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false)).transpose"}},{"id":"combine(*matrices,&block)-class-method","html_id":"combine(*matrices,&amp;block)-class-method","name":"combine","doc":"Create a matrix by combining matrices entrywise, using the given block\n\n```\nx = Matrix[[6, 6], [4, 4]]\ny = Matrix[[1, 2], [3, 4]]\nMatrix.combine(x, y) {|a, b| a - b}\n# => Matrix[[5, 4], [1, 0]]\n```","summary":"<p>Create a matrix by combining matrices entrywise, using the given block</p>","abstract":false,"args":[{"name":"matrices","doc":null,"default_value":"","external_name":"matrices","restriction":""}],"args_string":"(*matrices, &block)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L264","def":{"name":"combine","args":[{"name":"matrices","doc":null,"default_value":"","external_name":"matrices","restriction":""}],"double_splat":null,"splat_index":0,"yields":1,"block_arg":null,"return_type":"","visibility":"Public","body":"if matrices.empty?\n  return Matrix.empty\nend\nmatrices = matrices.map do |m|\n  m = m.is_a?(Matrix) ? m : rows(m)\nend\nx = matrices.first\nmatrices.each do |m|\n  if (x.row_count == m.row_count) && (x.column_count == m.column_count)\n  else\n    raise(ErrDimensionMismatch.new)\n  end\nend\nrows = Array(T).new(x.row_count) do |i|\n  Array(T).new(x.column_count) do |j|\n    yield matrices.map do |m|\n      m[i, j]\n    end\n  end\nend\nnew(rows, x.column_count)\n"}},{"id":"diagonal(*values:T)-class-method","html_id":"diagonal(*values:T)-class-method","name":"diagonal","doc":"Creates a matrix where the diagonal elements are composed of `values`.\n\n```\nMatrix.diagonal(9, 5, -3)\n# =>  [ 9,  0,  0,\n#       0,  5,  0,\n#       0,  0, -3 ]\n```","summary":"<p>Creates a matrix where the diagonal elements are composed of <code>values</code>.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"T"}],"args_string":"(*values : T)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L101","def":{"name":"diagonal","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"T"}],"double_splat":null,"splat_index":0,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"diagonal(values, nil)"}},{"id":"diagonal(values:Indexable(T),dummy=nil)-class-method","html_id":"diagonal(values:Indexable(T),dummy=nil)-class-method","name":"diagonal","doc":"Creates a matrix where the diagonal elements are composed of `values`.\n\n```\nMatrix.diagonal(9, 5, -3)\n# =>  [ 9,  0,  0,\n#       0,  5,  0,\n#       0,  0, -3 ]\n```","summary":"<p>Creates a matrix where the diagonal elements are composed of <code>values</code>.</p>","abstract":false,"args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Indexable(T)"},{"name":"dummy","doc":null,"default_value":"nil","external_name":"dummy","restriction":""}],"args_string":"(values : Indexable(T), dummy = <span class=\"n\">nil</span>)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L89","def":{"name":"diagonal","args":[{"name":"values","doc":null,"default_value":"","external_name":"values","restriction":"Indexable(T)"},{"name":"dummy","doc":null,"default_value":"nil","external_name":"dummy","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"size = values.size\nif size == 0\n  return Matrix(T).empty\nend\nrows = Array(Array(T)).new(size) do |j|\n  row = Array(T).new(size, T.new(0))\n  row[j] = values[j]\n  row\nend\nnew(rows)\n"}},{"id":"empty(row_count=0,column_count=0)-class-method","html_id":"empty(row_count=0,column_count=0)-class-method","name":"empty","doc":"Creates a empty matrix of `row_count` x `column_count`.\nAt least one of `row_count` or `column_count` must be 0.\n\n```\nm = Matrix(Int32).empty(2, 0)\nm == Matrix[ [], [] ]\n# => true\nn = Matrix(Int32).empty(0, 3)\nm * n\n# => Matrix[[0, 0, 0], [0, 0, 0]]\n```","summary":"<p>Creates a empty matrix of <code><a href=\"../../Apatite/LinearAlgebra/Matrix.html#row_count-instance-method\">#row_count</a></code> x <code><a href=\"../../Apatite/LinearAlgebra/Matrix.html#column_count:Int32-instance-method\">#column_count</a></code>.</p>","abstract":false,"args":[{"name":"row_count","doc":null,"default_value":"0","external_name":"row_count","restriction":""},{"name":"column_count","doc":null,"default_value":"0","external_name":"column_count","restriction":""}],"args_string":"(row_count = <span class=\"n\">0</span>, column_count = <span class=\"n\">0</span>)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L201","def":{"name":"empty","args":[{"name":"row_count","doc":null,"default_value":"0","external_name":"row_count","restriction":""},{"name":"column_count","doc":null,"default_value":"0","external_name":"column_count","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if (column_count != 0) && (row_count != 0)\n  raise(ArgumentError.new(\"One size must be 0\"))\nend\nif column_count < 0 || row_count < 0\n  raise(ArgumentError.new(\"Negative size\"))\nend\nnew([[] of T] * row_count, column_count)\n"}},{"id":"hstack(x,*matrices)-class-method","html_id":"hstack(x,*matrices)-class-method","name":"hstack","doc":"Create a matrix by stacking matrices horizontally\n\n```\nx = Matrix[[1, 2], [3, 4]]\ny = Matrix[[5, 6], [7, 8]]\nMatrix.hstack(x, y)\n# => Matrix[[1, 2, 5, 6], [3, 4, 7, 8]]\n```","summary":"<p>Create a matrix by stacking matrices horizontally</p>","abstract":false,"args":[{"name":"x","doc":null,"default_value":"","external_name":"x","restriction":""},{"name":"matrices","doc":null,"default_value":"","external_name":"matrices","restriction":""}],"args_string":"(x, *matrices)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L236","def":{"name":"hstack","args":[{"name":"x","doc":null,"default_value":"","external_name":"x","restriction":""},{"name":"matrices","doc":null,"default_value":"","external_name":"matrices","restriction":""}],"double_splat":null,"splat_index":1,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"result = x.rows\ntotal_column_count = x.column_count\nmatrices.each do |m|\n  m = m.is_a?(Matrix) ? m : rows(m)\n  if m.row_count != x.row_count\n    raise(ErrDimensionMismatch.new(\"The given matrices must have #{x.row_count} rows, but one has #{m.row_count}\"))\n  end\n  result.each_with_index do |row, i|\n    row.concat(m.rows[i])\n  end\n  total_column_count = total_column_count + m.column_count\nend\nnew(result, total_column_count)\n"}},{"id":"identity(n)-class-method","html_id":"identity(n)-class-method","name":"identity","doc":"Creates an `n` by `n` identity matrix.\n\nNOTE: An explicit type is required since it cannot be inferred.\n\n```\nMatrix(Int32).identity(2)\n# => [ 1, 0,\n#      0, 1 ]\n```","summary":"<p>Creates an <code>n</code> by <code>n</code> identity matrix.</p>","abstract":false,"args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"args_string":"(n)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L142","def":{"name":"identity","args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"scalar(n, T.new(1))"}},{"id":"row_vector(row)-class-method","html_id":"row_vector(row)-class-method","name":"row_vector","doc":"Creates a single-row matrix where the values of that row are as given in\n`row`.\n\n```\nMatrix.row_vector([4,5,6])\n# => [ 4, 5, 6 ]\n```","summary":"<p>Creates a single-row matrix where the values of that row are as given in <code><a href=\"../../Apatite/LinearAlgebra/Matrix.html#row(i)-instance-method\">#row</a></code>.</p>","abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""}],"args_string":"(row)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L171","def":{"name":"row_vector","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"row = row.to_a\nMatrix.new([row])\n"}},{"id":"rows(rows:Indexable(Indexable(T)),copy=true)-class-method","html_id":"rows(rows:Indexable(Indexable(T)),copy=true)-class-method","name":"rows","doc":"Creates a matrix where +rows+ is an array of arrays, each of which is a row\nof the matrix.  If the optional argument +copy+ is false, use the given\narrays as the internal structure of the matrix without copying.\n\n```\nMatrix.rows([[25, 93], [-1, 66]])\n# => [ 25, 93,\n#      -1, 66 ]\n```","summary":"<p>Creates a matrix where +rows+ is an array of arrays, each of which is a row of the matrix.</p>","abstract":false,"args":[{"name":"rows","doc":null,"default_value":"","external_name":"rows","restriction":"Indexable(Indexable(T))"},{"name":"copy","doc":null,"default_value":"true","external_name":"copy","restriction":""}],"args_string":"(rows : Indexable(Indexable(T)), copy = <span class=\"n\">true</span>)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L33","def":{"name":"rows","args":[{"name":"rows","doc":null,"default_value":"","external_name":"rows","restriction":"Indexable(Indexable(T))"},{"name":"copy","doc":null,"default_value":"true","external_name":"copy","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if copy\n  rows = rows.dup\nend\nrows = rows.map(&.to_a).to_a\nrows.map! do |row|\n  if row\n    row = row.dup\n  end\n  row.to_a\nend\nsize = (rows[0] || ([] of T)).size\nrows.each_with_index do |row, i|\n  if row.size == size\n  else\n    raise(ErrDimensionMismatch.new(\"row size differs (row at index `#{i}` should contain #{size} elements, instead has #{row.size})\"))\n  end\nend\nnew(rows, size)\n"}},{"id":"scalar(n,value:T)-class-method","html_id":"scalar(n,value:T)-class-method","name":"scalar","doc":"Creates an +n+ by +n+ diagonal matrix where each diagonal element is\n`value`.\n\n```\nMatrix.scalar(2, 5)\n# => [ 5, 0,\n#      0, 5 ]\n```","summary":"<p>Creates an +n+ by +n+ diagonal matrix where each diagonal element is <code>value</code>.</p>","abstract":false,"args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"T"}],"args_string":"(n, value : T)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L129","def":{"name":"scalar","args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":""},{"name":"value","doc":null,"default_value":"","external_name":"value","restriction":"T"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"diagonal(Array(T).new(n, value))"}},{"id":"unit(n:T)-class-method","html_id":"unit(n:T)-class-method","name":"unit","doc":"Creates an `n` by `n` identity matrix.\n\nNOTE: An explicit type is required since it cannot be inferred.\n\n```\nMatrix(Int32).identity(2)\n# => [ 1, 0,\n#      0, 1 ]\n```","summary":"<p>Creates an <code>n</code> by <code>n</code> identity matrix.</p>","abstract":false,"args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":"T"}],"args_string":"(n : T)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L147","def":{"name":"unit","args":[{"name":"n","doc":null,"default_value":"","external_name":"n","restriction":"T"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"identity(n)"}},{"id":"vstack(x,*matrices)-class-method","html_id":"vstack(x,*matrices)-class-method","name":"vstack","doc":"Create a matrix by stacking matrices vertically\n\n```\nx = Matrix[[1, 2], [3, 4]]\ny = Matrix[[5, 6], [7, 8]]\nMatrix.vstack(x, y)\n# => Matrix[[1, 2], [3, 4], [5, 6], [7, 8]]\n```","summary":"<p>Create a matrix by stacking matrices vertically</p>","abstract":false,"args":[{"name":"x","doc":null,"default_value":"","external_name":"x","restriction":""},{"name":"matrices","doc":null,"default_value":"","external_name":"matrices","restriction":""}],"args_string":"(x, *matrices)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L216","def":{"name":"vstack","args":[{"name":"x","doc":null,"default_value":"","external_name":"x","restriction":""},{"name":"matrices","doc":null,"default_value":"","external_name":"matrices","restriction":""}],"double_splat":null,"splat_index":1,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"result = x.rows\nmatrices.each do |m|\n  m = m.is_a?(Matrix) ? m : rows(m)\n  if m.column_count != x.column_count\n    raise(ErrDimensionMismatch.new(\"The given matrices must have #{x.column_count} columns, but one has #{m.column_count}\"))\n  end\n  result.concat(m.rows)\nend\nnew(result, x.column_count)\n"}},{"id":"zero(row_count,column_count=row_count)-class-method","html_id":"zero(row_count,column_count=row_count)-class-method","name":"zero","doc":"Creates a zero matrix. Note that a type definition is\nrequired.\n\n```\nMatrix(Int32).zero(2)\n# => [ 0, 0,\n#      0, 0 ]\n```","summary":"<p>Creates a zero matrix.</p>","abstract":false,"args":[{"name":"row_count","doc":null,"default_value":"","external_name":"row_count","restriction":""},{"name":"column_count","doc":null,"default_value":"row_count","external_name":"column_count","restriction":""}],"args_string":"(row_count, column_count = row_count)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L159","def":{"name":"zero","args":[{"name":"row_count","doc":null,"default_value":"","external_name":"row_count","restriction":""},{"name":"column_count","doc":null,"default_value":"row_count","external_name":"column_count","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"rows = Array(T).new(row_count) do\n  Array(T).new(column_count, T.new(0))\nend\nnew(rows, column_count)\n"}}],"constructors":[{"id":"new(pull:JSON::PullParser)-class-method","html_id":"new(pull:JSON::PullParser)-class-method","name":"new","doc":"Creates a new `Matrix` instance from a `JSON::PullParser`.\nDefaults to a Float64 matrix.","summary":"<p>Creates a new <code><a href=\"../../Apatite/LinearAlgebra/Matrix.html\">Matrix</a></code> instance from a <code>JSON::PullParser</code>.</p>","abstract":false,"args":[{"name":"pull","doc":null,"default_value":"","external_name":"pull","restriction":"JSON::PullParser"}],"args_string":"(pull : JSON::PullParser)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L107","def":{"name":"new","args":[{"name":"pull","doc":null,"default_value":"","external_name":"pull","restriction":"JSON::PullParser"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"arr = [] of Array(Float64)\nnew(pull) do |element|\n  arr << element\nend\nrows(arr)\n"}},{"id":"new(pull:JSON::PullParser,&block)-class-method","html_id":"new(pull:JSON::PullParser,&amp;block)-class-method","name":"new","doc":null,"summary":null,"abstract":false,"args":[{"name":"pull","doc":null,"default_value":"","external_name":"pull","restriction":"JSON::PullParser"}],"args_string":"(pull : JSON::PullParser, &block)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L115","def":{"name":"new","args":[{"name":"pull","doc":null,"default_value":"","external_name":"pull","restriction":"JSON::PullParser"}],"double_splat":null,"splat_index":null,"yields":1,"block_arg":null,"return_type":"","visibility":"Public","body":"pull.read_array do\n  yield Array(Float64).new(pull)\nend"}}],"instance_methods":[{"id":"*(other)-instance-method","html_id":"*(other)-instance-method","name":"*","doc":"Matrix multiplication\n\n```\nMatrix[[2,4], [6,8]] * Matrix.identity(2)\n# => [ 2, 4,\n#      6, 8 ]\n```","summary":"<p>Matrix multiplication</p>","abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L914","def":{"name":"*","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"case other\nwhen Number\n  rows = @rows.map do |row|\n    row.map do |e|\n      (e * other).as(T)\n    end\n  end\n  Matrix.new(rows, column_count)\nwhen Vector\n  m = Matrix.column_vector(other)\n  r = self * m\n  r.column(0)\nwhen Matrix\n  if column_count != other.column_count\n    raise(ErrDimensionMismatch.new)\n  end\n  rows = Array.new(row_count) do |i|\n    Array.new(column_count) do |j|\n      (0...column_count).reduce(0) do |vij, k|\n        vij + (self[i, k] * other[k, j])\n      end\n    end\n  end\n  Matrix.new(rows, column_count)\nelse\n  self * (Matrix.rows(other))\nend"}},{"id":"**(other)-instance-method","html_id":"**(other)-instance-method","name":"**","doc":"Matrix exponentiation.\n\nEquivalent to multiplying the matrix by itself N times.\nNon integer exponents will be handled by diagonalizing the matrix.\n\n```\nMatrix[[7,6], [3,9]] ** 2\n# => [ 67, 96,\n#      48, 99 ]\n```","summary":"<p>Matrix exponentiation.</p>","abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L1084","def":{"name":"**","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":""}},{"id":"+(other:Matrix|Indexable)-instance-method","html_id":"+(other:Matrix|Indexable)-instance-method","name":"+","doc":"Matrix addition\n\n```\nMatrix.scalar(2,5) + Matrix[[1,0], [-4,7]]\n# => [ 6,  0,\n#     -4,  1 ]\n```","summary":"<p>Matrix addition</p>","abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix | Indexable"}],"args_string":"(other : Matrix | Indexable)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L947","def":{"name":"+","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix | Indexable"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"case other\nwhen Vector\n  other = Matrix.column_vector(other)\nwhen Matrix\nelse\n  other = Matrix.rows(other)\nend\nif (row_count == other.row_count) && (column_count == other.column_count)\nelse\n  raise(ErrDimensionMismatch.new)\nend\nrows = Array.new(row_count) do |i|\n  Array.new(column_count) do |j|\n    (self[i, j] + other[i, j]).as(T)\n  end\nend\nMatrix.new(rows, column_count)\n"}},{"id":"-(other:Matrix|Indexable)-instance-method","html_id":"-(other:Matrix|Indexable)-instance-method","name":"-","doc":"Matrix subtraction\n\n```\nMatrix[[1,5], [4,2]] - Matrix[[9,3], [-4,1]]\n# => [-8, 2,\n#      8, 1 ]\n```","summary":"<p>Matrix subtraction</p>","abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix | Indexable"}],"args_string":"(other : Matrix | Indexable)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L974","def":{"name":"-","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix | Indexable"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"case other\nwhen Vector\n  other = Matrix.column_vector(other)\nwhen Matrix\nelse\n  other = Matrix.rows(other)\nend\nif (row_count == other.row_count) && (column_count == other.column_count)\nelse\n  raise(ErrDimensionMismatch.new)\nend\nrows = Array.new(row_count) do |i|\n  Array.new(column_count) do |j|\n    (self[i, j] - other[i, j]).as(T)\n  end\nend\nMatrix.new(rows, column_count)\n"}},{"id":"/(other)-instance-method","html_id":"/(other)-instance-method","name":"/","doc":"Matrix division (multiplication by the inverse).\n\n```\nMatrix[[7,6], [3,9]] / Matrix[[2,9], [3,1]]\n# => [ -7,  1,\n#      -3, -6 ]\n```","summary":"<p>Matrix division (multiplication by the inverse).</p>","abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"args_string":"(other)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L1001","def":{"name":"/","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"case other\nwhen Number\n  rows = @rows.map do |row|\n    row.map do |e|\n      (e / other).as(T)\n    end\n  end\n  return Matrix.new(rows, column_count)\nwhen Matrix\n  return self * other.inverse\nelse\n  self / (Matrix.rows(other))\nend"}},{"id":"(other:Matrix)-instance-method","html_id":"(other:Matrix)-instance-method","name":"<=>","doc":null,"summary":null,"abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"args_string":"(other : Matrix)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L296","def":{"name":"<=>","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"rows <=> other.rows"}},{"id":"==(other:Matrix)-instance-method","html_id":"==(other:Matrix)-instance-method","name":"==","doc":"Equality operator","summary":"<p>Equality operator</p>","abstract":false,"args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"args_string":"(other : Matrix)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L891","def":{"name":"==","args":[{"name":"other","doc":null,"default_value":"","external_name":"other","restriction":"Matrix"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"(rows == other.rows) && (column_count == other.column_count)"}},{"id":"[](i,j)-instance-method","html_id":"[](i,j)-instance-method","name":"[]","doc":"Returns element (`i`, `j`) of the matrix.  That is: row `i`, column `j`.\nRaises if either index is not found.","summary":"<p>Returns element (<code>i</code>, <code>j</code>) of the matrix.</p>","abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""},{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"args_string":"(i, j)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L314","def":{"name":"[]","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""},{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"@rows[i][j]"}},{"id":"[](i)-instance-method","html_id":"[](i)-instance-method","name":"[]","doc":"Returns row `i` of the matrix as an Array. Raises if the\nindex is not found.","summary":"<p>Returns row <code>i</code> of the matrix as an Array.</p>","abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"args_string":"(i)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L302","def":{"name":"[]","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"@rows[i]"}},{"id":"[]=(i,j,v:T)-instance-method","html_id":"[]=(i,j,v:T)-instance-method","name":"[]=","doc":"Set the value at index (`i`, `j`). That is: row `i`, column `j`.","summary":"<p>Set the value at index (<code>i</code>, <code>j</code>).</p>","abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""},{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""},{"name":"v","doc":null,"default_value":"","external_name":"v","restriction":"T"}],"args_string":"(i, j, v : T)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L325","def":{"name":"[]=","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""},{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""},{"name":"v","doc":null,"default_value":"","external_name":"v","restriction":"T"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"@rows[i][j] = v"}},{"id":"[]?(i,j)-instance-method","html_id":"[]?(i,j)-instance-method","name":"[]?","doc":"Returns element (`i`, `j`) of the matrix.  That is: row `i`, column `j`.\nReturns nil if either index is not found.","summary":"<p>Returns element (<code>i</code>, <code>j</code>) of the matrix.</p>","abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""},{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"args_string":"(i, j)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L320","def":{"name":"[]?","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""},{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"@rows[i]?.try(&.[]?(j))"}},{"id":"[]?(i)-instance-method","html_id":"[]?(i)-instance-method","name":"[]?","doc":"Returns row `i` of the matrix as an Array. Returns nil if the\nindex is not found.","summary":"<p>Returns row <code>i</code> of the matrix as an Array.</p>","abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"args_string":"(i)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L308","def":{"name":"[]?","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"@rows[i]?"}},{"id":"adjugate-instance-method","html_id":"adjugate-instance-method","name":"adjugate","doc":"Returns the adjugate of the matrix.\n\nMatrix[ [7,6],[3,9] ].adjugate\n# => [ 9, -6,\n#     -3,  7 ]\n```","summary":"<p>Returns the adjugate of the matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L649","def":{"name":"adjugate","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if square?\nelse\n  raise(ErrDimensionMismatch.new)\nend\nMatrix.build(row_count, column_count) do |row, column|\n  cofactor(column, row)\nend\n"}},{"id":"clone-instance-method","html_id":"clone-instance-method","name":"clone","doc":"Returns a clone of the matrix, so that the contents of each do not reference\nidentical objects.\n\nThere should be no good reason to do this since Matrices are immutable.","summary":"<p>Returns a clone of the matrix, so that the contents of each do not reference identical objects.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L899","def":{"name":"clone","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Matrix.new(@rows.map(&.dup), column_count)"}},{"id":"coerce(klass)-instance-method","html_id":"coerce(klass)-instance-method","name":"coerce","doc":"Attempt to coerce the elements in the matrix to another type.","summary":"<p>Attempt to coerce the elements in the matrix to another type.</p>","abstract":false,"args":[{"name":"klass","doc":null,"default_value":"","external_name":"klass","restriction":""}],"args_string":"(klass)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L1388","def":{"name":"coerce","args":[{"name":"klass","doc":null,"default_value":"","external_name":"klass","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"rws = @rows.map do |r|\n  r.map do |i|\n    klass.new(i)\n  end\nend\nMatrix.rows(rws)\n"}},{"id":"cofactor(row,column)-instance-method","html_id":"cofactor(row,column)-instance-method","name":"cofactor","doc":"Returns the (row, column) cofactor which is obtained by multiplying\nthe first minor by (-1)**(row + column).\n\n```\nMatrix.diagonal(9, 5, -3, 4).cofactor(1, 1)\n# => -108\n```","summary":"<p>Returns the (row, column) cofactor which is obtained by multiplying the first minor by (-1)**(row + column).</p>","abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"","external_name":"column","restriction":""}],"args_string":"(row, column)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L635","def":{"name":"cofactor","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"","external_name":"column","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if empty?\n  raise(\"cofactor of empty matrix is not defined\")\nend\nif square?\nelse\n  raise(ErrDimensionMismatch.new)\nend\ndet_of_minor = (first_minor(row, column)).determinant\ndet_of_minor * ((-1) ** (row + column))\n"}},{"id":"column(j,&block:T->)-instance-method","html_id":"column(j,&amp;block:T-&gt;)-instance-method","name":"column","doc":"Returns a block which yields every item in column `j` of the Matrix.","summary":"<p>Returns a block which yields every item in column <code>j</code> of the Matrix.</p>","abstract":false,"args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"args_string":"(j, &block : T -> )","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L376","def":{"name":"column","args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"double_splat":null,"splat_index":null,"yields":1,"block_arg":{"name":"block","doc":null,"default_value":"","external_name":"block","restriction":"(T -> )"},"return_type":"","visibility":"Public","body":"(column(j)).each(&block)"}},{"id":"column(j)-instance-method","html_id":"column(j)-instance-method","name":"column","doc":"Returns column vector `j` of the Matrix as a Vector (starting at 0).\nRaises if the column doesn't exist.","summary":"<p>Returns column vector <code>j</code> of the Matrix as a Vector (starting at 0).</p>","abstract":false,"args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"args_string":"(j)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L359","def":{"name":"column","args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if j >= column_count || j < (-column_count)\n  raise(IndexError.new)\nend\ncol = Array(T).new(row_count) do |i|\n  @rows[i][j]\nend\nVector.elements(col, false)\n"}},{"id":"column?(j)-instance-method","html_id":"column?(j)-instance-method","name":"column?","doc":"Returns column vector `j` of the Matrix as a Vector (starting at 0).\nReturns nil if the column doesn't exist.","summary":"<p>Returns column vector <code>j</code> of the Matrix as a Vector (starting at 0).</p>","abstract":false,"args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"args_string":"(j)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L369","def":{"name":"column?","args":[{"name":"j","doc":null,"default_value":"","external_name":"j","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"begin\n  column(j)\nrescue IndexError\n  nil\nend"}},{"id":"column_count:Int32-instance-method","html_id":"column_count:Int32-instance-method","name":"column_count","doc":"Returns the number of columns.","summary":"<p>Returns the number of columns.</p>","abstract":false,"args":[],"args_string":" : Int32","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L337","def":{"name":"column_count","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Int32","visibility":"Public","body":"@column_count"}},{"id":"column_vectors-instance-method","html_id":"column_vectors-instance-method","name":"column_vectors","doc":"Returns an array of the column vectors of the matrix. See `Vector`.","summary":"<p>Returns an array of the column vectors of the matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L1401","def":{"name":"column_vectors","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Array.new(column_count) do |i|\n  column(i)\nend"}},{"id":"combine(*matrices,&block)-instance-method","html_id":"combine(*matrices,&amp;block)-instance-method","name":"combine","doc":"Create a matrix by combining matrices entrywise, using the given block\n\n```\nx = Matrix[[6, 6], [4, 4]]\ny = Matrix[[1, 2], [3, 4]]\nMatrix.combine(x, y) {|a, b| a - b}\n# => Matrix[[5, 4], [1, 0]]\n```","summary":"<p>Create a matrix by combining matrices entrywise, using the given block</p>","abstract":false,"args":[{"name":"matrices","doc":null,"default_value":"","external_name":"matrices","restriction":""}],"args_string":"(*matrices, &block)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L283","def":{"name":"combine","args":[{"name":"matrices","doc":null,"default_value":"","external_name":"matrices","restriction":""}],"double_splat":null,"splat_index":0,"yields":0,"block_arg":{"name":"block","doc":null,"default_value":"","external_name":"block","restriction":""},"return_type":"","visibility":"Public","body":"Matrix.combine(self, *matrices, &block)"}},{"id":"conj-instance-method","html_id":"conj-instance-method","name":"conj","doc":"Returns the conjugate of the matrix.\n\n```\nMatrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]]\n# => 1+2i   i  0\n#       1   2  3\nMatrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]].conj\n# => 1-2i  -i  0\n#       1   2  3\n```","summary":"<p>Returns the conjugate of the matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L1336","def":{"name":"conj","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if real?\nelse\n  raise(ArgumentError.new(\"Matrix#conj only works with real matrices (i.e. Matrix(Complex))\"))\nend\nmap(&.conj)\n"}},{"id":"determinant-instance-method","html_id":"determinant-instance-method","name":"determinant","doc":"Returns the determinant of the matrix.\n\nBeware that using Float values can yield erroneous results\nbecause of their lack of precision.\nConsider using exact types like Rational or BigDecimal instead.\n\n```\nMatrix[[7,6], [3,9]].determinant\n# => 45\n```","summary":"<p>Returns the determinant of the matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L1102","def":{"name":"determinant","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if square?\nelse\n  raise(ErrDimensionMismatch.new)\nend\nm = rows\ncase row_count\nwhen 0\n  +1\nwhen 1\n  +m[0][0]\nwhen 2\n  ((+m[0][0]) * m[1][1]) - (m[0][1] * m[1][0])\nwhen 3\n  m0, m1, m2 = m\n  (((((((+m0[0]) * m1[1]) * m2[2]) - ((m0[0] * m1[2]) * m2[1])) - ((m0[1] * m1[0]) * m2[2])) + ((m0[1] * m1[2]) * m2[0])) + ((m0[2] * m1[0]) * m2[1])) - ((m0[2] * m1[1]) * m2[0])\nwhen 4\n  m0, m1, m2, m3 = m\n  ((((((((((((((((((((((((((+m0[0]) * m1[1]) * m2[2]) * m3[3]) - (((m0[0] * m1[1]) * m2[3]) * m3[2])) - (((m0[0] * m1[2]) * m2[1]) * m3[3])) + (((m0[0] * m1[2]) * m2[3]) * m3[1])) + (((m0[0] * m1[3]) * m2[1]) * m3[2])) - (((m0[0] * m1[3]) * m2[2]) * m3[1])) - (((m0[1] * m1[0]) * m2[2]) * m3[3])) + (((m0[1] * m1[0]) * m2[3]) * m3[2])) + (((m0[1] * m1[2]) * m2[0]) * m3[3])) - (((m0[1] * m1[2]) * m2[3]) * m3[0])) - (((m0[1] * m1[3]) * m2[0]) * m3[2])) + (((m0[1] * m1[3]) * m2[2]) * m3[0])) + (((m0[2] * m1[0]) * m2[1]) * m3[3])) - (((m0[2] * m1[0]) * m2[3]) * m3[1])) - (((m0[2] * m1[1]) * m2[0]) * m3[3])) + (((m0[2] * m1[1]) * m2[3]) * m3[0])) + (((m0[2] * m1[3]) * m2[0]) * m3[1])) - (((m0[2] * m1[3]) * m2[1]) * m3[0])) - (((m0[3] * m1[0]) * m2[1]) * m3[2])) + (((m0[3] * m1[0]) * m2[2]) * m3[1])) + (((m0[3] * m1[1]) * m2[0]) * m3[2])) - (((m0[3] * m1[1]) * m2[2]) * m3[0])) - (((m0[3] * m1[2]) * m2[0]) * m3[1])) + (((m0[3] * m1[2]) * m2[1]) * m3[0])\nelse\n  determinant_bareiss\nend\n"}},{"id":"diagonal?-instance-method","html_id":"diagonal?-instance-method","name":"diagonal?","doc":"Returns `true` if this is a diagonal matrix.\n","summary":"<p>Returns <code>true</code> if this is a diagonal matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L720","def":{"name":"diagonal?","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if square?\nelse\n  return false\nend\nels = [] of T\neach(:off_diagonal) do |e|\n  els << e\nend\nels.all?(&.zero?)\n"}},{"id":"each(which=:all,&block:T->)-instance-method","html_id":"each(which=:all,&amp;block:T-&gt;)-instance-method","name":"each","doc":"Yields all elements of the matrix, starting with those of the first row,\nor returns an Enumerator if no block given.\nElements can be restricted by passing an argument:\n* :all (default): yields all elements\n* :diagonal: yields only elements on the diagonal\n* :off_diagonal: yields all elements except on the diagonal\n* :lower: yields only elements on or below the diagonal\n* :strict_lower: yields only elements below the diagonal\n* :strict_upper: yields only elements above the diagonal\n* :upper: yields only elements on or above the diagonal\n\n```\nMatrix[ [1,2], [3,4] ].each { |e| puts e }\n# => prints the numbers 1 to 4\nMatrix[ [1,2], [3,4] ].each(:strict_lower).to_a # => [3]\n```","summary":"<p>Yields all elements of the matrix, starting with those of the first row, or returns an Enumerator if no block given.</p>","abstract":false,"args":[{"name":"which","doc":null,"default_value":":all","external_name":"which","restriction":""}],"args_string":"(which = <span class=\"n\">:all</span>, &block : T -> )","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L403","def":{"name":"each","args":[{"name":"which","doc":null,"default_value":":all","external_name":"which","restriction":""}],"double_splat":null,"splat_index":null,"yields":1,"block_arg":{"name":"block","doc":null,"default_value":"","external_name":"block","restriction":"(T -> )"},"return_type":"","visibility":"Public","body":"last = column_count\ncase which.to_s\nwhen \"all\"\n  @rows.each do |row|\n    row.each(&block)\n  end\nwhen \"diagonal\"\n  @rows.each_with_index do |row, row_index|\n    yield row.fetch(row_index) do\n      return self\n    end\n  end\nwhen \"off_diagonal\"\n  @rows.each_with_index do |row, row_index|\n    column_count.times do |col_index|\n      if row_index == col_index\n      else\n        yield row[col_index]\n      end\n    end\n  end\nwhen \"lower\"\n  @rows.each_with_index do |row, row_index|\n    0.upto([row_index, last].min) do |col_index|\n      yield row[col_index]\n    end\n  end\nwhen \"strict_lower\"\n  @rows.each_with_index do |row, row_index|\n    [row_index, column_count].min.times do |col_index|\n      yield row[col_index]\n    end\n  end\nwhen \"strict_upper\"\n  @rows.each_with_index do |row, row_index|\n    (row_index + 1).upto(last - 1) do |col_index|\n      yield row[col_index]\n    end\n  end\nwhen \"upper\"\n  @rows.each_with_index do |row, row_index|\n    row_index.upto(last - 1) do |col_index|\n      yield row[col_index]\n    end\n  end\nelse\n  raise(ArgumentError.new(\"expected #{which.inspect} to be one of :all, :diagonal, :off_diagonal, :lower, :strict_lower, :strict_upper or :upper\"))\nend\n"}},{"id":"each_with_index(which=:all,&block:T,Int32,Int32->)-instance-method","html_id":"each_with_index(which=:all,&amp;block:T,Int32,Int32-&gt;)-instance-method","name":"each_with_index","doc":"Same as #each, but the row index and column index in addition to the element\n\n```\nMatrix[ [1,2], [3,4] ].each_with_index do |e, row, col|\nputs \"#{e} at #{row}, #{col}\"\nend\n# => Prints:\n#    1 at 0, 0\n#    2 at 0, 1\n#    3 at 1, 0\n#    4 at 1, 1\n```","summary":"<p>Same as #each, but the row index and column index in addition to the element</p>","abstract":false,"args":[{"name":"which","doc":null,"default_value":":all","external_name":"which","restriction":""}],"args_string":"(which = <span class=\"n\">:all</span>, &block : T, Int32, Int32 -> )","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L461","def":{"name":"each_with_index","args":[{"name":"which","doc":null,"default_value":":all","external_name":"which","restriction":""}],"double_splat":null,"splat_index":null,"yields":3,"block_arg":{"name":"block","doc":null,"default_value":"","external_name":"block","restriction":"(T, Int32, Int32 -> )"},"return_type":"","visibility":"Public","body":"last = column_count\ncase which.to_s\nwhen \"all\"\n  @rows.each_with_index do |row, row_index|\n    row.each_with_index do |e, col_index|\n      block.call(e, row_index, col_index)\n    end\n  end\nwhen \"diagonal\"\n  @rows.each_with_index do |row, row_index|\n    block.call(row.fetch(row_index) do\n      return self\n    end, row_index, row_index)\n  end\nwhen \"off_diagonal\"\n  @rows.each_with_index do |row, row_index|\n    column_count.times do |col_index|\n      block.call(row[col_index], row_index, col_index)\n    end\n  end\nwhen \"lower\"\n  @rows.each_with_index do |row, row_index|\n    0.upto([row_index, last].min) do |col_index|\n      block.call(row[col_index], row_index, col_index)\n    end\n  end\nwhen \"strict_lower\"\n  @rows.each_with_index do |row, row_index|\n    [row_index, column_count].min.times do |col_index|\n      block.call(row[col_index], row_index, col_index)\n    end\n  end\nwhen \"strict_upper\"\n  @rows.each_with_index do |row, row_index|\n    (row_index + 1).upto(last - 1) do |col_index|\n      block.call(row[col_index], row_index, col_index)\n    end\n  end\nwhen \"upper\"\n  @rows.each_with_index do |row, row_index|\n    row_index.upto(last - 1) do |col_index|\n      block.call(row[col_index], row_index, col_index)\n    end\n  end\nelse\n  raise(ArgumentError.new(\"expected #{which.inspect} to be one of :all, :diagonal, :off_diagonal, :lower, :strict_lower, :strict_upper or :upper\"))\nend\n"}},{"id":"eigensystem-instance-method","html_id":"eigensystem-instance-method","name":"eigensystem","doc":"Returns the Eigensystem of the matrix\nSee `EigenvalueDecomposition`.\n\nNOTE: Not working yet\n\n```\nm = Matrix[[1, 2], [3, 4]]\nv, d, v_inv = m.eigensystem\nd.diagonal? # => true\nv.inv == v_inv # => true\n(v * d * v_inv).round(5) == m # => true\n```","summary":"<p>Returns the Eigensystem of the matrix See <code><a href=\"../../Apatite/LinearAlgebra/Matrix/EigenvalueDecomposition.html\">EigenvalueDecomposition</a></code>.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L1300","def":{"name":"eigensystem","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"EigenvalueDecomposition.new(self)"}},{"id":"empty?-instance-method","html_id":"empty?-instance-method","name":"empty?","doc":"Returns true if this matrix is empty.","summary":"<p>Returns true if this matrix is empty.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L728","def":{"name":"empty?","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"(column_count == 0) || (row_count == 0)"}},{"id":"first_minor(row,column)-instance-method","html_id":"first_minor(row,column)-instance-method","name":"first_minor","doc":"Returns the submatrix obtained by deleting the specified row and column.\n\n```\nMatrix.diagonal(9, 5, -3, 4).first_minor(1, 2)\n# => [ 9, 0, 0,\n#      0, 0, 0,\n#      0, 0, 4 ]\n```","summary":"<p>Returns the submatrix obtained by deleting the specified row and column.</p>","abstract":false,"args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"","external_name":"column","restriction":""}],"args_string":"(row, column)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L608","def":{"name":"first_minor","args":[{"name":"row","doc":null,"default_value":"","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"","external_name":"column","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if empty?\n  raise(\"first_minor of empty matrix is not defined\")\nend\nif 0 <= row && row < row_count\nelse\n  raise(ArgumentError.new(\"invalid row (#{row.inspect} for 0..#{row_count - 1})\"))\nend\nif 0 <= column && column < column_count\nelse\n  raise(ArgumentError.new(\"invalid column (#{column.inspect} for 0..#{column_count - 1})\"))\nend\narrays = to_a\narrays.delete_at(row)\narrays.each do |array|\n  array.delete_at(column)\nend\nMatrix.new(arrays, column_count - 1)\n"}},{"id":"hadamard_product(m)-instance-method","html_id":"hadamard_product(m)-instance-method","name":"hadamard_product","doc":"Hadamard product\n\n```\nMatrix[[1,2], [3,4]].hadamard_product Matrix[[1,2], [3,2]]\n# => [ 1,  4,\n#      9,  8 ]\n```","summary":"<p>Hadamard product</p>","abstract":false,"args":[{"name":"m","doc":null,"default_value":"","external_name":"m","restriction":""}],"args_string":"(m)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L1022","def":{"name":"hadamard_product","args":[{"name":"m","doc":null,"default_value":"","external_name":"m","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"combine(m) do |a, b|\n  a * b\nend"}},{"id":"hermitian?-instance-method","html_id":"hermitian?-instance-method","name":"hermitian?","doc":"Returns `true` if this is an hermitian matrix.","summary":"<p>Returns <code>true</code> if this is an hermitian matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L733","def":{"name":"hermitian?","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if square?\nelse\n  return false\nend\nels = [] of Tuple(T, Int32, Int32)\neach_with_index(:upper) do |e, i, j|\n  els << {e, i, j}\nend\nels.all? do |e, row, col|\n  e == rows[col][row]\nend\n"}},{"id":"hstack(*matrices)-instance-method","html_id":"hstack(*matrices)-instance-method","name":"hstack","doc":"Returns a new matrix resulting by stacking horizontally\nthe receiver with the given matrices\n\n```\nx = Matrix[[1, 2], [3, 4]]\ny = Matrix[[5, 6], [7, 8]]\nx.hstack(y) # => Matrix[[1, 2, 5, 6], [3, 4, 7, 8]]\n```","summary":"<p>Returns a new matrix resulting by stacking horizontally the receiver with the given matrices</p>","abstract":false,"args":[{"name":"matrices","doc":null,"default_value":"","external_name":"matrices","restriction":""}],"args_string":"(*matrices)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L1184","def":{"name":"hstack","args":[{"name":"matrices","doc":null,"default_value":"","external_name":"matrices","restriction":""}],"double_splat":null,"splat_index":0,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"self.class.hstack(self, *matrices)"}},{"id":"imag-instance-method","html_id":"imag-instance-method","name":"imag","doc":"Returns the imaginary part of the matrix.\n\n```\nMatrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]]\n# => [ 1+2i,  i,  0,\n#         1,  2,  3 ]\nMatrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]].imag\n# => [ 2i,  i,  0,\n#       0,  0,  0 ]\n```","summary":"<p>Returns the imaginary part of the matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L1351","def":{"name":"imag","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if real?\nelse\n  raise(ArgumentError.new(\"Matrix#imag only works with real matrices (i.e. Matrix(Complex))\"))\nend\nmap(&.imag)\n"}},{"id":"index(i,selector=:all)-instance-method","html_id":"index(i,selector=:all)-instance-method","name":"index","doc":"The index method is specialized to return the index as {row, column}\nIt also accepts an optional `selector` argument, see `#each` for details.\n\n```\nMatrix[ [1,1], [1,1] ].index(1, :strict_lower)\n# => {1, 0}\n```","summary":"<p>The index method is specialized to return the index as {row, column} It also accepts an optional <code>selector</code> argument, see <code><a href=\"../../Apatite/LinearAlgebra/Matrix.html#each(which=:all,&block:T-%3E)-instance-method\">#each</a></code> for details.</p>","abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""},{"name":"selector","doc":null,"default_value":":all","external_name":"selector","restriction":""}],"args_string":"(i, selector = <span class=\"n\">:all</span>)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L518","def":{"name":"index","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""},{"name":"selector","doc":null,"default_value":":all","external_name":"selector","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"res = nil\neach_with_index(selector) do |e, row_index, col_index|\n  if e == i\n    res = {row_index, col_index}\n    next\n  end\nend\nres\n"}},{"id":"index(selector=:all,&block:T->Bool)-instance-method","html_id":"index(selector=:all,&amp;block:T-&gt;Bool)-instance-method","name":"index","doc":"Returns the index as {row, column}, using `&block` to filter the\nresult. It also accepts an optional `selector` argument, see\n`#each` for details.\n\n```\nMatrix[ [1,2], [3,4] ].index(&.even?)\n# => {0, 1}\n```","summary":"<p>Returns the index as {row, column}, using <code>&block</code> to filter the result.</p>","abstract":false,"args":[{"name":"selector","doc":null,"default_value":":all","external_name":"selector","restriction":""}],"args_string":"(selector = <span class=\"n\">:all</span>, &block : T -> Bool)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L537","def":{"name":"index","args":[{"name":"selector","doc":null,"default_value":":all","external_name":"selector","restriction":""}],"double_splat":null,"splat_index":null,"yields":1,"block_arg":{"name":"block","doc":null,"default_value":"","external_name":"block","restriction":"(T -> Bool)"},"return_type":"","visibility":"Public","body":"res = nil\neach_with_index(selector) do |e, row_index, col_index|\n  if block.call(e)\n    res = {row_index, col_index}\n    next\n  end\nend\nres\n"}},{"id":"inverse-instance-method","html_id":"inverse-instance-method","name":"inverse","doc":"Returns the inverse of the matrix.\n\nNOTE: Always returns a `Float64` regardless of `T`s type. To coerce\nback into an `Int`, use `#coerce`.\n\n```\nMatrix[[-1, -1], [0, -1]].inverse\n# => [ -1.0,  1.0,\n#       0.0, -1.0 ]\n```","summary":"<p>Returns the inverse of the matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L1036","def":{"name":"inverse","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if square?\nelse\n  raise(ErrDimensionMismatch.new)\nend\nlast = row_count - 1\na = self.coerce(Float64)\nm = Matrix(Float64).identity(row_count)\n0.upto(last) do |k|\n  i = k\n  akk = a[k, k].abs\n  (k + 1).upto(last) do |j|\n    v = a[j, k].abs\n    if v > akk\n      i = j\n      akk = v\n    end\n  end\n  if akk == 0\n    raise(ErrNotRegular.new)\n  end\n  if i != k\n    a.swap_rows(i, k)\n    m.swap_rows(i, k)\n  end\n  akk = a[k, k]\n  0.upto(last) do |ii|\n    if ii == k\n      next\n    end\n    q = a[ii, k] / akk\n    a[ii, k] = 0.0\n    (k + 1).upto(last) do |j|\n      __temp_24 = ii\n      __temp_25 = j\n      a[__temp_24, __temp_25] = a[__temp_24, __temp_25] - (a[k, j] * q)\n    end\n    0.upto(last) do |j|\n      __temp_27 = ii\n      __temp_28 = j\n      m[__temp_27, __temp_28] = m[__temp_27, __temp_28] - (m[k, j] * q)\n    end\n  end\n  (k + 1).upto(last) do |j|\n    a[k, j] = a[k, j] / akk\n  end\n  0.upto(last) do |j|\n    m[k, j] = m[k, j] / akk\n  end\nend\nm\n"}},{"id":"laplace_expansion(*,row=nil,column=nil)-instance-method","html_id":"laplace_expansion(*,row=nil,column=nil)-instance-method","name":"laplace_expansion","doc":"Returns the Laplace expansion along given row or column.\n\n```\nMatrix[[7,6], [3,9]].laplace_expansion(column: 1)\n# => 45\n\nMatrix[[Vector[1, 0], Vector[0, 1]], [2, 3]].laplace_expansion(row: 0)\n# => Vector[3, -2]\n```","summary":"<p>Returns the Laplace expansion along given row or column.</p>","abstract":false,"args":[{"name":"","doc":null,"default_value":"","external_name":"","restriction":""},{"name":"row","doc":null,"default_value":"nil","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"nil","external_name":"column","restriction":""}],"args_string":"(*, row = <span class=\"n\">nil</span>, column = <span class=\"n\">nil</span>)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L665","def":{"name":"laplace_expansion","args":[{"name":"","doc":null,"default_value":"","external_name":"","restriction":""},{"name":"row","doc":null,"default_value":"nil","external_name":"row","restriction":""},{"name":"column","doc":null,"default_value":"nil","external_name":"column","restriction":""}],"double_splat":null,"splat_index":0,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"num = row || column\nif (!num) || (row && column)\n  raise(ArgumentError.new(\"exactly one the row or column arguments must be specified\"))\nend\nif square?\nelse\n  raise(ErrDimensionMismatch.new)\nend\nif empty?\n  raise(\"laplace_expansion of empty matrix is not defined\")\nend\nif 0 <= num && num < row_count\nelse\n  raise(ArgumentError.new(\"invalid num (#{num.inspect} for 0..#{row_count - 1})\"))\nend\nif row\n  (row(num)).map_with_index do |e, k|\n    e * (cofactor(num, k))\n  end.reduce(&.+)\nelse\n  (column(num)).map_with_index do |e, k|\n    e * (cofactor(k, num))\n  end.reduce(&.+)\nend\n"}},{"id":"lower_triangular?-instance-method","html_id":"lower_triangular?-instance-method","name":"lower_triangular?","doc":"Returns true if this matrix is a lower triangular matrix.","summary":"<p>Returns true if this matrix is a lower triangular matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L743","def":{"name":"lower_triangular?","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"els = [] of T\neach(:strict_upper) do |e|\n  els << e\nend\nels.all?(&.zero?)\n"}},{"id":"lup-instance-method","html_id":"lup-instance-method","name":"lup","doc":"Returns the LUP decomposition of the matrix\nSee +LUPDecomposition+.\n\nNOTE: Not working yet\n\n```\na = Matrix[[1, 2], [3, 4]]\nl, u, p = a.lup\nl.lower_triangular? # => true\nu.upper_triangular? # => true\np.permutation?      # => true\nl * u == p * a      # => true\na.lup.solve([2, 5]) # => Vector[(1/1), (1/2)]\n```","summary":"<p>Returns the LUP decomposition of the matrix See +LUPDecomposition+.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L1318","def":{"name":"lup","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"LUPDecomposition.new(self)"}},{"id":"map(&block:T->T)-instance-method","html_id":"map(&amp;block:T-&gt;T)-instance-method","name":"map","doc":"Returns a Matrix that is the result of iteration of the given block\nover all elements in the matrix.","summary":"<p>Returns a Matrix that is the result of iteration of the given block over all elements in the matrix.</p>","abstract":false,"args":[],"args_string":"(&block : T -> T)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L382","def":{"name":"map","args":[],"double_splat":null,"splat_index":null,"yields":1,"block_arg":{"name":"block","doc":null,"default_value":"","external_name":"block","restriction":"(T -> T)"},"return_type":"","visibility":"Public","body":"rows = @rows.map do |row|\n  row.map(&block)\nend\nMatrix.new(rows, column_count)\n"}},{"id":"minor(from_row:Int,nrows:Int,from_col:Int,ncols:Int)-instance-method","html_id":"minor(from_row:Int,nrows:Int,from_col:Int,ncols:Int)-instance-method","name":"minor","doc":"Returns a section of the Matrix.\n\n```\nMatrix.diagonal(9, 5, -3).minor(0, 2, 0, 3)\n# => [ 9, 0, 0,\n#      0, 5, 0 ]\n```","summary":"<p>Returns a section of the Matrix.</p>","abstract":false,"args":[{"name":"from_row","doc":null,"default_value":"","external_name":"from_row","restriction":"Int"},{"name":"nrows","doc":null,"default_value":"","external_name":"nrows","restriction":"Int"},{"name":"from_col","doc":null,"default_value":"","external_name":"from_col","restriction":"Int"},{"name":"ncols","doc":null,"default_value":"","external_name":"ncols","restriction":"Int"}],"args_string":"(from_row : Int, nrows : Int, from_col : Int, ncols : Int)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L586","def":{"name":"minor","args":[{"name":"from_row","doc":null,"default_value":"","external_name":"from_row","restriction":"Int"},{"name":"nrows","doc":null,"default_value":"","external_name":"nrows","restriction":"Int"},{"name":"from_col","doc":null,"default_value":"","external_name":"from_col","restriction":"Int"},{"name":"ncols","doc":null,"default_value":"","external_name":"ncols","restriction":"Int"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if nrows < 0 || ncols < 0\n  return nil\nend\nif from_row < 0\n  from_row = from_row + row_count\nend\nif from_col < 0\n  from_col = from_col + column_count\nend\nif ((from_row > row_count || from_col > column_count) || from_row < 0) || from_col < 0\n  return nil\nend\nrows = @rows[from_row, nrows].map do |row|\n  row[from_col, ncols]\nend\nMatrix.new(rows, [column_count - from_col, ncols].min)\n"}},{"id":"minor(row_range:Range,col_range:Range)-instance-method","html_id":"minor(row_range:Range,col_range:Range)-instance-method","name":"minor","doc":"Returns a section of the Matrix.\n\n```\nMatrix.diagonal(9, 5, -3).minor(0..1, 0..2)\n# => [ 9, 0, 0,\n#      0, 5, 0 ]\n```","summary":"<p>Returns a section of the Matrix.</p>","abstract":false,"args":[{"name":"row_range","doc":null,"default_value":"","external_name":"row_range","restriction":"Range"},{"name":"col_range","doc":null,"default_value":"","external_name":"col_range","restriction":"Range"}],"args_string":"(row_range : Range, col_range : Range)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L555","def":{"name":"minor","args":[{"name":"row_range","doc":null,"default_value":"","external_name":"row_range","restriction":"Range"},{"name":"col_range","doc":null,"default_value":"","external_name":"col_range","restriction":"Range"}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"from_row = row_range.first\nif from_row < 0\n  from_row = from_row + row_count\nend\nto_row = row_range.end\nif to_row < 0\n  to_row = to_row + row_count\nend\nif row_range.excludes_end?\nelse\n  to_row = to_row + 1\nend\nsize_row = to_row - from_row\nfrom_col = col_range.first\nif from_col < 0\n  from_col = from_col + column_count\nend\nto_col = col_range.end\nif to_col < 0\n  to_col = to_col + column_count\nend\nif col_range.excludes_end?\nelse\n  to_col = to_col + 1\nend\nsize_col = to_col - from_col\nif ((from_row > row_count || from_col > column_count) || from_row < 0) || from_col < 0\n  return nil\nend\nrows = @rows[from_row, size_row].map do |row|\n  row[from_col, size_col]\nend\nMatrix.new(rows, [column_count - from_col, size_col].min)\n"}},{"id":"normal?-instance-method","html_id":"normal?-instance-method","name":"normal?","doc":"Returns `true` if this is a normal matrix.\n\n```\nMatrix[[1, 1, 0], [0, 1, 1], [1, 0, 1]].normal?\n# => true\n```","summary":"<p>Returns <code>true</code> if this is a normal matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L755","def":{"name":"normal?","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if square?\nelse\n  return false\nend\nrows.each_with_index do |row_i, i|\n  rows.each_with_index do |row_j, j|\n    s = 0\n    rows.each_with_index do |row_k, k|\n      s = s + ((row_i[k] * row_j[k]) - (row_k[i] * row_k[j]))\n    end\n    if s == 0\n    else\n      return false\n    end\n  end\nend\ntrue\n"}},{"id":"orthogonal?-instance-method","html_id":"orthogonal?-instance-method","name":"orthogonal?","doc":"Returns `true` if this is an orthogonal matrix\n\n```\nMatrix[[1, 0], [0, 1]].orthogonal?\n# => true\n```","summary":"<p>Returns <code>true</code> if this is an orthogonal matrix</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L775","def":{"name":"orthogonal?","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if square?\nelse\n  return false\nend\nrows.each_with_index do |row, i|\n  column_count.times do |j|\n    s = 0\n    row_count.times do |k|\n      s = s + (row[k] * rows[k][j])\n    end\n    if s == (i == j ? 1 : 0)\n    else\n      return false\n    end\n  end\nend\ntrue\n"}},{"id":"permutation?-instance-method","html_id":"permutation?-instance-method","name":"permutation?","doc":"Returns `true` if this is a permutation matrix\n\n```\nMatrix[[1, 0], [0, 1]].permutation?\n# => true\n```","summary":"<p>Returns <code>true</code> if this is a permutation matrix</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L795","def":{"name":"permutation?","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if square?\nelse\n  return false\nend\ncols = Array.new(column_count, false)\nrows.each_with_index do |row, i|\n  found = false\n  row.each_with_index do |e, j|\n    if e == 1\n      if found || cols[j]\n        return false\n      end\n      found = cols[j] = true\n    else\n      if e != 0\n        return false\n      end\n    end\n  end\n  if found\n  else\n    return false\n  end\nend\ntrue\n"}},{"id":"pretty_print(pp):Nil-instance-method","html_id":"pretty_print(pp):Nil-instance-method","name":"pretty_print","doc":null,"summary":null,"abstract":false,"args":[{"name":"pp","doc":null,"default_value":"","external_name":"pp","restriction":""}],"args_string":"(pp) : Nil","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L1447","def":{"name":"pretty_print","args":[{"name":"pp","doc":null,"default_value":"","external_name":"pp","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"Nil","visibility":"Public","body":"pp.group(1, \"[\", \"]\") do\n  self.rows.each_with_index do |elem, i|\n    if i > 0\n      pp.comma\n    end\n    elem.pretty_print(pp)\n  end\nend"}},{"id":"rank-instance-method","html_id":"rank-instance-method","name":"rank","doc":"Returns the rank of the matrix.\n\nBeware that using Float values can yield erroneous results\nbecause of their lack of precision.\nConsider using exact types like Rational or BigDecimal instead.\n\n```\nMatrix[[7,6], [3,9]].rank\n# => 2\n```","summary":"<p>Returns the rank of the matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L1198","def":{"name":"rank","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"a = to_a\nlast_column = column_count - 1\nlast_row = row_count - 1\npivot_row = 0\nprevious_pivot = 1\n0.upto(last_column) do |k|\n  switch_row = (pivot_row..last_row).find do |row|\n    a[row][k] != 0\n  end\n  if switch_row\n    if pivot_row == switch_row\n    else\n      a[switch_row], a[pivot_row] = a[pivot_row], a[switch_row]\n    end\n    pivot = a[pivot_row][k]\n    (pivot_row + 1).upto(last_row) do |i|\n      ai = a[i]\n      (k + 1).upto(last_column) do |j|\n        ai[j] = ((pivot * ai[j]) - (ai[k] * a[pivot_row][j])) / previous_pivot\n      end\n    end\n    pivot_row = pivot_row + 1\n    previous_pivot = pivot\n  end\nend\npivot_row\n"}},{"id":"real-instance-method","html_id":"real-instance-method","name":"real","doc":"Returns the real part of the matrix.\n\n```\nMatrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]]\n# => [ 1+2i,  i,  0,\n#         1,  2,  3 ]\nMatrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]].real\n# => [ 1,  0,  0,\n#      1,  2,  3 ]\n```","summary":"<p>Returns the real part of the matrix.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L1366","def":{"name":"real","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if real?\nelse\n  raise(ArgumentError.new(\"Matrix#real only works with real matrices (i.e. Matrix(Complex))\"))\nend\nmap(&.real)\n"}},{"id":"real?-instance-method","html_id":"real?-instance-method","name":"real?","doc":"Returns `true` if this matrix contains real numbers,\ni.e. not `Complex`.\n\n```\nrequire \"complex\"\nMatrix[[Complex.new(1, 0)], [Complex.new(0, 1)]].real?\n# => false\n```","summary":"<p>Returns <code>true</code> if this matrix contains real numbers, i.e.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L821","def":{"name":"real?","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"!(T.to_s == \"Complex\")"}},{"id":"rect-instance-method","html_id":"rect-instance-method","name":"rect","doc":"Returns an array containing matrices corresponding to the real and imaginary\nparts of the matrix\n\n```\nm.rect == [m.real, m.imag]\n# ==> true for all matrices m\n```","summary":"<p>Returns an array containing matrices corresponding to the real and imaginary parts of the matrix</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L1378","def":{"name":"rect","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if real?\nelse\n  raise(ArgumentError.new(\"Matrix#real only works with real matrices (i.e. Matrix(Complex))\"))\nend\n[real, imag]\n"}},{"id":"regular?-instance-method","html_id":"regular?-instance-method","name":"regular?","doc":"Returns `true` if this is a regular (i.e. non-singular) matrix.","summary":"<p>Returns <code>true</code> if this is a regular (i.e.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L826","def":{"name":"regular?","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"!singular?"}},{"id":"round(n=0)-instance-method","html_id":"round(n=0)-instance-method","name":"round","doc":"Returns a matrix with entries rounded to the given precision\n(see `Float#round`)","summary":"<p>Returns a matrix with entries rounded to the given precision (see <code>Float#round</code>)</p>","abstract":false,"args":[{"name":"n","doc":null,"default_value":"0","external_name":"n","restriction":""}],"args_string":"(n = <span class=\"n\">0</span>)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L1228","def":{"name":"round","args":[{"name":"n","doc":null,"default_value":"0","external_name":"n","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"map do |e|\n  e.round(n)\nend"}},{"id":"row(i)-instance-method","html_id":"row(i)-instance-method","name":"row","doc":"Returns row vector number `i` of the Matrix as a Vector (starting\nat 0 like a good boy). Raises if the row doesn't exist.","summary":"<p>Returns row vector number <code>i</code> of the Matrix as a Vector (starting at 0 like a good boy).</p>","abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"args_string":"(i)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L339","def":{"name":"row","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"if i >= row_count || i < (-row_count)\n  raise(IndexError.new)\nend\nVector.elements(self[i])\n"}},{"id":"row(i,&block:Vector->)-instance-method","html_id":"row(i,&amp;block:Vector-&gt;)-instance-method","name":"row","doc":"Returns a block which yields every Vector in the row (starting at 0).","summary":"<p>Returns a block which yields every Vector in the row (starting at 0).</p>","abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"args_string":"(i, &block : Vector -> )","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L345","def":{"name":"row","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"double_splat":null,"splat_index":null,"yields":1,"block_arg":{"name":"block","doc":null,"default_value":"","external_name":"block","restriction":"(Vector -> )"},"return_type":"","visibility":"Public","body":"(row(i)).each(&block)"}},{"id":"row?(i)-instance-method","html_id":"row?(i)-instance-method","name":"row?","doc":"Returns row vector number `i` of the Matrix as a Vector (starting\nat 0 like a good boy). Returns nil if the row doesn't exist.","summary":"<p>Returns row vector number <code>i</code> of the Matrix as a Vector (starting at 0 like a good boy).</p>","abstract":false,"args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"args_string":"(i)","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L351","def":{"name":"row?","args":[{"name":"i","doc":null,"default_value":"","external_name":"i","restriction":""}],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"begin\n  row(i)\nrescue IndexError\n  nil\nend"}},{"id":"row_count-instance-method","html_id":"row_count-instance-method","name":"row_count","doc":"Returns the number of rows.","summary":"<p>Returns the number of rows.</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/linear_algebra/matrix.cr#L330","def":{"name":"row_count","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"@rows.size"}},{"id":"row_vectors-instance-method","html_id":"row_vectors-instance-method","name":"row_vectors","doc":"Returns an array of the row vectors of the matrix. 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`Array` is an ordered, integer-indexed collection of objects of type T.\n\nArray indexing starts at 0. A negative index is assumed to be\nrelative to the end of the array: -1 indicates the last element,\n-2 is the next to last element, and so on.\n\nAn `Array` can be created using the usual `new` method (several are provided), or with an array literal:\n\n```\nArray(Int32).new  # => []\n[1, 2, 3]         # Array(Int32)\n[1, \"hello\", 'x'] # Array(Int32 | String | Char)\n```\n\nAn `Array` can have mixed types, meaning T will be a union of types, but these are determined\nwhen the array is created, either by specifying T or by using an array literal. In the latter\ncase, T will be set to the union of the array literal elements' types.\n\nWhen creating an empty array you must always specify T:\n\n```\n[] of Int32 # same as Array(Int32)\n[]          # syntax error\n```\n\nAn `Array` is implemented using an internal buffer of some capacity\nand is reallocated when elements are pushed to it when more capacity\nis needed. This is normally known as a [dynamic array](http://en.wikipedia.org/wiki/Dynamic_array).\n\nYou can use a special array literal syntax with other types too, as long as they define an argless\n`new` method and a `<<` method. `Set` is one such type:\n\n```\nset = Set{1, 2, 3} # => Set{1, 2, 3}\nset.class          # => Set(Int32)\n```\n\nThe above is the same as this:\n\n```\nset = Set(typeof(1, 2, 3)).new\nset << 1\nset << 2\nset << 3\n```","summary":"<p>An <code><a href=\"Array.html\">Array</a></code> is an ordered, integer-indexed collection of objects of type T.</p>","class_methods":[],"constructors":[],"instance_methods":[{"id":"all?-instance-method","html_id":"all?-instance-method","name":"all?","doc":"Tests whether all elements evaluate to true","summary":"<p>Tests whether all elements evaluate to true</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/core_ext/array.cr#L3","def":{"name":"all?","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"each do |i|\n  if (!(!i)) == false\n    return false\n  end\nend\ntrue\n"}},{"id":"any?-instance-method","html_id":"any?-instance-method","name":"any?","doc":"Tests whether any of the elements evaluate to true","summary":"<p>Tests whether any of the elements evaluate to true</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/core_ext/array.cr#L11","def":{"name":"any?","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"each do |i|\n  if (!(!i)) == true\n    return true\n  end\nend\nfalse\n"}},{"id":"shape-instance-method","html_id":"shape-instance-method","name":"shape","doc":"Get the array's dimensions","summary":"<p>Get the array's dimensions</p>","abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/core_ext/array.cr#L19","def":{"name":"shape","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"max = max_by do |i|\n  i.is_a?(Array) ? i.size : i\nend\nmax.is_a?(Array) ? [size, max.size] : [max]\n"}},{"id":"to_vec-instance-method","html_id":"to_vec-instance-method","name":"to_vec","doc":null,"summary":null,"abstract":false,"args":[],"args_string":"","source_link":"https://github.com/watzon/apatite/blob/c19b317dcdeac142e8bda3c957a21679d1e62a01/src/apatite/core_ext/array.cr#L24","def":{"name":"to_vec","args":[],"double_splat":null,"splat_index":null,"yields":null,"block_arg":null,"return_type":"","visibility":"Public","body":"Apatite::Vector.create(self)"}}],"macros":[],"types":[]}]}})