Move into version control

1 files changed, 379 insertions, 0 deletions

diff --git a/src/armadillo/include/armadillo_bits/band_helper.hpp b/src/armadillo/include/armadillo_bits/band_helper.hpp
new file mode 100644
index 0000000..4493c70
--- /dev/null
+++ b/src/armadillo/include/armadillo_bits/band_helper.hpp
@@ -0,0 +1,379 @@
+// 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 band_helper
+//! @{
+
+
+namespace band_helper
+{
+
+
+
+template<typename eT>
+inline
+bool
+is_band(uword& out_KL, uword& out_KU, const Mat<eT>& A, const uword N_min)
+  {
+  arma_extra_debug_sigprint();
+  
+  // NOTE: assuming that A has a square size
+  // NOTE: assuming that N_min is >= 4
+  
+  const uword N = A.n_rows;
+  
+  if(N < N_min)  { return false; }
+  
+  // first, quickly check bottom-left and top-right corners
+  
+  const eT eT_zero = eT(0);
+  
+  const eT* A_col0 = A.memptr();
+  const eT* A_col1 = A_col0 + N;
+  
+  if( (A_col0[N-2] != eT_zero) || (A_col0[N-1] != eT_zero) || (A_col1[N-2] != eT_zero) || (A_col1[N-1] != eT_zero) )  { return false; }
+  
+  const eT* A_colNm2 = A.colptr(N-2);
+  const eT* A_colNm1 = A_colNm2 + N;
+  
+  if( (A_colNm2[0] != eT_zero) || (A_colNm2[1] != eT_zero) || (A_colNm1[0] != eT_zero) || (A_colNm1[1] != eT_zero) )  { return false; }
+  
+  // if we reached this point, go through the entire matrix to work out number of subdiagonals and superdiagonals
+  
+  const uword n_nonzero_threshold = (N*N)/4;  // empirically determined
+  
+  uword KL = 0;  // number of   subdiagonals
+  uword KU = 0;  // number of superdiagonals
+  
+  const eT* A_colptr = A.memptr();
+  
+  for(uword col=0; col < N; ++col)
+    {
+    uword first_nonzero_row = col;
+    uword  last_nonzero_row = col;
+    
+    for(uword row=0; row < col; ++row)
+      {
+      if( A_colptr[row] != eT_zero )  { first_nonzero_row = row; break; }
+      }
+    
+    for(uword row=(col+1); row < N; ++row)
+      {
+      last_nonzero_row = (A_colptr[row] != eT_zero) ? row : last_nonzero_row;
+      }
+    
+    const uword L_count = last_nonzero_row - col;
+    const uword U_count = col - first_nonzero_row;
+    
+    if( (L_count > KL) || (U_count > KU) )
+      {
+      KL = (std::max)(KL, L_count);
+      KU = (std::max)(KU, U_count);
+      
+      const uword n_nonzero = N*(KL+KU+1) - (KL*(KL+1) + KU*(KU+1))/2;
+      
+      // return as soon as we know that it's not worth analysing the matrix any further
+      
+      if(n_nonzero > n_nonzero_threshold)  { return false; }
+      }
+    
+    A_colptr += N;
+    }
+  
+  out_KL = KL;
+  out_KU = KU;
+  
+  return true;
+  }
+
+
+
+template<typename eT>
+inline
+bool
+is_band_lower(uword& out_KD, const Mat<eT>& A, const uword N_min)
+  {
+  arma_extra_debug_sigprint();
+  
+  // NOTE: assuming that A has a square size
+  // NOTE: assuming that N_min is >= 4
+  
+  const uword N = A.n_rows;
+  
+  if(N < N_min)  { return false; }
+  
+  // first, quickly check bottom-left corner
+  
+  const eT eT_zero = eT(0);
+  
+  const eT* A_col0 = A.memptr();
+  const eT* A_col1 = A_col0 + N;
+  
+  if( (A_col0[N-2] != eT_zero) || (A_col0[N-1] != eT_zero) || (A_col1[N-2] != eT_zero) || (A_col1[N-1] != eT_zero) )  { return false; }
+  
+  // if we reached this point, go through the bottom triangle to work out number of subdiagonals
+  
+  const uword n_nonzero_threshold = ( N*N - (N*(N-1))/2 ) / 4;  // empirically determined
+  
+  uword KL = 0;  // number of subdiagonals
+  
+  const eT* A_colptr = A.memptr();
+  
+  for(uword col=0; col < N; ++col)
+    {
+    uword last_nonzero_row = col;
+    
+    for(uword row=(col+1); row < N; ++row)
+      {
+      last_nonzero_row = (A_colptr[row] != eT_zero) ? row : last_nonzero_row;
+      }
+    
+    const uword L_count = last_nonzero_row - col;
+    
+    if(L_count > KL)
+      {
+      KL = L_count;
+      
+      const uword n_nonzero = N*(KL+1) - (KL*(KL+1))/2;
+      
+      // return as soon as we know that it's not worth analysing the matrix any further
+      
+      if(n_nonzero > n_nonzero_threshold)  { return false; }
+      }
+    
+    A_colptr += N;
+    }
+  
+  out_KD = KL;
+  
+  return true;
+  }
+
+
+
+template<typename eT>
+inline
+bool
+is_band_upper(uword& out_KD, const Mat<eT>& A, const uword N_min)
+  {
+  arma_extra_debug_sigprint();
+  
+  // NOTE: assuming that A has a square size
+  // NOTE: assuming that N_min is >= 4
+  
+  const uword N = A.n_rows;
+  
+  if(N < N_min)  { return false; }
+  
+  // first, quickly check top-right corner
+  
+  const eT eT_zero = eT(0);
+  
+  const eT* A_colNm2 = A.colptr(N-2);
+  const eT* A_colNm1 = A_colNm2 + N;
+  
+  if( (A_colNm2[0] != eT_zero) || (A_colNm2[1] != eT_zero) || (A_colNm1[0] != eT_zero) || (A_colNm1[1] != eT_zero) )  { return false; }
+  
+  // if we reached this point, go through the entire matrix to work out number of superdiagonals
+  
+  const uword n_nonzero_threshold = ( N*N - (N*(N-1))/2 ) / 4;  // empirically determined
+  
+  uword KU = 0;  // number of superdiagonals
+  
+  const eT* A_colptr = A.memptr();
+  
+  for(uword col=0; col < N; ++col)
+    {
+    uword first_nonzero_row = col;
+    
+    for(uword row=0; row < col; ++row)
+      {
+      if( A_colptr[row] != eT_zero )  { first_nonzero_row = row; break; }
+      }
+    
+    const uword U_count = col - first_nonzero_row;
+    
+    if(U_count > KU)
+      {
+      KU = U_count;
+      
+      const uword n_nonzero = N*(KU+1) - (KU*(KU+1))/2;
+      
+      // return as soon as we know that it's not worth analysing the matrix any further
+      
+      if(n_nonzero > n_nonzero_threshold)  { return false; }
+      }
+    
+    A_colptr += N;
+    }
+  
+  out_KD = KU;
+  
+  return true;
+  }
+
+
+
+template<typename eT>
+inline
+void
+compress(Mat<eT>& AB, const Mat<eT>& A, const uword KL, const uword KU, const bool use_offset)
+  {
+  arma_extra_debug_sigprint();
+  
+  // NOTE: assuming that A has a square size
+  
+  // band matrix storage format
+  // http://www.netlib.org/lapack/lug/node124.html  
+  
+  // for ?gbsv,  matrix AB size: 2*KL+KU+1 x N; band representation of A stored in rows KL+1 to 2*KL+KU+1  (note: fortran counts from 1)
+  // for ?gbsvx, matrix AB size:   KL+KU+1 x N; band representaiton of A stored in rows    1 to   KL+KU+1  (note: fortran counts from 1)
+  //
+  // the +1 in the above formulas is to take into account the main diagonal
+  
+  const uword AB_n_rows = (use_offset) ? uword(2*KL + KU + 1) : uword(KL + KU + 1);
+  const uword N         = A.n_rows;
+  
+  AB.set_size(AB_n_rows, N);
+  
+  if(A.is_empty())  { AB.zeros(); return; }
+  
+  if(AB_n_rows == uword(1))
+    {
+    eT* AB_mem = AB.memptr();
+    
+    for(uword i=0; i<N; ++i)  { AB_mem[i] = A.at(i,i); }
+    }
+  else
+    {
+    AB.zeros();  // paranoia
+    
+    for(uword j=0; j < N; ++j)
+      {
+      const uword A_row_start = (j > KU) ? uword(j - KU) : uword(0);
+      const uword A_row_endp1 = (std::min)(N, j+KL+1);
+      
+      const uword length = A_row_endp1 - A_row_start;
+      
+      const uword AB_row_start = (KU > j) ? (KU - j) : uword(0);
+      
+      const eT*  A_colptr =  A.colptr(j) +  A_row_start;
+            eT* AB_colptr = AB.colptr(j) + AB_row_start + ( (use_offset) ? KL : uword(0) );
+      
+      arrayops::copy( AB_colptr, A_colptr, length );
+      }
+    }
+  }
+
+
+
+template<typename eT>
+inline
+void
+uncompress(Mat<eT>& A, const Mat<eT>& AB, const uword KL, const uword KU, const bool use_offset)
+  {
+  arma_extra_debug_sigprint();
+  
+  const uword AB_n_rows = AB.n_rows;
+  const uword N         = AB.n_cols;
+  
+  arma_debug_check( (AB_n_rows != ((use_offset) ? uword(2*KL + KU + 1) : uword(KL + KU + 1))), "band_helper::uncompress(): detected inconsistency" );
+  
+  A.zeros(N,N);  // assuming there is no aliasing between A and AB
+  
+  if(AB_n_rows == uword(1))
+    {
+    const eT* AB_mem = AB.memptr();
+    
+    for(uword i=0; i<N; ++i)  { A.at(i,i) = AB_mem[i]; }
+    }
+  else
+    {
+    for(uword j=0; j < N; ++j)
+      {
+      const uword A_row_start = (j > KU) ? uword(j - KU) : uword(0);
+      const uword A_row_endp1 = (std::min)(N, j+KL+1);
+      
+      const uword length = A_row_endp1 - A_row_start;
+      
+      const uword AB_row_start = (KU > j) ? (KU - j) : uword(0);
+      
+      const eT* AB_colptr = AB.colptr(j) + AB_row_start + ( (use_offset) ? KL : uword(0) );
+            eT*  A_colptr =  A.colptr(j) +  A_row_start;
+      
+      arrayops::copy( A_colptr, AB_colptr, length );
+      }
+    }
+  }
+
+
+
+template<typename eT>
+inline
+void
+extract_tridiag(Mat<eT>& out, const Mat<eT>& A)
+  {
+  arma_extra_debug_sigprint();
+  
+  // NOTE: assuming that A has a square size and is at least 2x2
+  
+  const uword N = A.n_rows;
+  
+  out.set_size(N, 3);  // assuming there is no aliasing between 'out' and 'A'
+  
+  if(N < 2)  { return; }
+  
+  eT* DL = out.colptr(0);
+  eT* DD = out.colptr(1);
+  eT* DU = out.colptr(2);
+  
+  DD[0] = A[0];
+  DL[0] = A[1];
+  
+  const uword Nm1 = N-1;
+  const uword Nm2 = N-2;
+  
+  for(uword i=0; i < Nm2; ++i)
+    {
+    const uword ip1 = i+1;
+    
+    const eT* data = &(A.at(i, ip1));
+    
+    const eT tmp0 = data[0];
+    const eT tmp1 = data[1];
+    const eT tmp2 = data[2];
+    
+    DL[ip1] = tmp2;
+    DD[ip1] = tmp1;
+    DU[i  ] = tmp0;
+    }
+  
+  const eT* data = &(A.at(Nm2, Nm1));
+  
+  DL[Nm1] = 0;
+  DU[Nm2] = data[0];
+  DU[Nm1] = 0;
+  DD[Nm1] = data[1]; 
+  }
+
+
+
+}  // end of namespace band_helper
+
+
+//! @}