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-rw-r--r--lib/LinearAlgebra/Algorithms.hs19
1 files changed, 19 insertions, 0 deletions
diff --git a/lib/LinearAlgebra/Algorithms.hs b/lib/LinearAlgebra/Algorithms.hs
index 126549a..4ac6dde 100644
--- a/lib/LinearAlgebra/Algorithms.hs
+++ b/lib/LinearAlgebra/Algorithms.hs
@@ -19,6 +19,8 @@ module LinearAlgebra.Algorithms (
19 pinv, 19 pinv,
20 pinvTol, 20 pinvTol,
21 pinvTolg, 21 pinvTolg,
22 nullspacePrec,
23 nullVector,
22 Normed(..), NormType(..), 24 Normed(..), NormType(..),
23 det, 25 det,
24 eps, i 26 eps, i
@@ -240,3 +242,20 @@ instance Normed (Matrix Double) where
240 242
241instance Normed (Matrix (Complex Double)) where 243instance Normed (Matrix (Complex Double)) where
242 pnorm = pnormCM 244 pnorm = pnormCM
245
246-----------------------------------------------------------------------
247
248-- | The nullspace of a real matrix from its SVD decomposition.
249nullspacePrec :: Double -- ^ relative tolerance in 'eps' units
250 -> Matrix Double -- ^ input matrix
251 -> [Vector Double] -- ^ list of unitary vectors spanning the nullspace
252nullspacePrec t m = ns where
253 (_,s,v) = svdR' m
254 sl@(g:_) = toList s
255 tol = (fromIntegral (max (rows m) (cols m)) * g * t * eps)
256 rank = length (filter (> g*tol) sl)
257 ns = drop rank (toColumns v)
258
259-- | The nullspace of a real matrix, assumed to be one-dimensional, with default tolerance (shortcut for @last . nullspacePrec 1@).
260nullVector :: Matrix Double -> Vector Double
261nullVector = last . nullspacePrec 1