comparison armadillo-3.900.4/include/armadillo_bits/fn_norm.hpp @ 49:1ec0e2823891

Switch to using subrepo copies of qm-dsp, nnls-chroma, vamp-plugin-sdk; update Armadillo version; assume build without external BLAS/LAPACK

+// Copyright (C) 2008-2012 NICTA (www.nicta.com.au)
+// Copyright (C) 2008-2012 Conrad Sanderson
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public
+// License, v. 2.0. If a copy of the MPL was not distributed with this
+// file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+
+//! \addtogroup fn_norm
+//! @{
+
+
+
+template<typename T1>
+arma_hot
+inline
+typename T1::pod_type
+arma_vec_norm_1(const Proxy<T1>& P)
+  {
+  arma_extra_debug_sigprint();
+  
+  typedef typename T1::pod_type T;
+  
+  T acc = T(0);
+  
+  if(Proxy<T1>::prefer_at_accessor == false)
+    {
+    typename Proxy<T1>::ea_type A = P.get_ea();
+    
+    const uword N = P.get_n_elem();
+    
+    T acc1 = T(0);
+    T acc2 = T(0);
+    
+    uword i,j;
+    for(i=0, j=1; j<N; i+=2, j+=2)
+      {
+      acc1 += std::abs(A[i]);
+      acc2 += std::abs(A[j]);
+      }
+    
+    if(i < N)
+      {
+      acc1 += std::abs(A[i]);
+      }
+    
+    acc = acc1 + acc2;
+    }
+  else
+    {
+    const uword n_rows = P.get_n_rows();
+    const uword n_cols = P.get_n_cols();
+    
+    if(n_rows == 1)
+      {
+      for(uword col=0; col<n_cols; ++col)
+        {
+        acc += std::abs(P.at(0,col));
+        }
+      }
+    else
+      {
+      for(uword col=0; col<n_cols; ++col)
+        {
+        uword i,j;
+        
+        for(i=0, j=1; j<n_rows; i+=2, j+=2)
+          {
+          acc += std::abs(P.at(i,col));
+          acc += std::abs(P.at(j,col));
+          }
+        
+        if(i < n_rows)
+          {
+          acc += std::abs(P.at(i,col));
+          }
+        }
+      }
+    }
+    
+  return acc;
+  }
+
+
+
+template<typename T1>
+arma_hot
+inline
+typename T1::pod_type
+arma_vec_norm_2
+  (
+  const Proxy<T1>& P,
+  const typename arma_not_cx<typename T1::elem_type>::result* junk = 0
+  )
+  {
+  arma_extra_debug_sigprint();
+  arma_ignore(junk);
+  
+  typedef typename T1::pod_type T;
+  
+  T acc = T(0);
+  
+  if(Proxy<T1>::prefer_at_accessor == false)
+    {
+    typename Proxy<T1>::ea_type A = P.get_ea();
+    
+    const uword N = P.get_n_elem();
+    
+    T acc1 = T(0);
+    T acc2 = T(0);
+    
+    uword i,j;
+    
+    for(i=0, j=1; j<N; i+=2, j+=2)
+      {
+      const T tmp_i = A[i];
+      const T tmp_j = A[j];
+      
+      acc1 += tmp_i * tmp_i;
+      acc2 += tmp_j * tmp_j;
+      }
+    
+    if(i < N)
+      {
+      const T tmp_i = A[i];
+      
+      acc1 += tmp_i * tmp_i;
+      }
+    
+    acc = acc1 + acc2;
+    }
+  else
+    {
+    const uword n_rows = P.get_n_rows();
+    const uword n_cols = P.get_n_cols();
+    
+    if(n_rows == 1)
+      {
+      for(uword col=0; col<n_cols; ++col)
+        {
+        const T tmp = P.at(0,col);
+        
+        acc += tmp * tmp;
+        }
+      }
+    else
+      {
+      for(uword col=0; col<n_cols; ++col)
+        {
+        uword i,j;
+        for(i=0, j=1; j<n_rows; i+=2, j+=2)
+          {
+          const T tmp_i = P.at(i,col);
+          const T tmp_j = P.at(j,col);
+          
+          acc += tmp_i * tmp_i;
+          acc += tmp_j * tmp_j;
+          }
+        
+        if(i < n_rows)
+          {
+          const T tmp_i = P.at(i,col);
+          
+          acc += tmp_i * tmp_i;
+          }
+        }
+      }
+    }
+  
+  return std::sqrt(acc);
+  }
+
+
+
+template<typename T1>
+arma_hot
+inline
+typename T1::pod_type
+arma_vec_norm_2
+  (
+  const Proxy<T1>& P,
+  const typename arma_cx_only<typename T1::elem_type>::result* junk = 0
+  )
+  {
+  arma_extra_debug_sigprint();
+  arma_ignore(junk);
+  
+  typedef typename T1::pod_type T;
+  
+  T acc = T(0);
+  
+  if(Proxy<T1>::prefer_at_accessor == false)
+    {
+    typename Proxy<T1>::ea_type A = P.get_ea();
+    
+    const uword N = P.get_n_elem();
+    
+    for(uword i=0; i<N; ++i)
+      {
+      const T tmp = std::abs(A[i]);
+      acc += tmp*tmp;
+      }
+    }
+  else
+    {
+    const uword n_rows = P.get_n_rows();
+    const uword n_cols = P.get_n_cols();
+    
+    if(n_rows == 1)
+      {
+      for(uword col=0; col<n_cols; ++col)
+        {
+        const T tmp = std::abs(P.at(0,col));
+        acc += tmp*tmp;
+        }
+      }
+    else
+      {
+      for(uword col=0; col<n_cols; ++col)
+      for(uword row=0; row<n_rows; ++row)
+        {
+        const T tmp = std::abs(P.at(row,col));
+        acc += tmp*tmp;
+        }
+      }
+    }
+  
+  return std::sqrt(acc);
+  }
+
+
+
+template<typename T1>
+arma_hot
+inline
+typename T1::pod_type
+arma_vec_norm_k
+  (
+  const Proxy<T1>& P,
+  const int k
+  )
+  {
+  arma_extra_debug_sigprint();
+  
+  typedef typename T1::pod_type T;
+  
+  T acc = T(0);
+  
+  if(Proxy<T1>::prefer_at_accessor == false)
+    {
+    typename Proxy<T1>::ea_type A = P.get_ea();
+    
+    const uword N = P.get_n_elem();
+    
+    uword i,j;
+    
+    for(i=0, j=1; j<N; i+=2, j+=2)
+      {
+      acc += std::pow(std::abs(A[i]), k);
+      acc += std::pow(std::abs(A[j]), k);
+      }
+    
+    if(i < N)
+      {
+      acc += std::pow(std::abs(A[i]), k);
+      }
+    }
+  else
+    {
+    const uword n_rows = P.get_n_rows();
+    const uword n_cols = P.get_n_cols();
+    
+    if(n_rows != 1)
+      {
+      for(uword col=0; col < n_cols; ++col)
+      for(uword row=0; row < n_rows; ++row)
+        {
+        acc += std::pow(std::abs(P.at(row,col)), k);
+        }
+      }
+    else
+      {
+      for(uword col=0; col < n_cols; ++col)
+        {
+        acc += std::pow(std::abs(P.at(0,col)), k);
+        }
+      }
+    }
+  
+  return std::pow(acc, T(1)/T(k));
+  }
+
+
+
+template<typename T1>
+arma_hot
+inline
+typename T1::pod_type
+arma_vec_norm_max(const Proxy<T1>& P)
+  {
+  arma_extra_debug_sigprint();
+  
+  typedef typename T1::pod_type T;
+  
+  const uword N = P.get_n_elem();
+  
+  T max_val = (N != 1) ? priv::most_neg<T>() : std::abs(P[0]);
+  
+  if(Proxy<T1>::prefer_at_accessor == false)
+    {
+    typename Proxy<T1>::ea_type A = P.get_ea();
+    
+    uword i,j;
+    for(i=0, j=1; j<N; i+=2, j+=2)
+      {
+      const T tmp_i = std::abs(A[i]);
+      const T tmp_j = std::abs(A[j]);
+      
+      if(max_val < tmp_i) { max_val = tmp_i; }
+      if(max_val < tmp_j) { max_val = tmp_j; }
+      }
+    
+    if(i < N)
+      {
+      const T tmp_i = std::abs(A[i]);
+      
+      if(max_val < tmp_i) { max_val = tmp_i; }
+      }
+    }
+  else
+    {
+    const uword n_rows = P.get_n_rows();
+    const uword n_cols = P.get_n_cols();
+    
+    if(n_rows != 1)
+      {
+      for(uword col=0; col < n_cols; ++col)
+      for(uword row=0; row < n_rows; ++row)
+        {
+        const T tmp = std::abs(P.at(row,col));
+        
+        if(max_val < tmp) { max_val = tmp; }
+        }
+      }
+    else
+      {
+      for(uword col=0; col < n_cols; ++col)
+        {
+        const T tmp = std::abs(P.at(0,col));
+        
+        if(max_val < tmp) { max_val = tmp; }
+        }
+      }
+    }
+  
+  return max_val;
+  }
+
+
+
+template<typename T1>
+arma_hot
+inline
+typename T1::pod_type
+arma_vec_norm_min(const Proxy<T1>& P)
+  {
+  arma_extra_debug_sigprint();
+  
+  typedef typename T1::pod_type T;
+  
+  const uword N = P.get_n_elem();
+  
+  T min_val = (N != 1) ? priv::most_pos<T>() : std::abs(P[0]);
+  
+  if(Proxy<T1>::prefer_at_accessor == false)
+    {
+    typename Proxy<T1>::ea_type A = P.get_ea();
+    
+    uword i,j;
+    for(i=0, j=1; j<N; i+=2, j+=2)
+      {
+      const T tmp_i = std::abs(A[i]);
+      const T tmp_j = std::abs(A[j]);
+      
+      if(min_val > tmp_i) { min_val = tmp_i; }
+      if(min_val > tmp_j) { min_val = tmp_j; }
+      }
+    
+    if(i < N)
+      {
+      const T tmp_i = std::abs(A[i]);
+      
+      if(min_val > tmp_i) { min_val = tmp_i; }
+      }
+    }
+  else
+    {
+    const uword n_rows = P.get_n_rows();
+    const uword n_cols = P.get_n_cols();
+    
+    if(n_rows != 1)
+      {
+      for(uword col=0; col < n_cols; ++col)
+      for(uword row=0; row < n_rows; ++row)
+        {
+        const T tmp = std::abs(P.at(row,col));
+        
+        if(min_val > tmp) { min_val = tmp; }
+        }
+      }
+    else
+      {
+      for(uword col=0; col < n_cols; ++col)
+        {
+        const T tmp = std::abs(P.at(0,col));
+        
+        if(min_val > tmp) { min_val = tmp; }
+        }
+      }
+    }
+  
+  return min_val;
+  }
+
+
+
+template<typename T1>
+inline
+typename T1::pod_type
+arma_mat_norm_1(const Proxy<T1>& P)
+  {
+  arma_extra_debug_sigprint();
+  
+  // TODO: this can be sped up with a dedicated implementation
+  return as_scalar( max( sum(abs(P.Q), 0), 1) );
+  }
+
+
+
+template<typename T1>
+inline
+typename T1::pod_type
+arma_mat_norm_2(const Proxy<T1>& P)
+  {
+  arma_extra_debug_sigprint();
+  
+  typedef typename T1::pod_type   T;
+  
+  // TODO: is the SVD based approach only valid for square matrices?
+  
+  Col<T> S;
+  svd(S, P.Q);
+  
+  return (S.n_elem > 0) ? max(S) : T(0);
+  }
+
+
+
+template<typename T1>
+inline
+typename T1::pod_type
+arma_mat_norm_inf(const Proxy<T1>& P)
+  {
+  arma_extra_debug_sigprint();
+  
+  // TODO: this can be sped up with a dedicated implementation
+  return as_scalar( max( sum(abs(P.Q), 1), 0) );
+  }
+
+
+
+template<typename T1>
+inline
+arma_warn_unused
+typename enable_if2< is_arma_type<T1>::value, typename T1::pod_type >::result
+norm
+  (
+  const T1& X,
+  const uword k,
+  const typename arma_real_or_cx_only<typename T1::elem_type>::result* junk = 0
+  )
+  {
+  arma_extra_debug_sigprint();
+  arma_ignore(junk);
+  
+  typedef typename T1::pod_type T;
+  
+  const Proxy<T1> P(X);
+  
+  if(P.get_n_elem() == 0)
+    {
+    return T(0);
+    }
+  
+  const bool is_vec = (P.get_n_rows() == 1) || (P.get_n_cols() == 1);
+  
+  if(is_vec == true)
+    {
+    switch(k)
+      {
+      case 1:
+        return arma_vec_norm_1(P);
+        break;
+      
+      case 2:
+        return arma_vec_norm_2(P);
+        break;
+      
+      default:
+        {
+        arma_debug_check( (k == 0), "norm(): k must be greater than zero"   );
+        return arma_vec_norm_k(P, int(k));
+        }
+      }
+    }
+  else
+    {
+    switch(k)
+      {
+      case 1:
+        return arma_mat_norm_1(P);
+        break;
+      
+      case 2:
+        return arma_mat_norm_2(P);
+        break;
+      
+      default:
+        arma_stop("norm(): unsupported matrix norm type");
+        return T(0);
+      }
+    }
+  }
+
+
+
+template<typename T1>
+inline
+arma_warn_unused
+typename enable_if2< is_arma_type<T1>::value, typename T1::pod_type >::result
+norm
+  (
+  const T1& X,
+  const char* method,
+  const typename arma_real_or_cx_only<typename T1::elem_type>::result* junk = 0
+  )
+  {
+  arma_extra_debug_sigprint();
+  arma_ignore(junk);
+  
+  typedef typename T1::pod_type T;
+  
+  const Proxy<T1> P(X);
+  
+  if(P.get_n_elem() == 0)
+    {
+    return T(0);
+    }
+  
+  const char sig    = method[0];
+  const bool is_vec = (P.get_n_rows() == 1) || (P.get_n_cols() == 1);
+  
+  if(is_vec == true)
+    {
+    if( (sig == 'i') || (sig == 'I') || (sig == '+') )   // max norm
+      {
+      return arma_vec_norm_max(P);
+      }
+    else
+    if(sig == '-')   // min norm
+      {
+      return arma_vec_norm_min(P);
+      }
+    else
+    if( (sig == 'f') || (sig == 'F') )
+      {
+      return arma_vec_norm_2(P);
+      }
+    else
+      {
+      arma_stop("norm(): unsupported vector norm type");
+      return T(0);
+      }
+    }
+  else
+    {
+    if( (sig == 'i') || (sig == 'I') || (sig == '+') )   // inf norm
+      {
+      return arma_mat_norm_inf(P);
+      }
+    else
+    if( (sig == 'f') || (sig == 'F') )
+      {
+      return arma_vec_norm_2(P);
+      }
+    else
+      {
+      arma_stop("norm(): unsupported matrix norm type");
+      return T(0);
+      }
+    }
+  }
+
+
+
+//
+// norms for sparse matrices
+
+
+
+template<typename T1>
+inline
+typename T1::pod_type
+arma_mat_norm_1(const SpProxy<T1>& P)
+  {
+  arma_extra_debug_sigprint();
+  
+  // TODO: this can be sped up with a dedicated implementation
+  return as_scalar( max( sum(abs(P.Q), 0), 1) );
+  }
+
+
+
+// template<typename T1>
+// inline
+// typename T1::pod_type
+// arma_mat_norm_2(const SpProxy<T1>& P)
+//   {
+//   arma_extra_debug_sigprint();
+//   
+//   // TODO: norm = sqrt( largest eigenvalue of (A^H)*A ), where ^H is the conjugate transpose
+//   // TODO: can use ARPACK or directly implement the Arnoldi iteration
+//   // http://math.stackexchange.com/questions/4368/computing-the-largest-eigenvalue-of-a-very-large-sparse-matrix
+//   }
+
+
+
+template<typename T1>
+inline
+typename T1::pod_type
+arma_mat_norm_inf(const SpProxy<T1>& P)
+  {
+  arma_extra_debug_sigprint();
+  
+  // TODO: this can be sped up with a dedicated implementation
+  return as_scalar( max( sum(abs(P.Q), 1), 0) );
+  }
+
+
+
+template<typename T1>
+inline
+arma_warn_unused
+typename enable_if2< is_arma_sparse_type<T1>::value, typename T1::pod_type >::result
+norm
+  (
+  const T1& X,
+  const uword k,
+  const typename arma_real_or_cx_only<typename T1::elem_type>::result* junk = 0
+  )
+  {
+  arma_extra_debug_sigprint();
+  arma_ignore(junk);
+  
+  typedef typename T1::elem_type eT;
+  typedef typename T1::pod_type   T;
+  
+  const SpProxy<T1> P(X);
+  
+  if(P.get_n_nonzero() == 0)
+    {
+    return T(0);
+    }
+  
+  const bool is_vec = (P.get_n_rows() == 1) || (P.get_n_cols() == 1);
+  
+  if(is_vec == true)
+    {
+    const unwrap_spmat<typename SpProxy<T1>::stored_type> tmp(P.Q);
+    const SpMat<eT>& A = tmp.M;
+    
+    // create a fake dense vector to allow reuse of code for dense vectors
+    Col<eT> fake_vector( access::rwp(A.values), A.n_nonzero, false );
+    
+    const Proxy< Col<eT> > P_fake_vector(fake_vector);
+    
+    switch(k)
+      {
+      case 1:
+        return arma_vec_norm_1(P_fake_vector);
+        break;
+      
+      case 2:
+        return arma_vec_norm_2(P_fake_vector);
+        break;
+      
+      default:
+        {
+        arma_debug_check( (k == 0), "norm(): k must be greater than zero"   );
+        return arma_vec_norm_k(P_fake_vector, int(k));
+        }
+      }
+    }
+  else
+    {
+    switch(k)
+      {
+      case 1:
+        return arma_mat_norm_1(P);
+        break;
+      
+      // case 2:
+      //   return arma_mat_norm_2(P);
+      //   break;
+      
+      default:
+        arma_stop("norm(): unsupported or unimplemented norm type for sparse matrices");
+        return T(0);
+      }
+    }
+  }
+
+
+
+template<typename T1>
+inline
+arma_warn_unused
+typename enable_if2< is_arma_sparse_type<T1>::value, typename T1::pod_type >::result
+norm
+  (
+  const T1& X,
+  const char* method,
+  const typename arma_real_or_cx_only<typename T1::elem_type>::result* junk = 0
+  )
+  {
+  arma_extra_debug_sigprint();
+  arma_ignore(junk);
+  
+  typedef typename T1::elem_type eT;
+  typedef typename T1::pod_type   T;
+  
+  const SpProxy<T1> P(X);
+  
+  if(P.get_n_nonzero() == 0)
+    {
+    return T(0);
+    }
+  
+  
+  const unwrap_spmat<typename SpProxy<T1>::stored_type> tmp(P.Q);
+  const SpMat<eT>& A = tmp.M;
+  
+  // create a fake dense vector to allow reuse of code for dense vectors
+  Col<eT> fake_vector( access::rwp(A.values), A.n_nonzero, false );
+  
+  const Proxy< Col<eT> > P_fake_vector(fake_vector);
+  
+  
+  const char sig    = method[0];
+  const bool is_vec = (P.get_n_rows() == 1) || (P.get_n_cols() == 1);
+  
+  if(is_vec == true)
+    {
+    if( (sig == 'i') || (sig == 'I') || (sig == '+') )   // max norm
+      {
+      return arma_vec_norm_max(P_fake_vector);
+      }
+    else
+    if(sig == '-')   // min norm
+      {
+      const T val = arma_vec_norm_min(P_fake_vector);
+      
+      if( P.get_n_nonzero() < P.get_n_elem() )
+        {
+        return (std::min)(T(0), val);
+        }
+      else
+        {
+        return val;
+        }
+      }
+    else
+    if( (sig == 'f') || (sig == 'F') )
+      {
+      return arma_vec_norm_2(P_fake_vector);
+      }
+    else
+      {
+      arma_stop("norm(): unsupported vector norm type");
+      return T(0);
+      }
+    }
+  else
+    {
+    if( (sig == 'i') || (sig == 'I') || (sig == '+') )   // inf norm
+      {
+      return arma_mat_norm_inf(P);
+      }
+    else
+    if( (sig == 'f') || (sig == 'F') )
+      {
+      return arma_vec_norm_2(P_fake_vector);
+      }
+    else
+      {
+      arma_stop("norm(): unsupported matrix norm type");
+      return T(0);
+      }
+    }
+  }
+
+
+
+//! @}