orth

3 files changed, 20 insertions, 1 deletions

diff --git a/CHANGES.md b/CHANGES.md
index a5f6aee..2788c52 100644
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -5,6 +5,11 @@
 
 - msadams and msbdf methods for ode
 
+- Numeric.LinearAlgebra.Util
+
+- (<\>) extended to multiple right-hand sides
+
+- orth
 
 0.13.0.0
 --------
diff --git a/lib/Numeric/LinearAlgebra/Algorithms.hs b/lib/Numeric/LinearAlgebra/Algorithms.hs
index 435cc5a..9ae5e32 100644
--- a/lib/Numeric/LinearAlgebra/Algorithms.hs
+++ b/lib/Numeric/LinearAlgebra/Algorithms.hs
@@ -64,6 +64,7 @@ module Numeric.LinearAlgebra.Algorithms (
     nullspacePrec,
     nullVector,
     nullspaceSVD,
+    orth,
 -- * Norms
     Normed(..), NormType(..),
     relativeError,
@@ -445,6 +446,13 @@ nullspacePrec t m = nullspaceSVD (Left (t*eps)) m (rightSV m)
 nullVector :: Field t => Matrix t -> Vector t
 nullVector = last . nullspacePrec 1
 
+orth :: Field t => Matrix t -> [Vector t]
+-- ^ Return an orthonormal basis of the range space of a matrix
+orth m = take r $ toColumns u
+  where
+    (u,s,_) = compactSVD m
+    r = ranksv eps (max (rows m) (cols m)) (toList s)
+
 ------------------------------------------------------------------------
 
 {-  Pseudoinverse of a real matrix with the desired tolerance, expressed as a
diff --git a/lib/Numeric/LinearAlgebra/Util.hs b/lib/Numeric/LinearAlgebra/Util.hs
index 416b23f..79b8774 100644
--- a/lib/Numeric/LinearAlgebra/Util.hs
+++ b/lib/Numeric/LinearAlgebra/Util.hs
@@ -18,7 +18,8 @@ module Numeric.LinearAlgebra.Util(
     col,
     (&),(!), (#),
     rand, randn,
-    cross
+    cross,
+    norm
 ) where
 
 import Numeric.LinearAlgebra
@@ -96,3 +97,8 @@ cross x y | dim x == 3 && dim y == 3 = fromList [z1,z2,z3]
     z2 = x3*y1-x1*y3
     z3 = x1*y2-x2*y1
 
+norm :: Vector Double -> Double
+-- ^ 2-norm of real vectors
+norm = pnorm PNorm2
+
+