Generate vector with linearly spaced elements

The linspace() function generates a vector of linearly spaced values from start to end (it includes end). The arguments can be start, end or start, end, N, where N is optional and indicates the number of elements in the vector (N is 100 by default).

The usage is:

vec v = linspace(start, end, N)
vector_type v = linspace<vector_type>(start, end, N)

Examples

[[cpp11::register]] doubles linspace1_(const int& n) {
  vec a = linspace(1, 2, n);
  rowvec b = linspace<rowvec>(3, 4, n);

  vec res = a + b.t();

  return as_doubles(res);
}

Caveat

For N = 1, the generated vector will have a single element equal to end.

Generate vector with logarithmically spaced elements

The logspace() function generates a vector of logarithmically spaced values from 10^start to 10^end (it includes 10^end). The arguments can be start, end or start, end, N, where N is optional and indicates the number of elements in the vector (N is 50 by default).

The usage is:

vec v = logspace(start, end, N)
vector_type v = logspace<vector_type>(start, end, N)

Examples

[[cpp11::register]] doubles logspace1_(const int& n) {
  vec a = logspace(1, 2, n);
  rowvec b = logspace<rowvec>(3, 4, n);

  vec res = a + b.t();

  return as_doubles(res);
}

Generate vector with regularly spaced elements

The regspace() function generates a vector of regularly spaced values start, start + delta, start + 2*delta, ..., start + M * delta where M is M = floor((end - start) / delta). The arguments can be start, end or start, delta, end, where delta is optional (delta = 1 if start <= end and delta = -1 if start > end by default).

The usage is:

vec v = regspace(start, end)
vec v = regspace(start, delta, end)
vector_type v = regspace<vector_type>(start, end)
vector_type v = regspace<vector_type>(start, delta, end)

The output vector will be empty if any of the following conditions are met:

start < end and delta < 0
start > end and delta > 0
delta = 0

Examples

[[cpp11::register]] doubles regspace1_(const double& delta) {
  vec a = regspace(1, delta, 2);
  rowvec b = regspace<rowvec>(3, delta, 4);

  vec res = a + b.t();

  return as_doubles(res);
}

Caveats

This is different from Matlab/Octave.
Do not use regspace() to specify ranges for contiguous submatrix views, use span() instead.

Generate vector with random permutation of a sequence of integers

The randperm() function generates a vector of permutation of integers from 0 to N-1. The argument can be empty, N, or N, M, where N (N = 10 by default) is the range of integers and M (M = N by default) is the length of the output.

The usage is:

uvec v = randperm(N)
uvec v = randperm(N, M)

Examples

[[cpp11::register]] integers randperm1_(const int& n, const int& m) {
  uvec a = randperm(n);
  uvec b = randperm(n, m);

  uvec res = a + b;

  return as_integers(res);
}

Generate identity matrix

The eye() function generates a matrix of size n x m. The argument can be n_rows, n_cols or size(X). When n_rows = n_cols, the output is an identity matrix.

The usage is:

mat X = eye(n_rows, n_cols)
matrix_type X = eye<matrix_type>(n_rows, n_cols) 
matrix_type X = eye<matrix_type>(size(X))

Examples

[[cpp11::register]] doubles_matrix<> eye1_(const int& n) {
  mat A = eye(5,5);  // or:  mat A(5,5,fill::eye);

  fmat B = 123.0 * eye<fmat>(5,5);

cx_mat C = eye<cx_mat>( size(B) );

  return as_doubles(res);
}

Generate object filled with ones

The ones() function generates a vector, matrix or cube. The arguments can be n_elem, n_rows, n_cols, n_rows, n_cols, n_slices, or size(X). The

The usage is:

vector_type v = ones<vector_type>(n_elem)
matrix_type X = ones<matrix_type>(n_rows, n_cols)
matrix_type Y = ones<matrix_type>(size(X))
cube_type Q = ones<cube_type>(n_rows, n_cols, n_slices)
cube_type R = ones<cube_type>(size(Q))

Examples

[[cpp11::register]] doubles_matrix<> ones2_(const int& n) {
  vec v = ones(n);  // or: vec v(10, fill::ones);
  uvec u = ones<uvec>(n);
  rowvec r = ones<rowvec>(n);

  mat A = ones(n, n);  // or: mat A(n, n, fill::ones);
  fmat B = ones<fmat>(n, n);

  cube Q = ones(n, n, n + 1);  // or: cube Q(n, n, n + 1, fill::ones);

  mat res = diagmat(v) + diagmat(conv_to<vec>::from(u)) + diagmat(r) + A + B +
    Q.slice(0);

  return as_doubles_matrix(res);
}

Caveat

Specifying fill::ones during object construction is more compact. For example, mat A(5, 6, fill::ones).

Generate object filled with zeros

The zeros() function generates a vector, matrix or cube. The arguments can be n_elem, n_rows, n_cols, n_rows, n_cols, n_slices, or size(X).

The usage is:

vector_type v = zeros<vector_type>(n_elem)
matrix_type X = zeros<matrix_type>(n_rows, n_cols)
matrix_type Y = zeros<matrix_type>(size(X))
cube_type Q = zeros<cube_type>(n_rows, n_cols, n_slices)
cube_type R = zeros<cube_type>(size(Q))

Examples

[[cpp11::register]] doubles_matrix<> zeros2_(const int& n) {
  vec v = zeros(n);  // or: vec v(10, fill::zeros);
  uvec u = zeros<uvec>(n);
  rowvec r = zeros<rowvec>(n);

  mat A = zeros(n, n);  // or: mat A(n, n, fill::zeros);
  fmat B = zeros<fmat>(n, n);

  cube Q = zeros(n, n, n + 1);  // or: cube Q(n, n, n + 1, fill::zeros);

  mat res = diagmat(v) + diagmat(conv_to<vec>::from(u)) + diagmat(r) + A + B +
    Q.slice(0);

  return as_doubles_matrix(res);
}

Caveat

Specifying fill::zeros during object construction is more compact. For example, mat A(5, 6, fill::zeros).

Generate object with random values from a uniform distribution

The randu() function generates a vector, matrix or cube with the elements set to random floating point values uniformly distributed in the [a,b] interval. The arguments can be distr_param(a,b), n_elem, n_elem, distr_param(a,b), n_rows, n_cols, n_rows, n_cols, distr_param(a,b), n_rows, n_cols, n_slices, n_rows, n_cols, n_slices, distr_param(a,b), size(X), or size(X), distr_param(a,b).

The usage is:

// the scalar type can be: float, double, cx_float, or cx_double

scalar_type s = randu<scalar_type>()
scalar_type s = randu<scalar_type>(distr_param(a,b))

vector_type v = randu<vector_type>(n_elem)
vector_type v = randu<vector_type>(n_elem, distr_param(a,b))

matrix_type X = randu<matrix_type>(n_rows, n_cols)
matrix_type X = randu<matrix_type>(n_rows, n_cols, distr_param(a,b))

cube_type Q = randu<cube_type>(n_rows, n_cols, n_slices)
cube_type Q = randu<cube_type>(n_rows, n_cols, n_slices, distr_param(a,b))

Examples

[[cpp11::register]] doubles_matrix<> randu3_(const int& n) {
  double a = randu();
  double b = randu(distr_param(10, 20));

  vec v1 = randu(n);  // or vec v1(n, fill::randu);
  vec v2 = randu(n, distr_param(10, 20));

  rowvec r1 = randu<rowvec>(n);
  rowvec r2 = randu<rowvec>(n, distr_param(10, 20));

  mat A1 = randu(n, n);  // or mat A1(n, n, fill::randu);
  mat A2 = randu(n, n, distr_param(10, 20));

  fmat B1 = randu<fmat>(n, n);
  fmat B2 = randu<fmat>(n, n, distr_param(10, 20));

  mat res = diagmat(v1) + diagmat(v2) + diagmat(r1) + diagmat(r2) + A1 + A2 +
    B1 + B2;

  res.each_col([a](vec& x) { x += a; });
  res.each_row([b](rowvec& y) { y /= b; });

  return as_doubles_matrix(res);
}

Caveat

To generate a matrix with random integer values instead of floating point values, use randi() instead.

Generate object with random values from a normal/gaussian distribution

The randn() function generates a vector, matrix or cube with the elements set to random floating point values normally distributed with mean 0 and standard deviation 1. The arguments can be n_elem, distr_param(mean, stddev), n_elem, n_elem, distr_param(mean, stddev), n_rows, n_cols, n_rows, n_cols, distr_param(mean, stddev), n_rows, n_cols, n_slices, n_rows, n_cols, n_slices, distr_param(mean, stddev), size(X), or size(X), distr_param(mean, stddev).

The usage is:

// the scalar type can be: float, double, cx_float, or cx_double

scalar_type s = randn<scalar_type>()
scalar_type s = randn<scalar_type>(distr_param(mean, stddev))

vector_type v = randn<vector_type>(n_elem)
vector_type v = randn<vector_type>(n_elem, distr_param(mean, stddev))

matrix_type X = randn<matrix_type>(n_rows, n_cols)
matrix_type X = randn<matrix_type>(n_rows, n_cols, distr_param(mean, stddev))

cube_type Q = randn<cube_type>(n_rows, n_cols, n_slices)
cube_type Q = randn<cube_type>(n_rows, n_cols, n_slices, distr_param(mean, stddev))

Examples

[[cpp11::register]] doubles_matrix<> randn3_(const int& n) {
  vec v1 = randn(n);  // or vec v1(n, fill::randn);
  vec v2 = randn(n, distr_param(10, 20));

  rowvec r1 = randn<rowvec>(n);
  rowvec r2 = randn<rowvec>(n, distr_param(10, 20));

  mat A1 = randn(n, n);  // or mat A1(n, n, fill::randn);
  mat A2 = randn(n, n, distr_param(10, 20));

  fmat B1 = randn<fmat>(n, n);
  fmat B2 = randn<fmat>(n, n, distr_param(10, 20));

  mat res = diagmat(v1) + diagmat(v2) + diagmat(r1) + diagmat(r2) + A1 + A2 +
    B1 + B2;

  return as_doubles_matrix(res);
}

Generate object with random values from a gamma distribution

The randg() function generates a vector, matrix or cube with the elements set to random floating point values gamma distributed with shape a and scale b. The arguments can be distr_param(a, b), n_elem, n_elem, distr_param(a, b), n_rows, n_cols, n_rows, n_cols, distr_param(a, b), n_rows, n_cols, n_slices, n_rows, n_cols, n_slices, distr_param(a, b), size(X), or size(X), distr_param(a, b).

The usage is:

// the scalar type can be: float, double, cx_float, or cx_double

scalar_type s = randg<scalar_type>()
scalar_type s = randg<scalar_type>(distr_param(a, b))

vector_type v = randg<vector_type>(n_elem)
vector_type v = randg<vector_type>(n_elem, distr_param(a, b))

matrix_type X = randg<matrix_type>(n_rows, n_cols)
matrix_type X = randg<matrix_type>(n_rows, n_cols, distr_param(a, b))

cube_type Q = randg<cube_type>(n_rows, n_cols, n_slices)
cube_type Q = randg<cube_type>(n_rows, n_cols, n_slices, distr_param(a, b))

Examples

[[cpp11::register]] doubles_matrix<> randg3_(const int& n) {
  int a = randi();
  int b = randi(distr_param(-10, +20));

  imat A1 = randi(n, n);
  imat A2 = randi(n, n, distr_param(-10, +20));

  mat B1 = randi<mat>(n, n);
  mat B2 = randi<mat>(n, n, distr_param(-10, +20));

  mat res = A1 + A2 + B1 + B2;

  res.each_col([a](vec& x) { x *= a; });
  res.each_row([b](rowvec& y) { y -= b; });

  return as_doubles_matrix(res);
}

Generate object with random integer values in specified interval

The randi() function generates a vector, matrix or cube with the elements set to random integer values uniformly distributed in the [a,b] interval. The arguments can be distr_param(a, b), n_elem, n_elem, distr_param(a, b), n_rows, n_cols, n_rows, n_cols, distr_param(a, b), n_rows, n_cols, n_slices, n_rows, n_cols, n_slices, distr_param(a, b), size(X), or size(X), distr_param(a, b). The default values are a = 0 and b = maximum_int.

The usage is:

scalar_type s = randi<scalar_type>()
scalar_type s = randi<scalar_type>(distr_param(a, b))

vector_type v = randi<vector_type>(n_elem)
vector_type v = randi<vector_type>(n_elem, distr_param(a, b))

matrix_type X = randi<matrix_type>(n_rows, n_cols)
matrix_type X = randi<matrix_type>(n_rows, n_cols, distr_param(a, b))

cube_type Q = randi<cube_type>(n_rows, n_cols, n_slices)
cube_type Q = randi<cube_type>(n_rows, n_cols, n_slices, distr_param(a, b))

Examples

[[cpp11::register]] integers_matrix<> randi3_(const int& n) {
  uvec v1 = randi(n);  // or uvec v1(n, fill::randi);
  uvec v2 = randi(n, distr_param(10, 20));

  umat A1 = randi(n, n);  // or umat A1(n, n, fill::randi);
  umat A2 = randi(n, n, distr_param(10, 20));

  icube Q1 = randi(icube(n, n, n + 1));  // or icube Q1(n, n, n + 1, fill::randi);
  icube Q2 = randi(icube(n, n, n + 1), distr_param(10, 20));

  mat res = diagmat(conv_to<vec>::from(v1)) + diagmat(conv_to<vec>::from(v2)) +
    A1 + A2 + Q1.slice(0) + Q2.slice(0);

  return as_integers_matrix(res);
}

Caveat

To generate a matrix with random floating point values (e.g., float or double) instead of integers, use randu() instead.

Generate sparse identity matrix

The speye() function generates a sparse matrix of size n x n with the elements on the diagonal set to 1 and the remaining elements set to 0. The argument can be n_rows, n_cols or size(X). An identity matrix is generated when n_rows = n_cols.

The usage is:

sparse_matrix_type X = speye(n_rows, n_cols)
sparse_matrix_type X = speye<sparse_matrix_type>(size(X))

Examples

[[cpp11::register]] doubles_matrix<> speye1_(const int& n) {
  sp_mat A = speye<sp_mat>(n, n);
  mat B = mat(A);
  return as_doubles_matrix(B);
}

Generate sparse matrix with non-zero elements set to one

The spones(X) function generates a sparse matrix with the same size as X and all the non-zero elements set to 1.

Examples

[[cpp11::register]] doubles_matrix<> spones1_(const int& n) {
  sp_mat A = sprandu<sp_mat>(n, n, 0.1);
  sp_mat B = spones(A);
  mat C = mat(B);
  return as_doubles_matrix(C);
}

Generate sparse matrix with non-zero elements set to random values from a uniform distribution

The sprandu() function generates a sparse matrix of size n_rows x n_cols with random floating point values uniformly distributed in the [0,1] interval. The arguments can be n_rows, n_cols, density or size(X), density.

The usage is:

sparse_matrix_type X = sprandu<sparse_matrix_type>(n_rows, n_cols, density)
sparse_matrix_type X = sprandu<sparse_matrix_type>(size(X), density)

Examples

[[cpp11::register]] doubles_matrix<> sprandu1_(const int& n) {
  sp_mat A = sprandu<sp_mat>(n, n, 0.05);
  mat B = mat(A);
  return as_doubles_matrix(B);
}

Generate sparse matrix with non-zero elements set to random values from a normal/gaussian distribution

The sprandn() function generates a sparse matrix of size n_rows x n_cols with random floating point values normally distributed with mean 0 and standard deviation 1. The arguments can be n_rows, n_cols, density or size(X), density.

The usage is:

sparse_matrix_type X = sprandn<sparse_matrix_type>(n_rows, n_cols, density)
sparse_matrix_type X = sprandn<sparse_matrix_type>(size(X), density)

Examples

[[cpp11::register]] doubles_matrix<> sprandn1_(const int& n) {
  sp_mat A = sprandn<sp_mat>(n, n, 0.05);
  mat B = mat(A);
  return as_doubles_matrix(B);
}

Generate Toeplitz matrix

The toeplitz() function generates a toeplitz matrix. The arguments can be a or a, b, where a is a vector that determines the first column and b is an optional vector that determines the first row.

Alternatively, circ_toeplitz() generates a circulant toeplitz matrix.

Examples

[[cpp11::register]] doubles_matrix<> toeplitz1_() {
  vec a = linspace(1, 5, 5);
  vec b = linspace(1, 5, 5);

  mat A = toeplitz(a, b);
  mat B = circ_toeplitz(a);

  return as_doubles_matrix(A + B);
}

Generated vectors, matrices, and cubes

Generate vector with linearly spaced elements

Examples

Caveat

Generate vector with logarithmically spaced elements

Examples

Generate vector with regularly spaced elements

Examples

Caveats

Generate vector with random permutation of a sequence of integers

Examples

Generate identity matrix

Examples

Generate object filled with ones

Examples

Caveat

Generate object filled with zeros

Examples

Caveat

Generate object with random values from a uniform distribution

Examples

Caveat

Generate object with random values from a normal/gaussian distribution

Examples

Generate object with random values from a gamma distribution

Examples

Generate object with random integer values in specified interval

Examples

Caveat

Generate sparse identity matrix

Examples

Generate sparse matrix with non-zero elements set to one

Examples

Generate sparse matrix with non-zero elements set to random values from a uniform distribution

Examples

Generate sparse matrix with non-zero elements set to random values from a normal/gaussian distribution

Examples

Generate Toeplitz matrix

Examples