// 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_gen
//! @{
template<typename T1>
inline
void
op_inv_gen_default::apply(Mat<typename T1::elem_type>& out, const Op<T1,op_inv_gen_default>& X)
{
arma_debug_sigprint();
const bool status = op_inv_gen_default::apply_direct(out, X.m, "inv()");
if(status == false)
{
out.soft_reset();
arma_stop_runtime_error("inv(): matrix is singular");
}
}
template<typename T1>
inline
bool
op_inv_gen_default::apply_direct(Mat<typename T1::elem_type>& out, const Base<typename T1::elem_type,T1>& expr, const char* caller_sig)
{
arma_debug_sigprint();
return op_inv_gen_full::apply_direct<T1,false>(out, expr, caller_sig, uword(0));
}
//
template<typename T1>
inline
void
op_inv_gen_full::apply(Mat<typename T1::elem_type>& out, const Op<T1,op_inv_gen_full>& X)
{
arma_debug_sigprint();
const uword flags = X.aux_uword_a;
const bool status = op_inv_gen_full::apply_direct(out, X.m, "inv()", flags);
if(status == false)
{
out.soft_reset();
arma_stop_runtime_error("inv(): matrix is singular");
}
}
template<typename T1, const bool has_user_flags>
inline
bool
op_inv_gen_full::apply_direct(Mat<typename T1::elem_type>& out, const Base<typename T1::elem_type,T1>& expr, const char* caller_sig, 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_gen_full: has_user_flags = true"); }
if(has_user_flags == false) { arma_debug_print("op_inv_gen_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_gen_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(): options 'fast' and 'allow_approx' are mutually exclusive" );
arma_conform_check( (fast && no_ugly ), "inv(): options 'fast' and 'no_ugly' are mutually exclusive" );
arma_conform_check( (no_ugly && allow_approx), "inv(): options 'no_ugly' and 'allow_approx' are mutually exclusive" );
}
if(no_ugly)
{
op_inv_gen_state<T> inv_state;
const bool status = op_inv_gen_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_gen_state<T> inv_state;
Mat<eT> tmp;
const bool status = op_inv_gen_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))
{
Mat<eT> A = expr.get_ref();
if(inv_state.is_diag) { return op_pinv::apply_diag(out, A, T(0) ); }
if(inv_state.is_sym ) { return op_pinv::apply_sym (out, A, T(0), uword(0)); }
return op_pinv::apply_gen(out, A, T(0), uword(0));
}
out.steal_mem(tmp);
return true;
}
out = expr.get_ref();
arma_conform_check( (out.is_square() == false), caller_sig, ": given matrix must be square sized", [&](){ out.soft_reset(); } );
const uword N = out.n_rows;
if(N == 0) { return true; }
if(is_cx<eT>::no)
{
if(N == 1)
{
const eT a = out[0];
out[0] = eT(1) / a;
return (a != eT(0));
}
else
if(N == 2)
{
const bool status = op_inv_gen_full::apply_tiny_2x2(out);
if(status) { return true; }
}
else
if(N == 3)
{
const bool status = op_inv_gen_full::apply_tiny_3x3(out);
if(status) { return true; }
}
// fallthrough if optimisation failed
}
if(is_op_diagmat<T1>::value || out.is_diagmat())
{
arma_debug_print("op_inv_gen_full: detected diagonal matrix");
eT* colmem = out.memptr();
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)) { return false; }
out_ii = inv_val;
colmem += N;
}
return true;
}
const strip_trimat<T1> strip(expr.get_ref());
const bool is_triu_expr = strip.do_triu;
const bool is_tril_expr = strip.do_tril;
const bool is_triu_mat = (is_triu_expr || is_tril_expr) ? false : ( trimat_helper::is_triu(out));
const bool is_tril_mat = (is_triu_expr || is_tril_expr) ? false : ((is_triu_mat) ? false : trimat_helper::is_tril(out));
if(is_triu_expr || is_tril_expr || is_triu_mat || is_tril_mat)
{
return auxlib::inv_tr(out, ((is_triu_expr || is_triu_mat) ? uword(0) : uword(1)));
}
const bool try_sympd = arma_config::optimise_sym && sym_helper::guess_sympd(out);
if(try_sympd)
{
arma_debug_print("op_inv_gen_full: attempting sympd optimisation");
Mat<eT> tmp = out;
bool sympd_state = false;
const bool status = auxlib::inv_sympd(tmp, sympd_state);
if(status) { out.steal_mem(tmp); return true; }
if((status == false) && (sympd_state == true)) { return false; }
arma_debug_print("op_inv_gen_full: sympd optimisation failed");
// fallthrough if optimisation failed
}
return auxlib::inv(out);
}
template<typename eT>
inline
bool
op_inv_gen_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
constexpr T det_min = std::numeric_limits<T>::epsilon();
constexpr T det_max = T(1) / std::numeric_limits<T>::epsilon();
eT* Xm = X.memptr();
const eT a = Xm[pos<0,0>::n2];
const eT b = Xm[pos<0,1>::n2];
const eT c = Xm[pos<1,0>::n2];
const eT d = Xm[pos<1,1>::n2];
const eT det_val = (a*d - b*c);
const T abs_det_val = std::abs(det_val);
if((abs_det_val < det_min) || (abs_det_val > det_max) || arma_isnan(det_val)) { return false; }
Xm[pos<0,0>::n2] = d / det_val;
Xm[pos<0,1>::n2] = -b / det_val;
Xm[pos<1,0>::n2] = -c / det_val;
Xm[pos<1,1>::n2] = a / det_val;
return true;
}
template<typename eT>
inline
bool
op_inv_gen_full::apply_tiny_3x3(Mat<eT>& X)
{
arma_debug_sigprint();
typedef typename get_pod_type<eT>::result T;
// NOTE: assuming matrix X is square sized
constexpr T det_min = std::numeric_limits<T>::epsilon();
constexpr T det_max = T(1) / std::numeric_limits<T>::epsilon();
Mat<eT> Y(3, 3, arma_nozeros_indicator());
eT* Xm = X.memptr();
eT* Ym = Y.memptr();
const eT det_val = op_det::apply_tiny_3x3(X);
const T abs_det_val = std::abs(det_val);
if((abs_det_val < det_min) || (abs_det_val > det_max) || arma_isnan(det_val)) { return false; }
Ym[pos<0,0>::n3] = (Xm[pos<2,2>::n3]*Xm[pos<1,1>::n3] - Xm[pos<2,1>::n3]*Xm[pos<1,2>::n3]) / det_val;
Ym[pos<1,0>::n3] = -(Xm[pos<2,2>::n3]*Xm[pos<1,0>::n3] - Xm[pos<2,0>::n3]*Xm[pos<1,2>::n3]) / det_val;
Ym[pos<2,0>::n3] = (Xm[pos<2,1>::n3]*Xm[pos<1,0>::n3] - Xm[pos<2,0>::n3]*Xm[pos<1,1>::n3]) / det_val;
Ym[pos<0,1>::n3] = -(Xm[pos<2,2>::n3]*Xm[pos<0,1>::n3] - Xm[pos<2,1>::n3]*Xm[pos<0,2>::n3]) / det_val;
Ym[pos<1,1>::n3] = (Xm[pos<2,2>::n3]*Xm[pos<0,0>::n3] - Xm[pos<2,0>::n3]*Xm[pos<0,2>::n3]) / det_val;
Ym[pos<2,1>::n3] = -(Xm[pos<2,1>::n3]*Xm[pos<0,0>::n3] - Xm[pos<2,0>::n3]*Xm[pos<0,1>::n3]) / det_val;
Ym[pos<0,2>::n3] = (Xm[pos<1,2>::n3]*Xm[pos<0,1>::n3] - Xm[pos<1,1>::n3]*Xm[pos<0,2>::n3]) / det_val;
Ym[pos<1,2>::n3] = -(Xm[pos<1,2>::n3]*Xm[pos<0,0>::n3] - Xm[pos<1,0>::n3]*Xm[pos<0,2>::n3]) / det_val;
Ym[pos<2,2>::n3] = (Xm[pos<1,1>::n3]*Xm[pos<0,0>::n3] - Xm[pos<1,0>::n3]*Xm[pos<0,1>::n3]) / det_val;
const eT check_val = Xm[pos<0,0>::n3]*Ym[pos<0,0>::n3] + Xm[pos<0,1>::n3]*Ym[pos<1,0>::n3] + Xm[pos<0,2>::n3]*Ym[pos<2,0>::n3];
const T max_diff = (is_float<T>::value) ? T(1e-4) : T(1e-10); // empirically determined; may need tuning
if(std::abs(T(1) - check_val) >= max_diff) { return false; }
arrayops::copy(Xm, Ym, uword(3*3));
return true;
}
template<typename T1>
inline
bool
op_inv_gen_rcond::apply_direct(Mat<typename T1::elem_type>& out, op_inv_gen_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(): given matrix must be square sized", [&](){ out.soft_reset(); } );
if(is_op_diagmat<T1>::value || out.is_diagmat())
{
arma_debug_print("op_inv_gen_rcond: detected diagonal matrix");
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)) { 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;
}
const strip_trimat<T1> strip(expr.get_ref());
const bool is_triu_expr = strip.do_triu;
const bool is_tril_expr = strip.do_tril;
const bool is_triu_mat = (is_triu_expr || is_tril_expr) ? false : ( trimat_helper::is_triu(out));
const bool is_tril_mat = (is_triu_expr || is_tril_expr) ? false : ((is_triu_mat) ? false : trimat_helper::is_tril(out));
if(is_triu_expr || is_tril_expr || is_triu_mat || is_tril_mat)
{
return auxlib::inv_tr_rcond(out, out_state.rcond, ((is_triu_expr || is_triu_mat) ? uword(0) : uword(1)));
}
const bool try_sympd = arma_config::optimise_sym && ((auxlib::crippled_lapack(out)) ? false : sym_helper::guess_sympd(out));
if(try_sympd)
{
arma_debug_print("op_inv_gen_rcond: attempting sympd optimisation");
out_state.is_sym = true;
Mat<eT> tmp = out;
bool sympd_state = false;
const bool status = auxlib::inv_sympd_rcond(tmp, sympd_state, out_state.rcond);
if(status) { out.steal_mem(tmp); return true; }
if((status == false) && (sympd_state == true)) { return false; }
arma_debug_print("op_inv_gen_rcond: sympd optimisation failed");
// fallthrough if optimisation failed
}
return auxlib::inv_rcond(out, out_state.rcond);
}
//! @}