A module for Square Matrix
Square Matrix type
{ matrixSpace : MatrixSpace a
, innerProduct : SquareMatrix a -> SquareMatrix a -> Result String a
, norm : SquareMatrix a -> Result String (Real Basics.Float)
, distance : SquareMatrix a -> SquareMatrix a -> Result String (Real Basics.Float)
}
Type to represent an Inner Product Space
zeroSquareMatrix : Field a -> Basics.Int -> SquareMatrix a
Create square Matrix with n dimension filled with zeros
realMatrixInnerProductSpace : InnerProductSpace (Real Basics.Float)
Real Numbered Inner Product Space for Matrix
complexMatrixInnerProductSpace : InnerProductSpace (ComplexNumbers.ComplexNumber Basics.Float)
Complex Numbered Inner Product Space for Matrix
empty : SquareMatrix a
Monoid empty for SquareMatrix
createMatrixFromColumnVectors : List (ColumnVector a) -> SquareMatrix a
Create a Matrix from a list of Column Vectors
identity : Field a -> Basics.Int -> SquareMatrix a
Create Square Identity Matrix with n dimension
dimension : SquareMatrix a -> Basics.Int
Dimension of the matrix
isSquare : Matrix a -> Result String (Matrix a)
Determine whether a matirx is square
normReal : SquareMatrix (Real Basics.Float) -> Result String (Real Basics.Float)
Calculate the norm of a Matrix
normComplex : SquareMatrix (ComplexNumbers.ComplexNumber Basics.Float) -> Result String (Real Basics.Float)
Calculate the norm of a Matrix
distanceReal : SquareMatrix (Real Basics.Float) -> SquareMatrix (Real Basics.Float) -> Result String (Real Basics.Float)
Calculate distance between two vectors
isRightStochastic : SquareMatrix (Real Basics.Float) -> Result String (SquareMatrix (Real Basics.Float))
Predicate if matrix is right stochastic
isLeftStochastic : SquareMatrix (Real Basics.Float) -> Result String (SquareMatrix (Real Basics.Float))
Predicate if matrix is left stochastic
getDiagonalProduct : Field a -> SquareMatrix a -> Maybe a
Get the Product of the diagonal of a Matrix
subMatrix : Basics.Int -> Basics.Int -> Basics.Int -> Basics.Int -> SquareMatrix a -> SquareMatrix a
Calculate the submatrix given a starting and ending row and column index
transpose : SquareMatrix a -> SquareMatrix a
Transpose a Matrix
all : (a -> Basics.Bool) -> SquareMatrix a -> Basics.Bool
Predicate to determine if all values in the matric satisfy the given predicate
scalarMultiplication : Field a -> a -> SquareMatrix a -> SquareMatrix a
Scalar multiplication over a Square Matrix
adjoint : SquareMatrix (ComplexNumbers.ComplexNumber number) -> SquareMatrix (ComplexNumbers.ComplexNumber number)
Perform the adjoint operation on a Complex Numbered Matrix
map : (a -> b) -> SquareMatrix a -> SquareMatrix b
Map over a Matrix
dotProduct : RowVector.InnerProductSpace a -> SquareMatrix a -> SquareMatrix a -> Result String a
Calculate the dot product of two Matricies
multiply : RowVector.InnerProductSpace a -> SquareMatrix a -> SquareMatrix a -> SquareMatrix a
Square Matrix Square Matrix multiplication
multiplyIfCan : RowVector.InnerProductSpace a -> SquareMatrix a -> SquareMatrix a -> Result String (SquareMatrix a)
Square Matrix Square Matrix multiplication
multiplyMatrixVector : RowVector.InnerProductSpace a -> SquareMatrix a -> ColumnVector a -> Result String (ColumnVector a)
Multiply a ColumnVector by a Matrix
add : Field a -> SquareMatrix a -> SquareMatrix a -> SquareMatrix a
Add two Square Matrices together
subtract : Field a -> SquareMatrix a -> SquareMatrix a -> SquareMatrix a
Subtract two Square Matrices
getAt : ( Basics.Int, Basics.Int ) -> SquareMatrix a -> Maybe a
Get the value in a matrix at the specified row and column
setAt : ( Basics.Int, Basics.Int ) -> a -> SquareMatrix a -> SquareMatrix a
Set the value in a Square Matrix at the specified row and column
appendHorizontal : SquareMatrix a -> SquareMatrix a -> SquareMatrix a
Append Matricies together horizontally
equal : (a -> a -> Basics.Bool) -> Typeclasses.Classes.Equality.Equality (SquareMatrix a)
Compare two matricies using comparator
equalImplementation : (a -> a -> Basics.Bool) -> SquareMatrix a -> SquareMatrix a -> Basics.Bool
Compare two Matrices for equality
gaussJordan : RowVector.VectorSpace a -> SquareMatrix a -> SquareMatrix a
Function composition of Gaussian Elimination and Jordan Elimination
upperTriangle : RowVector.VectorSpace a -> SquareMatrix a -> SquareMatrix a
Put a matrix into Upper Triangular Form