PsiLAB Help Manual Page

Section: Linear Algebra

Name: LinAlg

Linear Algebra module.
This module provides several generic functions to solve linear equations, solving linear least square problems, and some special matrix operations. Matrix Inversion
LinAlg.inva a:(float, 'a, 'b) Matrix.t
LinAlg.invab a:(float, 'a, 'b) Matrix.t b:(float, 'a, 'b) Matrix.t

The inva function inverts the matrix a inplace using LAPACK's DGETRF and DEGTRI routines, and the inab function inverts matrix a and stores the result in the already allocated matrix b .
Matrix transpoition
LinAlg.transpose a:('a, 'b, 'c) Matrix.t

The transpose function transpose matrix a inplace. Supported formats: [ float, complex ] .
Solving linear equation systems
LinAlg.solve
a:(float, 'a, 'b) Matrix.t
b:(float, 'a, 'b) Matrix.t
x:(float, 'a, 'b) Matrix.t

This functions solves the linear equation 
A * x = b

using LAPACK's DGESV routine with
A : Matrix of size (n,m)
b : Right hand side vector, size (n)
x : Solution vector, size (m)

Determinat of a matrix
[ d:float ] = LinAlg.detnn a:(float, 'a, 'b) Matrix.t

This function calculates the determinant of a square matrix a using LAPACK's DGETRF routine and returns the float value d .
Linear Least Square Problems
[ sig:float ] = LinAlg.lls
a:(float, 'a, 'b) Matrix.t
b:(float, 'a, 'b) Matrix.t
x:(float, 'a, 'b) Matrix.t

The lls function solves the minimization problem 
minimize x || b - A * x || 2

using LAPACK's DGELS routine. It returns the standard deviation sigma. More special regression function based on this LLS can be found in the Reg module.
Examples: 
[] let a = fmatrix ~const:[ 
	 (-1.0,1.0,2.0); 
	 (3.0,-1.0,1.0); 
	 (-1.0,3.0,4.0)] () ;; 
[] print_fmat a ;; 
| 	 -1 	 1 	 2 	 | 
| 	 3 	 -1 	 1 	 | 
| 	 -1 	 3 	 4 	 | 
- : unit = () 
[] let b = fmatrix ~const:[2.0;6.0;4.0] () ;; 
[] let x = fmatrix ~dim:[3] () ;; 
[] LinAlg.solve a b x ;; 
- : unit = () 
[] print_fmat x ;; 
| 	 1 	 | 
| 	 -1 	 | 
| 	 2 	 | 
- : unit = ()

Printed by PsiLAB