[{"name":"Matrix","comment":" A module for Matrix\n\n\n# Types\n\n@docs Matrix\n@docs RowVector\n\n@docs addRealMatrices\n@docs addComplexMatrices\n@docs sumRealMatrices\n@docs sumComplexMatrices\n@docs map\n@docs equal\n@docs transpose\n@docs conjugate\n@docs adjoint\n@docs apply\n@docs liftA2\n@docs multiplyComplexMatrices\n@docs multiplyRealMatrices\n@docs identityMatrix\n\n","unions":[{"name":"Matrix","comment":" Matrix type\n","args":["a"],"cases":[["Matrix",["List.List (Matrix.RowVector a)"]]]},{"name":"RowVector","comment":" Row Vector\n","args":["a"],"cases":[["RowVector",["Vector.Vector a"]]]}],"aliases":[],"values":[{"name":"addComplexMatrices","comment":" Add two Complex Matrices together\n","type":"Matrix.Matrix (ComplexNumbers.ComplexNumberCartesian number) -> Matrix.Matrix (ComplexNumbers.ComplexNumberCartesian number) -> Matrix.Matrix (ComplexNumbers.ComplexNumberCartesian number)"},{"name":"addRealMatrices","comment":" Add two Real Matrices together\n","type":"Matrix.Matrix number -> Matrix.Matrix number -> Matrix.Matrix number"},{"name":"adjoint","comment":" Perform the adjoint operation on a Complex Numbered Matrix\n","type":"Matrix.Matrix (ComplexNumbers.ComplexNumberCartesian number) -> Matrix.Matrix (ComplexNumbers.ComplexNumberCartesian number)"},{"name":"apply","comment":" Apply for Matrix\n","type":"Matrix.Matrix (a -> b) -> Matrix.Matrix a -> Matrix.Matrix b"},{"name":"conjugate","comment":" Take the complex conjugate of a Complex Numbered Matrix\n","type":"Matrix.Matrix (ComplexNumbers.ComplexNumberCartesian number) -> Matrix.Matrix (ComplexNumbers.ComplexNumberCartesian number)"},{"name":"equal","comment":" Compare two Matrices for equality\n","type":"(a -> a -> Basics.Bool) -> Matrix.Matrix a -> Matrix.Matrix a -> Basics.Bool"},{"name":"identityMatrix","comment":" Create Identity Matrix with n dimension\n","type":"Basics.Int -> Matrix.Matrix Basics.Int"},{"name":"liftA2","comment":" Lift a function to work on Matrix\n","type":"(a -> b -> c) -> Matrix.Matrix a -> Matrix.Matrix b -> Matrix.Matrix c"},{"name":"map","comment":" Map over a Matrix\n","type":"(a -> b) -> Matrix.Matrix a -> Matrix.Matrix b"},{"name":"multiplyComplexMatrices","comment":" Matrix Matrix multiplication for a Complex Numbered Matrix\n","type":"Matrix.Matrix (a -> b) -> Matrix.Matrix a -> Matrix.Matrix b"},{"name":"multiplyRealMatrices","comment":" Matrix Matrix multiplication for a Real Numbered Matrix\n","type":"Matrix.Matrix (Vector.Vector number) -> Matrix.Matrix (Vector.Vector number) -> Matrix.Matrix number"},{"name":"sumComplexMatrices","comment":" Monoidally add two Complex numbered Matrices together\n","type":"Matrix.Matrix (ComplexNumbers.ComplexNumberCartesian number) -> Monoid.Monoid (Matrix.Matrix (ComplexNumbers.ComplexNumberCartesian number))"},{"name":"sumRealMatrices","comment":" Monoidally add two Real numbered Matrices together\n","type":"Matrix.Matrix number -> Monoid.Monoid (Matrix.Matrix number)"},{"name":"transpose","comment":" Transpose a Matrix\n","type":"Matrix.Matrix a -> Matrix.Matrix a"}],"binops":[]},{"name":"Vector","comment":" A module for Vectors\n\n\n# Types\n\n@docs Vector\n\n@docs addComplexVectors\n@docs addRealVectors\n@docs map\n@docs multiplyRealVectors\n@docs multiplyComplexVectors\n@docs equal\n@docs sumEmpty\n@docs sumReal\n@docs sumComplex\n@docs apply\n@docs liftA2\n@docs foldl\n@docs realVectorDotProduct\n@docs complexVectorDotProduct\n@docs concat\n\n","unions":[{"name":"Vector","comment":" Vector type\n","args":["a"],"cases":[["Vector",["List.List a"]]]}],"aliases":[],"values":[{"name":"addComplexVectors","comment":" Add Complex Vectors together\n","type":"Vector.Vector (ComplexNumbers.ComplexNumberCartesian number) -> Vector.Vector (ComplexNumbers.ComplexNumberCartesian number) -> Vector.Vector (ComplexNumbers.ComplexNumberCartesian number)"},{"name":"addRealVectors","comment":" Add Real Vectors together\n","type":"Vector.Vector number -> Vector.Vector number -> Vector.Vector number"},{"name":"apply","comment":" Apply for Vector\n","type":"Vector.Vector (a -> b) -> Vector.Vector a -> Vector.Vector b"},{"name":"complexVectorDotProduct","comment":" Dot product on two Complex Numbered Vectors\n","type":"Vector.Vector (ComplexNumbers.ComplexNumberCartesian number) -> Vector.Vector (ComplexNumbers.ComplexNumberCartesian number) -> ComplexNumbers.ComplexNumberCartesian number"},{"name":"concat","comment":" Concat two Vectors together\n","type":"Vector.Vector a -> Vector.Vector a -> Vector.Vector a"},{"name":"equal","comment":" Compare two Vectors for equality\n","type":"(a -> a -> Basics.Bool) -> Vector.Vector a -> Vector.Vector a -> Basics.Bool"},{"name":"foldl","comment":" Left fold over a Vector\n","type":"(a -> b -> b) -> b -> Vector.Vector a -> b"},{"name":"liftA2","comment":" Lift a binary function to work with Vectors\n","type":"(a -> b -> c) -> Vector.Vector a -> Vector.Vector b -> Vector.Vector c"},{"name":"map","comment":" Map over a vector\n","type":"(a -> b) -> Vector.Vector a -> Vector.Vector b"},{"name":"multiplyComplexVectors","comment":" Multiply two Complex Vectors together\n","type":"Vector.Vector (ComplexNumbers.ComplexNumberCartesian number) -> Vector.Vector (ComplexNumbers.ComplexNumberCartesian number) -> Vector.Vector (ComplexNumbers.ComplexNumberCartesian number)"},{"name":"multiplyRealVectors","comment":" Multiply two Real Vectors together\n","type":"Vector.Vector number -> Vector.Vector number -> Vector.Vector number"},{"name":"realVectorDotProduct","comment":" Dot product on two Real Numbered Vectors\n","type":"Vector.Vector number -> Vector.Vector number -> number"},{"name":"sumComplex","comment":" Monoidally add Complex Vectors together\n","type":"List.List (ComplexNumbers.ComplexNumberCartesian number) -> Monoid.Monoid (Vector.Vector (ComplexNumbers.ComplexNumberCartesian number))"},{"name":"sumEmpty","comment":" Monoid empty for Vector\n","type":"List.List a -> Vector.Vector a"},{"name":"sumReal","comment":" Monoidally add Real Vectors together\n","type":"List.List number -> Monoid.Monoid (Vector.Vector number)"}],"binops":[]}]