specmat.h

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#ifndef SPECMAT_H
#define SPECMAT_H

#include <itpp/base/vec.h>
#include <itpp/base/mat.h>


namespace itpp
{

ivec find(const bvec &invector);




vec ones(int size);
bvec ones_b(int size);
ivec ones_i(int size);
cvec ones_c(int size);

mat ones(int rows, int cols);
bmat ones_b(int rows, int cols);
imat ones_i(int rows, int cols);
cmat ones_c(int rows, int cols);

vec zeros(int size);
bvec zeros_b(int size);
ivec zeros_i(int size);
cvec zeros_c(int size);

mat zeros(int rows, int cols);
bmat zeros_b(int rows, int cols);
imat zeros_i(int rows, int cols);
cmat zeros_c(int rows, int cols);

mat eye(int size);
bmat eye_b(int size);
imat eye_i(int size);
cmat eye_c(int size);
template <class T>
void eye(int size, Mat<T> &m);

vec impulse(int size);
vec linspace(double from, double to, int length = 100);
vec zigzag_space(double t0, double t1, int K = 5);

imat hadamard(int size);

imat jacobsthal(int p);

imat conference(int n);

template <typename Num_T>
const Mat<Num_T> toeplitz(const Vec<Num_T> &c, const Vec<Num_T> &r)
{
  int n_rows = c.size();
  int n_cols = r.size();
  Mat<Num_T> output(n_rows, n_cols);
  for (int i = 0; i < n_rows; ++i) {
    int j_limit = std::min(n_cols, n_rows - i);
    for (int j = 0; j < j_limit; ++j) {
      output(i + j, j) = c(i);
    }
  }
  for (int j = 1; j < n_cols; ++j) {
    int i_limit = std::min(n_rows, n_cols - j);
    for (int i = 0; i < i_limit; ++i) {
      output(i, i + j) = r(j);
    }
  }
  return output;
}

template <typename Num_T>
const Mat<Num_T> toeplitz(const Vec<Num_T> &c)
{
  int s = c.size();
  Mat<Num_T> output(s, s);
  for (int i = 0; i < s; ++i) {
    for (int j = 0; j < s - i; ++j) {
      output(i + j, j) = c(i);
    }
  }
  for (int j = 1; j < s; ++j) {
    for (int i = 0; i < s - j; ++i) {
      output(i, i + j) = c(j);
    }
  }
  return output;
}

template <>
const cmat toeplitz(const cvec &c);



mat rotation_matrix(int dim, int plane1, int plane2, double angle);

void house(const vec &x, vec &v, double &beta);

void givens(double a, double b, double &c, double &s);

void givens(double a, double b, mat &m);

mat givens(double a, double b);

void givens_t(double a, double b, mat &m);

mat givens_t(double a, double b);

template <class T>
Vec<T> vec_1(T v0)
{
  Vec<T> v(1);
  v(0) = v0;
  return v;
}

template <class T>
Vec<T> vec_2(T v0, T v1)
{
  Vec<T> v(2);
  v(0) = v0;
  v(1) = v1;
  return v;
}

template <class T>
Vec<T> vec_3(T v0, T v1, T v2)
{
  Vec<T> v(3);
  v(0) = v0;
  v(1) = v1;
  v(2) = v2;
  return v;
}

template <class T>
Mat<T> mat_1x1(T m00)
{
  Mat<T> m(1, 1);
  m(0, 0) = m00;
  return m;
}

template <class T>
Mat<T> mat_1x2(T m00, T m01)
{
  Mat<T> m(1, 2);
  m(0, 0) = m00;
  m(0, 1) = m01;
  return m;
}

template <class T>
Mat<T> mat_2x1(T m00,
               T m10)
{
  Mat<T> m(2, 1);
  m(0, 0) = m00;
  m(1, 0) = m10;
  return m;
}

template <class T>
Mat<T> mat_2x2(T m00, T m01,
               T m10, T m11)
{
  Mat<T> m(2, 2);
  m(0, 0) = m00;
  m(0, 1) = m01;
  m(1, 0) = m10;
  m(1, 1) = m11;
  return m;
}

template <class T>
Mat<T> mat_1x3(T m00, T m01, T m02)
{
  Mat<T> m(1, 3);
  m(0, 0) = m00;
  m(0, 1) = m01;
  m(0, 2) = m02;
  return m;
}

template <class T>
Mat<T> mat_3x1(T m00,
               T m10,
               T m20)
{
  Mat<T> m(3, 1);
  m(0, 0) = m00;
  m(1, 0) = m10;
  m(2, 0) = m20;
  return m;
}

template <class T>
Mat<T> mat_2x3(T m00, T m01, T m02,
               T m10, T m11, T m12)
{
  Mat<T> m(2, 3);
  m(0, 0) = m00;
  m(0, 1) = m01;
  m(0, 2) = m02;
  m(1, 0) = m10;
  m(1, 1) = m11;
  m(1, 2) = m12;
  return m;
}

template <class T>
Mat<T> mat_3x2(T m00, T m01,
               T m10, T m11,
               T m20, T m21)
{
  Mat<T> m(3, 2);
  m(0, 0) = m00;
  m(0, 1) = m01;
  m(1, 0) = m10;
  m(1, 1) = m11;
  m(2, 0) = m20;
  m(2, 1) = m21;
  return m;
}

template <class T>
Mat<T> mat_3x3(T m00, T m01, T m02,
               T m10, T m11, T m12,
               T m20, T m21, T m22)
{
  Mat<T> m(3, 3);
  m(0, 0) = m00;
  m(0, 1) = m01;
  m(0, 2) = m02;
  m(1, 0) = m10;
  m(1, 1) = m11;
  m(1, 2) = m12;
  m(2, 0) = m20;
  m(2, 1) = m21;
  m(2, 2) = m22;
  return m;
}

} //namespace itpp

#endif // #ifndef SPECMAT_H

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