Geom2D.CubicBezier.Numeric

Some numerical computations used by the cubic bezier functions

Documentation

sign :: (Ord a, Num a1, Num a) => a -> a1

quadraticRoot :: Double -> Double -> Double -> [Double]

quadraticRoot a b c find the real roots of the quadratic equation a x^2 + b x + c = 0. It will return one, two or zero roots.

solveLinear2x2 :: (Eq a, Fractional a) => a -> a -> a -> a -> a -> a -> Maybe (a, a)

solveLinear2x2 a b c d e f solves the linear equation with two variables (x and y) and two systems:

a x + b y + c = 0
d x + e y + f = 0

Returns Nothing if no solution is found.

data SparseMatrix a

Constructors

SparseMatrix (Vector Int) (Vector (Int, Int)) (Matrix a)

makeSparse

Arguments

:: Unbox a

=> Vector Int

The column index of the first element of each row. Should be ascending in order.

-> Matrix a

The adjacent coefficients in each row

-> SparseMatrix a

A sparse matrix.

sparseRanges :: Vector Int -> Int -> Int -> Vector (Int, Int)

lsqMatrix

Arguments

:: (Num a, Unbox a)

=> SparseMatrix a

The input system.

-> Matrix a

The resulting symmetric matrix as a sparse matrix. The first element of each row is the element on the diagonal.

Given a rectangular matrix M, calculate the symmetric square matrix MᵀM which can be used to find a least squares solution to the overconstrained system.

addMatrix :: (Num a, Unbox a) => Matrix a -> Matrix a -> Matrix a

addVec :: (Num a, Unbox a) => Vector a -> Vector a -> Vector a

sparseMulT :: (Num a, Unbox a) => Vector a -> SparseMatrix a -> Vector a

Multiply the vector by the transpose of the sparse matrix.

sparseMul :: (Num a, Unbox a) => SparseMatrix a -> Vector a -> Vector a

Sparse matrix * vector multiplication.

decompLDL :: (Fractional a, Unbox a) => Matrix a -> Matrix a

LDL* decomposition of the sparse hermitian matrix. The first element of each row is the diagonal component of the D matrix. The following elements are the elements next to the diagonal in the L* matrix (the diagonal components in L* are 1). For efficiency it mutates the matrix inplace.

solveLDL :: (Fractional a, Unbox a) => Matrix a -> Vector a -> Vector a

lsqSolve

Arguments

:: (Fractional a, Unbox a)

=> SparseMatrix a

sparse matrix

-> Vector a

Right hand side vector.

-> Vector a

Solution vector

lsqSolve rowStart M y Find a least squares solution x to the system xM = y.

lsqSolveDist

Arguments

:: (Fractional a, Unbox a)

=> SparseMatrix (a, a)

sparse matrix

-> Vector (a, a)

Right hand side vector.

-> Vector a

Solution vector

lsqSolveDist rowStart M y Find a least squares solution of the distance between the points.