 'fast' and 'allow_approx' are mutually exclusive" );
|
|
arma_conform_check( (fast && no_ugly ), "inv_sympd(): options 'fast' and 'no_ugly' are mutually exclusive" );
|
|
arma_conform_check( (no_ugly && allow_approx), "inv_sympd(): options 'no_ugly' and 'allow_approx' are mutually exclusive" );
|
|
}
|
|
|
|
if(no_ugly)
|
|
{
|
|
op_inv_spd_state<T> inv_state;
|
|
|
|
const bool status = op_inv_spd_rcond::apply_direct(out, inv_state, expr);
|
|
|
|
// workaround for bug in gcc 4.8
|
|
const uword local_size = inv_state.size;
|
|
const T local_rcond = inv_state.rcond;
|
|
|
|
if((status == false) || (local_rcond < ((std::max)(local_size, uword(1)) * std::numeric_limits<T>::epsilon())) || arma_isnan(local_rcond)) { return false; }
|
|
|
|
return true;
|
|
}
|
|
|
|
if(allow_approx)
|
|
{
|
|
op_inv_spd_state<T> inv_state;
|
|
|
|
Mat<eT> tmp;
|
|
|
|
const bool status = op_inv_spd_rcond::apply_direct(tmp, inv_state, expr);
|
|
|
|
// workaround for bug in gcc 4.8
|
|
const uword local_size = inv_state.size;
|
|
const T local_rcond = inv_state.rcond;
|
|
|
|
if((status == false) || (local_rcond < ((std::max)(local_size, uword(1)) * std::numeric_limits<T>::epsilon())) || arma_isnan(local_rcond))
|
|
{
|
|
const Mat<eT> A = expr.get_ref();
|
|
|
|
if(inv_state.is_diag) { return op_pinv::apply_diag(out, A, T(0)); }
|
|
|
|
return op_pinv::apply_sym(out, A, T(0), uword(0));
|
|
}
|
|
|
|
out.steal_mem(tmp);
|
|
|
|
return true;
|
|
}
|
|
|
|
out = expr.get_ref();
|
|
|
|
arma_conform_check( (out.is_square() == false), "inv_sympd(): given matrix must be square sized", [&](){ out.soft_reset(); } );
|
|
|
|
if((arma_config::check_conform) && (arma_config::warn_level > 0))
|
|
{
|
|
if(auxlib::rudimentary_sym_check(out) == false)
|
|
{
|
|
if(is_cx<eT>::no ) { arma_warn(1, "inv_sympd(): given matrix is not symmetric"); }
|
|
if(is_cx<eT>::yes) { arma_warn(1, "inv_sympd(): given matrix is not hermitian"); }
|
|
}
|
|
else
|
|
if((is_cx<eT>::yes) && (sym_helper::check_diag_imag(out) == false))
|
|
{
|
|
arma_warn(1, "inv_sympd(): imaginary components on diagonal are non-zero");
|
|
}
|
|
}
|
|
|
|
const uword N = out.n_rows;
|
|
|
|
if(N == 0) { return true; }
|
|
|
|
if(is_cx<eT>::no)
|
|
{
|
|
if(N == 1)
|
|
{
|
|
const T a = access::tmp_real(out[0]);
|
|
|
|
out[0] = eT(T(1) / a);
|
|
|
|
return (a > T(0));
|
|
}
|
|
else
|
|
if(N == 2)
|
|
{
|
|
const bool status = op_inv_spd_full::apply_tiny_2x2(out);
|
|
|
|
if(status) { return true; }
|
|
}
|
|
|
|
// fallthrough if optimisation failed
|
|
}
|
|
|
|
if(is_op_diagmat<T1>::value || out.is_diagmat())
|
|
{
|
|
arma_debug_print("op_inv_spd_full: diag optimisation");
|
|
|
|
eT* colmem = out.memptr();
|
|
|
|
for(uword i=0; i<N; ++i)
|
|
{
|
|
eT& out_ii = colmem[i];
|
|
const T out_ii_real = access::tmp_real(out_ii);
|
|
|
|
if(out_ii_real <= T(0)) { return false; }
|
|
|
|
out_ii = eT(T(1) / out_ii_real);
|
|
|
|
colmem += N;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
bool sympd_state_junk = false;
|
|
|
|
return auxlib::inv_sympd(out, sympd_state_junk);
|
|
}
|
|
|
|
|
|
|
|
template<typename eT>
|
|
inline
|
|
bool
|
|
op_inv_spd_full::apply_tiny_2x2(Mat<eT>& X)
|
|
{
|
|
arma_debug_sigprint();
|
|
|
|
typedef typename get_pod_type<eT>::result T;
|
|
|
|
// NOTE: assuming matrix X is square sized
|
|
// NOTE: assuming matrix X is symmetric
|
|
// NOTE: assuming matrix X is real
|
|
|
|
constexpr T det_min = std::numeric_limits<T>::epsilon();
|
|
constexpr T det_max = T(1) / std::numeric_limits<T>::epsilon();
|
|
|
|
eT* Xm = X.memptr();
|
|
|
|
T a = access::tmp_real(Xm[0]);
|
|
T c = access::tmp_real(Xm[1]);
|
|
T d = access::tmp_real(Xm[3]);
|
|
|
|
const T det_val = (a*d - c*c);
|
|
|
|
// positive definite iff all leading principal minors are positive
|
|
// a = first leading principal minor (top-left 1x1 submatrix)
|
|
// det_val = second leading principal minor (top-left 2x2 submatrix)
|
|
|
|
if(a <= T(0)) { return false; }
|
|
|
|
// NOTE: since det_min is positive, this also checks whether det_val is positive
|
|
if((det_val < det_min) || (det_val > det_max) || arma_isnan(det_val)) { return false; }
|
|
|
|
d /= det_val;
|
|
c /= det_val;
|
|
a /= det_val;
|
|
|
|
Xm[0] = d;
|
|
Xm[1] = -c;
|
|
Xm[2] = -c;
|
|
Xm[3] = a;
|
|
|
|
return true;
|
|
}
|
|
|
|
|
|
|
|
//
|
|
|
|
|
|
|
|
template<typename T1>
|
|
inline
|
|
bool
|
|
op_inv_spd_rcond::apply_direct(Mat<typename T1::elem_type>& out, op_inv_spd_state<typename T1::pod_type>& out_state, const Base<typename T1::elem_type,T1>& expr)
|
|
{
|
|
arma_debug_sigprint();
|
|
|
|
typedef typename T1::elem_type eT;
|
|
typedef typename T1::pod_type T;
|
|
|
|
out = expr.get_ref();
|
|
out_state.size = out.n_rows;
|
|
out_state.rcond = T(0);
|
|
|
|
arma_conform_check( (out.is_square() == false), "inv_sympd(): given matrix must be square sized", [&](){ out.soft_reset(); } );
|
|
|
|
if((arma_config::check_conform) && (arma_config::warn_level > 0))
|
|
{
|
|
if(auxlib::rudimentary_sym_check(out) == false)
|
|
{
|
|
if(is_cx<eT>::no ) { arma_warn(1, "inv_sympd(): given matrix is not symmetric"); }
|
|
if(is_cx<eT>::yes) { arma_warn(1, "inv_sympd(): given matrix is not hermitian"); }
|
|
}
|
|
else
|
|
if((is_cx<eT>::yes) && (sym_helper::check_diag_imag(out) == false))
|
|
{
|
|
arma_warn(1, "inv_sympd(): imaginary components on diagonal are non-zero");
|
|
}
|
|
}
|
|
|
|
if(is_op_diagmat<T1>::value || out.is_diagmat())
|
|
{
|
|
arma_debug_print("op_inv_spd_rcond: diag optimisation");
|
|
|
|
out_state.is_diag = true;
|
|
|
|
eT* colmem = out.memptr();
|
|
|
|
T max_abs_src_val = T(0);
|
|
T max_abs_inv_val = T(0);
|
|
|
|
const uword N = out.n_rows;
|
|
|
|
for(uword i=0; i<N; ++i)
|
|
{
|
|
eT& out_ii = colmem[i];
|
|
|
|
const eT src_val = out_ii;
|
|
const eT inv_val = eT(1) / src_val;
|
|
|
|
if( (src_val == eT(0)) || (access::tmp_real(src_val) <= T(0)) ) { return false; }
|
|
|
|
out_ii = inv_val;
|
|
|
|
const T abs_src_val = std::abs(src_val);
|
|
const T abs_inv_val = std::abs(inv_val);
|
|
|
|
max_abs_src_val = (abs_src_val > max_abs_src_val) ? abs_src_val : max_abs_src_val;
|
|
max_abs_inv_val = (abs_inv_val > max_abs_inv_val) ? abs_inv_val : max_abs_inv_val;
|
|
|
|
colmem += N;
|
|
}
|
|
|
|
out_state.rcond = T(1) / (max_abs_src_val * max_abs_inv_val);
|
|
|
|
return true;
|
|
}
|
|
|
|
if(auxlib::crippled_lapack(out))
|
|
{
|
|
arma_debug_print("op_inv_spd_rcond: workaround for crippled lapack");
|
|
|
|
Mat<eT> tmp = out;
|
|
|
|
bool sympd_state = false;
|
|
|
|
auxlib::inv_sympd(out, sympd_state);
|
|
|
|
if(sympd_state == false) { out.soft_reset(); out_state.rcond = T(0); return false; }
|
|
|
|
out_state.rcond = auxlib::rcond(tmp);
|
|
|
|
if(out_state.rcond == T(0)) { out.soft_reset(); return false; }
|
|
|
|
return true;
|
|
}
|
|
|
|
return auxlib::inv_sympd_rcond(out, out_state.rcond);
|
|
}
|
|
|
|
|
|
|
|
//! @}
|