From 0c3bdccc5f3b91f3f9f100a9b3756c6b19c7f195 Mon Sep 17 00:00:00 2001
From: Alberto Ruiz <aruiz@um.es>
Date: Mon, 8 Sep 2014 11:23:15 +0200
Subject: documentation, thanks

linearSolve examples, install, changelog
---
 packages/base/src/Data/Packed/Numeric.hs           | 24 +++++++++++++++-
 packages/base/src/Numeric/LinearAlgebra/HMatrix.hs | 32 +++++++++++++++++++++-
 2 files changed, 54 insertions(+), 2 deletions(-)

(limited to 'packages/base/src')

diff --git a/packages/base/src/Data/Packed/Numeric.hs b/packages/base/src/Data/Packed/Numeric.hs
index 7aa53f1..6027f43 100644
--- a/packages/base/src/Data/Packed/Numeric.hs
+++ b/packages/base/src/Data/Packed/Numeric.hs
@@ -160,7 +160,29 @@ instance Mul Vector Matrix Vector where
 
 --------------------------------------------------------------------------------
 
--- | least squares solution of a linear system, similar to the \\ operator of Matlab\/Octave (based on linearSolveSVD)
+{- | Least squares solution of a linear system, similar to the \\ operator of Matlab\/Octave (based on linearSolveSVD)
+
+@
+a = (3><2)
+ [ 1.0,  2.0
+ , 2.0,  4.0
+ , 2.0, -1.0 ]
+@
+
+@
+v = vector [13.0,27.0,1.0]
+@
+
+>>> let x = a <\> v
+>>> x
+fromList [3.0799999999999996,5.159999999999999]
+
+>>> a #> x
+fromList [13.399999999999999,26.799999999999997,1.0]
+
+It also admits multiple right-hand sides stored as columns in a matrix.
+
+-}
 infixl 7 <\>
 (<\>) :: (LSDiv c, Field t) => Matrix t -> c t -> c t
 (<\>) = linSolve
diff --git a/packages/base/src/Numeric/LinearAlgebra/HMatrix.hs b/packages/base/src/Numeric/LinearAlgebra/HMatrix.hs
index d2cae6c..c0cc622 100644
--- a/packages/base/src/Numeric/LinearAlgebra/HMatrix.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/HMatrix.hs
@@ -194,7 +194,37 @@ mul :: Numeric t => Matrix t -> Matrix t -> Matrix t
 mul = mXm
 
 
--- | Solve a linear system (for square coefficient matrix and several right-hand sides) using the LU decomposition, returning Nothing for a singular system. For underconstrained or overconstrained systems use 'linearSolveLS' or 'linearSolveSVD'. 
+{- | Solve a linear system (for square coefficient matrix and several right-hand sides) using the LU decomposition, returning Nothing for a singular system. For underconstrained or overconstrained systems use 'linearSolveLS' or 'linearSolveSVD'.
+
+@
+a = (2><2)
+ [ 1.0, 2.0
+ , 3.0, 5.0 ]
+@
+
+@
+b = (2><3)
+ [  6.0, 1.0, 10.0
+ , 15.0, 3.0, 26.0 ]
+@
+
+>>> linearSolve a b
+Just (2><3)
+ [ -1.4802973661668753e-15,     0.9999999999999997, 1.999999999999997
+ ,       3.000000000000001, 1.6653345369377348e-16, 4.000000000000002 ]
+
+>>> let Just x = it
+>>> disp 5 x
+2x3
+-0.00000  1.00000  2.00000
+ 3.00000  0.00000  4.00000
+
+>>> a <> x
+(2><3)
+ [  6.0, 1.0, 10.0
+ , 15.0, 3.0, 26.0 ]
+
+-}
 linearSolve m b = A.mbLinearSolve m b
 
 -- | return an orthonormal basis of the null space of a matrix. See also 'nullspaceSVD'.
-- 
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