lapack-0.5: Numerical Linear Algebra using LAPACK

Numeric.LAPACK.Singular

Synopsis

# 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 #

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.)

type family RealOf x Source #

#### Instances

Instances details
 type RealOf Double Source # Instance detailsDefined in Numeric.LAPACK.Scalar type RealOf Double = Double type RealOf Float Source # Instance detailsDefined in Numeric.LAPACK.Scalar type RealOf Float = Float type RealOf (Complex a) Source # Instance detailsDefined in Numeric.LAPACK.Scalar type RealOf (Complex a) = a