| Safe Haskell | Safe |
|---|---|
| Language | Haskell98 |
Matrix.QR.Givens
Synopsis
- leastSquares :: (Ix i, Enum i, Ix j, Enum j, RealFloat a) => Matrix i j a -> Array i a -> Array j a
- decompose :: (Ix i, Enum i, Ix j, Enum j, RealFloat a) => Matrix i j a -> ([Rotation i a], Upper i j a)
- solve :: (Ix i, Ix j, Fractional a) => ([Rotation i a], Upper i j a) -> Array i a -> Array j a
- det :: (Ix i, Enum i, Ix j, Enum j, RealFloat a) => Matrix i j a -> a
- detAbs :: (Ix i, Enum i, Ix j, Enum j, RealFloat a) => Matrix i j a -> a
- data Rotation i a
- rotateVector :: (Ix i, Num a) => Rotation i a -> Array i a -> Array i a
- data Upper i j a
- solveUpper :: (Ix i, Ix j, Fractional a) => Upper i j a -> Array i a -> Array j a
- detUpper :: (Ix i, Ix j, Fractional a) => Upper i j a -> a
Documentation
leastSquares :: (Ix i, Enum i, Ix j, Enum j, RealFloat a) => Matrix i j a -> Array i a -> Array j a Source #
Solve a sparse overconstrained linear problem, i.e. minimize ||Ax-b||.
A must have dimensions m x n with m>=n and it must have full-rank.
None of these conditions is checked.
Arguments
| :: (Ix i, Enum i, Ix j, Enum j, RealFloat a) | |
| => Matrix i j a | A |
| -> ([Rotation i a], Upper i j a) | QR(A) |
The decomposition routine is pretty simple. It does not try to minimize fill-up by a clever ordering of rotations. However, for banded matrices it will work as expected.
solve :: (Ix i, Ix j, Fractional a) => ([Rotation i a], Upper i j a) -> Array i a -> Array j a Source #
det :: (Ix i, Enum i, Ix j, Enum j, RealFloat a) => Matrix i j a -> a Source #
Only sensible for square matrices, but the function does not check whether the matrix is square.
detAbs :: (Ix i, Enum i, Ix j, Enum j, RealFloat a) => Matrix i j a -> a Source #
Absolute value of the determinant. This is also sound for non-square matrices.
solveUpper :: (Ix i, Ix j, Fractional a) => Upper i j a -> Array i a -> Array j a Source #
Assumes that Upper matrix is at least as high as wide
and that it has full rank.