| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell98 |
Numeric.LAPACK.Singular
Synopsis
- values :: (Measure meas, C vert, C horiz) => (C height, C width, Floating a) => Full meas vert horiz height width a -> RectangularDiagonal meas vert horiz height width (RealOf a)
- valuesTall :: (Measure meas, C vert, C height, C width, Floating a) => Full meas vert Small height width a -> RealVector width a
- valuesWide :: (Measure meas, C horiz, C height, C width, Floating a) => Full meas Small horiz height width a -> RealVector height a
- decompose :: (Measure meas, C vert, C horiz) => (C height, C width, Floating a) => Full meas vert horiz height width a -> (Square height a, RectangularDiagonal meas vert horiz height width (RealOf a), Square width a)
- decomposeTall :: (Measure meas, C vert, C height, C width, Floating a) => Full meas vert Small height width a -> (Full meas vert Small height width a, RealVector width a, Square width a)
- decomposeWide :: (Measure meas, C horiz, C height, C width, Floating a) => Full meas Small horiz height width a -> (Square height a, RealVector height a, Full meas Small horiz height width a)
- determinantAbsolute :: (C height, C width, Floating a) => General height width a -> RealOf a
- leastSquaresMinimumNormRCond :: (Measure meas, C vert, C horiz, C height, Eq height, C width, C nrhs, Floating a) => RealOf a -> Full meas horiz vert height width a -> Full meas vert horiz height nrhs a -> (Int, Full meas vert horiz width nrhs a)
- pseudoInverseRCond :: (Measure meas, C vert, C horiz, C height, C width, Floating a) => RealOf a -> Full meas vert horiz height width a -> (Int, Full meas horiz vert width height a)
- decomposePolar :: (Measure meas, C vert, C horiz, C height, C width, Floating a) => Full meas vert horiz height width a -> (Full meas vert horiz height width a, Hermitian width a)
- type family RealOf x
Documentation
values :: (Measure meas, C vert, C horiz) => (C height, C width, Floating a) => Full meas vert horiz height width a -> RectangularDiagonal meas vert horiz height width (RealOf a) Source #
The RectangularDiagonal type maintains
the shape information of the original matrix,
but is a bit cumbersome to work with.
You might access its elements using #!
or extract the diagonal as vector by:
Singular.values m #*| Vector.one (Matrix.height m)
Vector.one (Matrix.width m) -*# Singular.values m
.
valuesTall :: (Measure meas, C vert, C height, C width, Floating a) => Full meas vert Small height width a -> RealVector width a Source #
valuesWide :: (Measure meas, C horiz, C height, C width, Floating a) => Full meas Small horiz height width a -> RealVector height a Source #
decompose :: (Measure meas, C vert, C horiz) => (C height, C width, Floating a) => Full meas vert horiz height width a -> (Square height a, RectangularDiagonal meas vert horiz height width (RealOf a), Square width a) Source #
decomposeTall :: (Measure meas, C vert, C height, C width, Floating a) => Full meas vert Small height width a -> (Full meas vert Small height width a, RealVector width a, Square width a) Source #
let (u,s,vt) = Singular.decomposeTall a in a == u ##*# Matrix.scaleRowsReal s vt
decomposeWide :: (Measure meas, C horiz, C height, C width, Floating a) => Full meas Small horiz height width a -> (Square height a, RealVector height a, Full meas Small horiz height width a) Source #
let (u,s,vt) = Singular.decomposeWide a in a == u #*## Matrix.scaleRowsReal s vt
determinantAbsolute :: (C height, C width, Floating a) => General height width a -> RealOf a Source #
leastSquaresMinimumNormRCond :: (Measure meas, C vert, C horiz, C height, Eq height, C width, C nrhs, Floating a) => RealOf a -> Full meas horiz vert height width a -> Full meas vert horiz height nrhs a -> (Int, Full meas vert horiz width nrhs a) Source #
pseudoInverseRCond :: (Measure meas, C vert, C horiz, C height, C width, Floating a) => RealOf a -> Full meas vert horiz height width a -> (Int, Full meas horiz vert width height a) Source #
decomposePolar :: (Measure meas, C vert, C horiz, C height, C width, Floating a) => Full meas vert horiz height width a -> (Full meas vert horiz height width a, Hermitian width a) Source #
In decomposePolar a = (u,h),
u is the orthogonal matrix closest to a
with respect to the 2- and the Frobenius norm.
(Higham: Functions of Matrices - Theory and Computation.)