Class: FastMatrix::Matrix

Inherits:
Data
  • Object
show all
Defined in:
lib/matrix/matrix.rb,
lib/scalar.rb,
lib/matrix/constructors.rb,
lib/lup_decomposition/lup_decomposition.rb,
ext/fast_matrix/Matrix/matrix.c

Overview

Constructors as in the standard matrix

Defined Under Namespace

Classes: LUPDecomposition

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(rows_count, columns_count) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 48

VALUE matrix_initialize(VALUE self, VALUE rows_count, VALUE columns_count)
{
    int m = raise_rb_value_to_int(columns_count);
    int n = raise_rb_value_to_int(rows_count);
    
    if(m <= 0 || n <= 0)
        rb_raise(fm_eIndexError, "Size cannot be negative or zero");

	struct matrix* data = get_matrix_from_rb_value(self);
    c_matrix_init(data, m, n);
	return self;
}

Class Method Details

.[](*rows) ⇒ Object

Creates a matrix where each argument is a row.

Matrix[ [25, 93], [-1, 66] ]
   =>  25 93
       -1 66



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# File 'lib/matrix/constructors.rb', line 57

def self.[](*rows)
  self.rows(rows)
end

.build(row_count, column_count = row_count, &block) ⇒ Object

Creates a matrix of size row_count x column_count. It fills the values by calling the given block, passing the current row and column. Returns random matrix if no block is given.

m = Matrix.build(2, 4) {|row, col| col - row }
  => Matrix[[0, 1, 2, 3], [-1, 0, 1, 2]]
m = Matrix.build(3) { rand }
  => a 3x3 matrix with random elements

Raises:

  • (NotImplementedError) 


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# File 'lib/matrix/constructors.rb', line 20

def self.build(row_count, column_count = row_count, &block)
  matrix = create_with_check(row_count, column_count)
  raise NotImplementedError, 'Issue#17' unless block_given?

  matrix.each_with_index! { |_, i, j| block.call(i, j) }
end

.column_vector(column) ⇒ Object

Creates a single-column matrix where the values of that column are as given in column.

Matrix.column_vector([4,5,6])
  => 4
     5
     6



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# File 'lib/matrix/constructors.rb', line 69

def self.column_vector(column)
  matrix = create_with_check(column.size, 1)
  column.each_with_index { |elem, i| matrix[i, 0] = elem }
  matrix
end

.columns(columns) ⇒ Object

Creates a matrix using columns as an array of column vectors.

Matrix.columns([[25, 93], [-1, 66]])
   =>  25 -1
       93 66



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# File 'lib/matrix/constructors.rb', line 47

def self.columns(columns)
  lines(columns, false)
end

.combine(*matrices) ⇒ Object

Create a matrix by combining matrices entrywise, using the given block

x = Matrix[[6, 6], [4, 4]]
y = Matrix[[1, 2], [3, 4]]
Matrix.combine(x, y) {|a, b| a - b} # => Matrix[[5, 4], [1, 0]]

TODO: optimize in C



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# File 'lib/matrix/constructors.rb', line 146

def self.combine(*matrices)
  return empty if matrices.empty?

  result = convert(matrices.first)
  matrices[1..matrices.size].each do |m|
    raise IndexError unless result.row_count == m.row_count &&
                            result.column_count == m.column_count

    result.each_with_index! { |elem, i, j| yield elem, m[i, j] }
  end
  result
end

.convert(matrix) ⇒ Object

Create fast matrix from standard matrix



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# File 'lib/matrix/matrix.rb', line 137

def self.convert(matrix)
  fast_matrix = Matrix.new(matrix.row_count, matrix.column_count)
  (0...matrix.row_count).each do |i|
    (0...matrix.column_count).each do |j|
      fast_matrix[i, j] = matrix[i, j]
    end
  end
  fast_matrix
end

.diagonal(*values) ⇒ Object

Creates a matrix where the diagonal elements are composed of values.

Matrix.diagonal(9, 5, -3)
  =>  9  0  0
      0  5  0
      0  0 -3



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# File 'lib/matrix/constructors.rb', line 94

def self.diagonal(*values)
  build(values.size, values.size) { |i, j| i == j ? values[i] : 0 }
end

.empty(_ = 0, _ = 0) ⇒ Object

Empty matrices does not supported

Raises:



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# File 'lib/matrix/constructors.rb', line 135

def self.empty(_ = 0, _ = 0)
  raise NotSupportedError, 'Empty matrices does not supported'
end

.fill(value, row_count, column_count = row_count) ⇒ Object

Creates a filled matrix Matrix.fill(42, 2, 4)

=>  42 42 42 42
    42 42 42 42



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# File 'lib/matrix/constructors.rb', line 118

def self.fill(value, row_count, column_count = row_count)
  create_with_check(row_count, column_count).fill!(value)
end

.hstack(*args) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 418

VALUE matrix_hstack(int argc, VALUE *argv, VALUE obj)
{
    raise_check_no_arguments(argc);
    
    struct matrix** mtrs;
    convert_matrix_array(argc, argv, &mtrs);

    if(!c_matrix_equal_by_n(argc, mtrs))
    {
        free(mtrs);
        rb_raise(fm_eIndexError, "Columns of different size");
    }

    int m = c_matrix_sum_by_m(argc, mtrs);
    int n = mtrs[0]->n;

    MAKE_MATRIX_AND_RB_VALUE(C, result, m, n);
    c_matrix_hstack(argc, mtrs, C->data, m);

    free(mtrs);
    return result;
}

.identity(n) ⇒ Object Also known as: unit, I

Creates an n by n identity matrix.

Matrix.identity(2)
  => 1 0
     0 1



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# File 'lib/matrix/constructors.rb', line 104

def self.identity(n)
  scalar(n, 1)
end

.row_vector(row) ⇒ Object

Creates a single-row matrix where the values of that row are as given in row.

Matrix.row_vector([4,5,6])
  => 4 5 6



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# File 'lib/matrix/constructors.rb', line 81

def self.row_vector(row)
  matrix = create_with_check(1, row.size)
  row.each_with_index { |elem, j| matrix[0, j] = elem }
  matrix
end

.rows(rows, copy = true) ⇒ Object

Creates a matrix where rows is an array of arrays, each of which is a row of the matrix. The optional argument copy exists only for compatibility with standard. The optional argument copy cannot be false, unlike standard.

Matrix.rows([[25, 93], [-1, 66]])
   =>  25 93
       -1 66



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# File 'lib/matrix/constructors.rb', line 36

def self.rows(rows, copy = true)
  check_flag_copy(copy)
  lines(rows, true)
end

.scalar(size, value) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 441

VALUE matrix_scalar(VALUE obj, VALUE size, VALUE value)
{
    int n = raise_rb_value_to_int(size);
    double v = raise_rb_value_to_double(value);

    MAKE_MATRIX_AND_RB_VALUE(C, result, n, n);
    c_matrix_scalar(n, C->data, v);
    return result;
}

.vstack(*args) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 396

VALUE matrix_vstack(int argc, VALUE *argv, VALUE obj)
{
    raise_check_no_arguments(argc);
    
    struct matrix** mtrs;
    convert_matrix_array(argc, argv, &mtrs);

    if(!c_matrix_equal_by_m(argc, mtrs))
    {
        free(mtrs);
        rb_raise(fm_eIndexError, "Rows of different size");
    }

    int m = mtrs[0]->m;
    int n = c_matrix_sum_by_n(argc, mtrs);

    MAKE_MATRIX_AND_RB_VALUE(C, result, m, n);
    c_matrix_vstack(argc, mtrs, C->data);
    free(mtrs);
    return result;
}

.zero(row_count, column_count = row_count) ⇒ Object

Creates a zero matrix row_count by column_count.

Matrix.zero(2, 3)
  => 0 0 0
     0 0 0



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# File 'lib/matrix/constructors.rb', line 128

def self.zero(row_count, column_count = row_count)
  fill(0, row_count, column_count)
end

Instance Method Details

#*(v) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 159

VALUE matrix_multiply(VALUE self, VALUE v)
{
    if(RB_FLOAT_TYPE_P(v) || FIXNUM_P(v)
        || RB_TYPE_P(v, T_BIGNUM))
        return matrix_multiply_mn(self, v);
    if(RBASIC_CLASS(v) == cMatrix)
        return matrix_strassen(self, v);
    if(RBASIC_CLASS(v) == cVector)
        return matrix_multiply_mv(self, v);
    rb_raise(fm_eTypeError, "Invalid klass for multiply");
}

#**(value) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 686

VALUE matrix_exponentiation(VALUE self, VALUE value)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    int d = raise_rb_value_to_int(value);
    
    MAKE_MATRIX_AND_RB_VALUE(C, result, A->m, A->n);
    if(!c_matrix_exponentiation(A->m, A->n, A->data, C->data, d))
        rb_raise(fm_eIndexError, "Invalid exponentiation");
    return result;
}

#+(other) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 241

VALUE matrix_add_with(VALUE self, VALUE other)
{
    raise_check_rbasic(other, cMatrix, "matrix");
	struct matrix* A = get_matrix_from_rb_value(self);
	struct matrix* B = get_matrix_from_rb_value(other);

    raise_check_equal_size_matrix(A, B);

    MAKE_MATRIX_AND_RB_VALUE(C, result, A->m, A->n);
    add_d_arrays_to_result(A->n * A->m, A->data, B->data, C->data);

    return result;
}

#+@ ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 478

VALUE matrix_plus(VALUE self)
{
    return self;
}

#-(other) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 268

VALUE matrix_sub_with(VALUE self, VALUE other)
{
    raise_check_rbasic(other, cMatrix, "matrix");
	struct matrix* A = get_matrix_from_rb_value(self);
	struct matrix* B = get_matrix_from_rb_value(other);

    raise_check_equal_size_matrix(A, B);

    MAKE_MATRIX_AND_RB_VALUE(C, result, A->m, A->n);
    sub_d_arrays_to_result(A->n * A->m, A->data, B->data, C->data);
    return result;
}

#-@ ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 470

VALUE matrix_minus(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    MAKE_MATRIX_AND_RB_VALUE(C, result, A->m, A->n);
    multiply_d_array_to_result(A->n * A->m, A->data, -1, C->data);
    return result;
}

#/(v) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 203

VALUE matrix_division(VALUE self, VALUE v)
{
    if(RB_FLOAT_TYPE_P(v) || FIXNUM_P(v)
        || RB_TYPE_P(v, T_BIGNUM))
        return matrix_division_mn(self, v);
    if(RBASIC_CLASS(v) == cMatrix)
        return matrix_division_mm(self, v);
    rb_raise(fm_eTypeError, "Invalid klass for division");
}

#<(other) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 372

VALUE matrix_less(VALUE self, VALUE other)
{
    raise_check_rbasic(other, cMatrix, "matrix");
	struct matrix* A = get_matrix_from_rb_value(self);
	struct matrix* B = get_matrix_from_rb_value(other);

    raise_check_equal_size_matrix(A, B);

    if(less_d_array(A->n * A->m, A->data, B->data))
        return Qtrue;
    return Qfalse;
}

#<=(other) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 346

VALUE matrix_less_or_equal(VALUE self, VALUE other)
{
    raise_check_rbasic(other, cMatrix, "matrix");
	struct matrix* A = get_matrix_from_rb_value(self);
	struct matrix* B = get_matrix_from_rb_value(other);

    raise_check_equal_size_matrix(A, B);

    if(less_or_equal_d_array(A->n * A->m, A->data, B->data))
        return Qtrue;
    return Qfalse;
}

#==(other) ⇒ Object

FIXME: for compare with standard matrix



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# File 'lib/matrix/matrix.rb', line 243

def ==(other)
  return eql?(other) if other.class == Matrix
  return false unless %i[row_size column_size \[\]].all? { |x| other.respond_to? x }
  return false unless self.row_size == other.row_size && self.column_size == other.column_size

  result = true
  each_with_index do |elem, i, j|
    result &&= elem == other[i, j].to_f
  end
  result
end

#>(other) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 359

VALUE matrix_greater(VALUE self, VALUE other)
{
    raise_check_rbasic(other, cMatrix, "matrix");
	struct matrix* A = get_matrix_from_rb_value(self);
	struct matrix* B = get_matrix_from_rb_value(other);

    raise_check_equal_size_matrix(A, B);

    if(greater_d_array(A->n * A->m, A->data, B->data))
        return Qtrue;
    return Qfalse;
}

#>=(other) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 333

VALUE matrix_greater_or_equal(VALUE self, VALUE other)
{
    raise_check_rbasic(other, cMatrix, "matrix");
	struct matrix* A = get_matrix_from_rb_value(self);
	struct matrix* B = get_matrix_from_rb_value(other);

    raise_check_equal_size_matrix(A, B);

    if(greater_or_equal_d_array(A->n * A->m, A->data, B->data))
        return Qtrue;
    return Qfalse;
}

#[](row, column) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 82

VALUE matrix_get(VALUE self, VALUE row, VALUE column)
{
    int m = raise_rb_value_to_int(column);
    int n = raise_rb_value_to_int(row);
	struct matrix* data = get_matrix_from_rb_value(self);
    
    m = (m < 0) ? data->m + m : m;
    n = (n < 0) ? data->n + n : n;
    
    if(m < 0 || n < 0 || n >= data->n || m >= data->m)
        return Qnil;

    return DBL2NUM(data->data[m + data->m * n]);
}

#[]=(row, column, v) ⇒ Object

[]=



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# File 'ext/fast_matrix/Matrix/matrix.c', line 62

VALUE matrix_set(VALUE self, VALUE row, VALUE column, VALUE v)
{
	struct matrix* data = get_matrix_from_rb_value(self);
    raise_check_frozen_matrix(data);

    int m = raise_rb_value_to_int(column);
    int n = raise_rb_value_to_int(row);
    double x = raise_rb_value_to_double(v);

    m = (m < 0) ? data->m + m : m;
    n = (n < 0) ? data->n + n : n;

    raise_check_range(m, 0, data->m);
    raise_check_range(n, 0, data->n);

    data->data[m + data->m * n] = x;
    return v;
}

#abs ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 325

VALUE matrix_abs(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    MAKE_MATRIX_AND_RB_VALUE(R, result, A->m, A->n);
    abs_d_array(A->n * A->m, A->data, R->data);
    return result;
}

#add!(other) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 255

VALUE matrix_add_from(VALUE self, VALUE other)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    raise_check_frozen_matrix(A);
    raise_check_rbasic(other, cMatrix, "matrix");
	struct matrix* B = get_matrix_from_rb_value(other);

    raise_check_equal_size_matrix(A, B);

    add_d_arrays_to_first(A->n * B->m, A->data, B->data);
    return self;
}

#adjugate ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 676

VALUE matrix_adjugate(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    raise_check_square_matrix(A);
    MAKE_MATRIX_AND_RB_VALUE(R, result, A->n, A->n);
    if(!c_matrix_adjugate(R->n, A->data, R->data))
        rb_raise(fm_eIndexError, "The discriminant is zero");
    return result;
}

#antisymmetric? ⇒ Boolean Also known as: skew_symmetric?

Returns:

  • (Boolean) 


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# File 'ext/fast_matrix/Matrix/matrix.c', line 451

VALUE matrix_antisymmetric(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    raise_check_square_matrix(A);

    if(c_matrix_antisymmetric(A->n, A->data))
        return Qtrue;
    return Qfalse;
}

#clone ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 213

VALUE matrix_copy(VALUE self)
{
	struct matrix* M = get_matrix_from_rb_value(self);
    MAKE_MATRIX_AND_RB_VALUE(R, result, M->m, M->n);
    copy_d_array(M->m * M->n, M->data, R->data);
    return result;
}

#coerce(other) ⇒ Object

The coerce method provides support for Ruby type coercion. This coercion mechanism is used by Ruby to handle mixed-type numeric operations: it is intended to find a compatible common type between the two operands of the operator. See also Numeric#coerce.



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# File 'lib/scalar.rb', line 14

def coerce(other)
  case other
  when Numeric
    [Scalar.new(other), self]
  else
    raise TypeError, "#{self.class} can't be coerced into #{other.class}"
  end
end

#cofactor(row, column) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 563

VALUE matrix_cofactor(VALUE self, VALUE row, VALUE column)
{
    int i = raise_rb_value_to_int(column);
    int j = raise_rb_value_to_int(row);
	struct matrix* A = get_matrix_from_rb_value(self);

    int m = A->m;
    int n = A->n;
    if(i < 0 || i >= m || j < 0 || j >= n)
        rb_raise(fm_eIndexError, "Index out of range");
    raise_check_square_matrix(A);

    double* D = malloc(sizeof(double) * (n - 1) * (n - 1));
    c_matrix_minor(n, n, A->data, D, i, j);

    int coefficient = ((i + j) % 2 == 1) ? -1 : 1;
    double det = c_matrix_determinant(n - 1, D);

    free(D);
    return DBL2NUM(coefficient * det);
}

#collect ⇒ Object 



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# File 'lib/matrix/matrix.rb', line 110

def collect
  collected_rows = []
  rows.each do |i|
    collected_rows.push(yield i)
  end
  collected_rows
end

#column(v) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 500

VALUE matrix_column_vector(VALUE self, VALUE v)
{
    int idx = raise_rb_value_to_int(v);
	struct matrix* A = get_matrix_from_rb_value(self);

    int m = A->m;
    int n = A->n;
    idx = (idx < 0) ? n + idx : idx;
    
    if(idx < 0 || idx >= n)
        return Qnil;

    MAKE_VECTOR_AND_RB_VALUE(C, result, n);
    c_matrix_column_vector(m, n, A->data, C->data, idx);
    return result;
}

#column_count ⇒ Object Also known as: column_size 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 221

VALUE matrix_row_size(VALUE self)
{
	struct matrix* data = get_matrix_from_rb_value(self);
    return INT2NUM(data->m);
}

#component ⇒ Object 



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# File 'lib/matrix/matrix.rb', line 25

alias component []

#convert ⇒ Object

Convert to standard ruby matrix.



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# File 'lib/matrix/matrix.rb', line 238

def convert
  ::Matrix.build(row_size, column_size) { |i, j| self[i, j] }
end

#determinant ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 294

VALUE matrix_determinant(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    raise_check_square_matrix(A);
    return DBL2NUM(c_matrix_determinant(A->n, A->data));
}

#diagonal? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'ext/fast_matrix/Matrix/matrix.c', line 517

VALUE matrix_diagonal(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    raise_check_square_matrix(A);
    
    if(c_matrix_diagonal(A->n, A->data))
        return Qtrue;
    return Qfalse;
}

#each(which = :all) ⇒ Object

Yields all elements of the matrix, starting with those of the first row

Matrix[ [1,2], [3,4] ].each { |e| puts e }
  # => prints the numbers 1 to 4



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# File 'lib/matrix/matrix.rb', line 152

def each(which = :all) # :yield: e
  return to_enum :each, which unless block_given?
  case which
  when :all
    (0...row_count).each do |i|
      (0...column_count).each do |j|
        yield self[i, j]
      end
    end
  when :diagonal
    (0...[row_count, column_count].min).each do |i|
          yield self[i, i]
    end
  when :off_diagonal
    (0...row_count).each do |i|
      (0...column_count).each do |j|
        if i != j
          yield self[i, j]
        end
      end
    end
  when :lower
    (0...row_count).each do |i|
      (0..[i,column_count-1].min).each do |j|
        yield self[i, j]
      end
    end
  when :strict_lower
    (1...row_count).each do |i|
      (0...[i,column_count].min).each do |j|
          yield self[i, j]
      end
    end
  when :strict_upper
    (0...row_count).each do |i|
      (i+1...column_count).each do |j|
        yield self[i, j]
      end
    end
  when :upper
    (0...row_count).each do |i|
      (i...column_count).each do |j|
        yield self[i, j]
      end
    end
  else
    raise ArgumentError, "expected #{which.inspect} to be one of :all, :diagonal, :off_diagonal, :lower, :strict_lower, :strict_upper or :upper"
  end
  self
end

#each_with_index ⇒ Object

Same as #each, but the row index and column index in addition to the element

Matrix[ [1,2], [3,4] ].each_with_index do |e, row, col|
  puts "#{e} at #{row}, #{col}"
end
  # => Prints:
  #    1 at 0, 0
  #    2 at 0, 1
  #    3 at 1, 0
  #    4 at 1, 1

Raises:



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# File 'lib/matrix/matrix.rb', line 214

def each_with_index
  raise NotSupportedError unless block_given?

  (0...row_count).each do |i|
    (0...column_count).each do |j|
      yield self[i, j], i, j
    end
  end
  self
end

#each_with_index! ⇒ Object

don’t use (Issue#1)



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# File 'lib/matrix/matrix.rb', line 226

def each_with_index!
  (0...row_count).each do |i|
    (0...column_count).each do |j|
      self[i, j] = yield self[i, j], i, j
    end
  end
  self
end

#element ⇒ Object

Returns element (i,j) of the matrix. That is: row i, column j.



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# File 'lib/matrix/matrix.rb', line 24

alias element []

#empty? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/matrix/matrix.rb', line 44

def empty?
  row_count * column_count == 0
end

#eql?(other) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'ext/fast_matrix/Matrix/matrix.c', line 310

VALUE matrix_equal(VALUE self, VALUE other)
{
    if(RBASIC_CLASS(other) != cMatrix)
        return Qfalse;
	struct matrix* A = get_matrix_from_rb_value(self);
	struct matrix* B = get_matrix_from_rb_value(other);

    if(A->n != B->n || A->m != B->m)
        return Qfalse;
        
    if(equal_d_arrays(A->n * A->m, A->data, B->data))
		return Qtrue;
	return Qfalse;
}

#fill!(value) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 301

VALUE matrix_fill(VALUE self, VALUE value)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    raise_check_frozen_matrix(A);
    double d = raise_rb_value_to_double(value);
    fill_d_array(A->m * A->n, A->data, d);
    return self;
}

#first_minor(row, column) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 547

VALUE matrix_first_minor(VALUE self, VALUE row, VALUE column)
{
    int i = raise_rb_value_to_int(column);
    int j = raise_rb_value_to_int(row);
	struct matrix* A = get_matrix_from_rb_value(self);

    int m = A->m;
    int n = A->n;
    if(i < 0 || i >= m || j < 0 || j >= n)
        rb_raise(fm_eIndexError, "Index out of range");

    MAKE_MATRIX_AND_RB_VALUE(C, result, m - 1, n - 1);
    c_matrix_minor(m, n, A->data, C->data, i, j);
    return result;
}

#freeze ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 744

VALUE matrix_freeze(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    A->frozen = true;
    return self;
}

#hadamard_product(other) ⇒ Object Also known as: entrywise_product 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 527

VALUE matrix_hadamard_product(VALUE self, VALUE other)
{
    raise_check_rbasic(other, cMatrix, "matrix");
	struct matrix* A = get_matrix_from_rb_value(self);
	struct matrix* B = get_matrix_from_rb_value(other);

    raise_check_equal_size_matrix(A, B);

    MAKE_MATRIX_AND_RB_VALUE(C, result, A->m, A->n);
    multiply_elems_d_array_to_result(A->n * A->m, A->data, B->data, C->data);
    return result;
}

#imaginary ⇒ Object Also known as: imag

Returns the imaginary part of the matrix. Always returns a zero matrix



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# File 'lib/matrix/matrix.rb', line 73

def imaginary()
  Matrix.zero(row_count, column_count)
end

#inverse ⇒ Object Also known as: inv 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 666

VALUE matrix_inverse(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    raise_check_square_matrix(A);
    MAKE_MATRIX_AND_RB_VALUE(R, result, A->n, A->n);
    if(!c_matrix_inverse(R->n, A->data, R->data))
        rb_raise(fm_eIndexError, "The discriminant is zero");
    return result;
}

#laplace_expansion(row: nil, column: nil) ⇒ Object Also known as: cofactor_expansion

Laplace expansion is equal to the determinant in the real numbers



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# File 'lib/matrix/matrix.rb', line 82

def laplace_expansion(row: nil, column: nil) 
  determinant
end

#lower_triangular? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'ext/fast_matrix/Matrix/matrix.c', line 615

VALUE matrix_lower_triangular(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    raise_check_square_matrix(A);

    if(c_matrix_lower_triangular(A->n, A->data))
        return Qtrue;
    return Qfalse;
}

#lup ⇒ Object Also known as: lup_decomposition 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 751

VALUE matrix_lup(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    raise_check_square_matrix(A);

    int n = A->n;

    struct lupdecomposition lp;
    lp.n = n;
    lp.data = malloc(n * n * sizeof(double));
    lp.permutation = malloc(n * sizeof(double));
    c_matrix_lup(n, A->data, lp.data, lp.permutation, &(lp.pivot_sign), &(lp.singular));
    
    struct lupdecomposition* p_lp;
    VALUE result = TypedData_Make_Struct(cLUPDecomposition, struct lupdecomposition, &lup_type, p_lp); 
    *p_lp = lp;

    return result;
}

#normal? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'ext/fast_matrix/Matrix/matrix.c', line 697

VALUE matrix_normal(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    if(A->m != A-> n)
        return Qfalse;
    
    int n = A->n;
    double* B = malloc(n * n * sizeof(double));
    double* C = malloc(n * n * sizeof(double));
    double* D = malloc(n * n * sizeof(double));
    
    c_matrix_transpose(n, n, A->data, B);
    c_matrix_strassen(n, n, n, A->data, B, C);
    c_matrix_strassen(n, n, n, B, A->data, D);
    
    VALUE res = Qfalse;
    if(equal_d_arrays(n * n, C, D))
        res = Qtrue;
    
    free(B);
    free(C);
    free(D);
    return res;
}

#orthogonal? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'ext/fast_matrix/Matrix/matrix.c', line 645

VALUE matrix_orthogonal(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    raise_check_square_matrix(A);
    
    int n = A->n;
    double* B = malloc(sizeof(double) * n * n);
    double* C = malloc(sizeof(double) * n * n);

    c_matrix_transpose(n, n, A->data, B);
    fill_d_array(n * n, C, 0);
    c_matrix_strassen(n, n, n, A->data, B, C);
    bool result = c_matrix_identity(n, C);

    free(B);
    free(C);
    if(result)
        return Qtrue;
    return Qfalse;
}

#permutation? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'ext/fast_matrix/Matrix/matrix.c', line 635

VALUE matrix_permutation(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    raise_check_square_matrix(A);

    if(c_matrix_permutation(A->n, A->data))
        return Qtrue;
    return Qfalse;
}

#rank ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 593

VALUE matrix_rank(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    return INT2NUM(c_matrix_rank(A->m, A->n, A->data));
}

#real? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/matrix/matrix.rb', line 106

def real?
  true
end

#rect ⇒ Object Also known as: rectangular

Returns an array containing matrices corresponding to the real and imaginary parts of the matrix



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# File 'lib/matrix/matrix.rb', line 90

def rect
  [real, imag]
end

#regular? ⇒ Boolean

Returns true if this is a regular (i.e. non-singular) matrix.

Returns:

  • (Boolean) 


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# File 'lib/matrix/matrix.rb', line 58

def regular?
  not singular?
end

#round(*args) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 599

VALUE matrix_round(int argc, VALUE *argv, VALUE self)
{
    if(argc > 1)
        rb_raise(fm_eTypeError, "Wrong number of arguments");
    int d;
    if(argc == 1)
        d = raise_rb_value_to_int(argv[0]);
    else
        d = 0;

    struct matrix* A = get_matrix_from_rb_value(self);
    MAKE_MATRIX_AND_RB_VALUE(R, result, A->m, A->n);
    round_d_array(A->m * A->n, A->data, R->data, d);
    return result;
}

#row(v) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 483

VALUE matrix_row_vector(VALUE self, VALUE v)
{
    int idx = raise_rb_value_to_int(v);
	struct matrix* A = get_matrix_from_rb_value(self);

    int m = A->m;
    int n = A->n;
    idx = (idx < 0) ? m + idx : idx;
    
    if(idx < 0 || idx >= m)
        return Qnil;
    
    MAKE_VECTOR_AND_RB_VALUE(C, result, n);
    copy_d_array(m, A->data + idx * m, C->data);
    return result;
}

#row_count ⇒ Object Also known as: row_size 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 227

VALUE matrix_column_size(VALUE self)
{
	struct matrix* data = get_matrix_from_rb_value(self);
    return INT2NUM(data->n);
}

#singular? ⇒ Boolean

Returns true if this is a singular matrix.

Returns:

  • (Boolean) 


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# File 'lib/matrix/matrix.rb', line 51

def singular?
  determinant == 0
end

#square? ⇒ Boolean

Returns true if this is a square matrix.

Returns:

  • (Boolean) 


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# File 'lib/matrix/matrix.rb', line 65

def square?
  column_count == row_count
end

#sub!(other) ⇒ Object 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 281

VALUE matrix_sub_from(VALUE self, VALUE other)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    raise_check_frozen_matrix(A);
    raise_check_rbasic(other, cMatrix, "matrix");
	struct matrix* B = get_matrix_from_rb_value(other);

    raise_check_equal_size_matrix(A, B);

    sub_d_arrays_to_first(A->n * B->m, A->data, B->data);
    return self;
}

#symmetric? ⇒ Boolean Also known as: hermitian?

Returns:

  • (Boolean) 


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# File 'ext/fast_matrix/Matrix/matrix.c', line 461

VALUE matrix_symmetric(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    raise_check_square_matrix(A);
    if(c_matrix_symmetric(A->n, A->data))
        return Qtrue;
    return Qfalse;
}

#to_a ⇒ Object 



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# File 'lib/matrix/matrix.rb', line 130

def to_a
  rows.collect(&:dup)
end

#to_matrix ⇒ Object Also known as: conjugate, real

Explicit conversion to a Matrix. Returns self



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# File 'lib/matrix/matrix.rb', line 40

def to_matrix
  self
end

#to_s ⇒ Object Also known as: to_str

Overrides Object#to_s



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# File 'lib/matrix/matrix.rb', line 121

def to_s
  "#{self.class}[#{collect do |row|
    '[' + row.join(', ') + ']'
  end.join(', ')}]"
end

#trace ⇒ Object Also known as: tr 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 540

VALUE matrix_trace(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    raise_check_square_matrix(A);
    return DBL2NUM(c_matrix_trace(A->n, A->data));
}

#transpose ⇒ Object Also known as: t 



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# File 'ext/fast_matrix/Matrix/matrix.c', line 233

VALUE matrix_transpose(VALUE self)
{
	struct matrix* M = get_matrix_from_rb_value(self);
    MAKE_MATRIX_AND_RB_VALUE(R, result, M->n, M->m);
    c_matrix_transpose(M->m, M->n, M->data, R->data);
    return result;
}

#unitary? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'ext/fast_matrix/Matrix/matrix.c', line 722

VALUE matrix_unitary(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    if(A->m != A-> n)
        return Qfalse;
    
    int n = A->n;
    double* B = malloc(n * n * sizeof(double));
    double* C = malloc(n * n * sizeof(double));
    
    c_matrix_transpose(n, n, A->data, B);
    c_matrix_strassen(n, n, n, A->data, B, C);
    
    VALUE res = Qfalse;
    if(c_matrix_identity(n, C))
        res = Qtrue;
    
    free(B);
    free(C);
    return res;
}

#upper_triangular? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'ext/fast_matrix/Matrix/matrix.c', line 625

VALUE matrix_upper_triangular(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    raise_check_square_matrix(A);

    if(c_matrix_upper_triangular(A->n, A->data))
        return Qtrue;
    return Qfalse;
}

#zero? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'ext/fast_matrix/Matrix/matrix.c', line 585

VALUE matrix_zero(VALUE self)
{
	struct matrix* A = get_matrix_from_rb_value(self);
    if(zero_d_array(A->m * A->n, A->data))
            return Qtrue;
    return Qfalse;
}