numal.lowprecision
Class AnalyticProblems

java.lang.Object
  numal.lowprecision.AnalyticProblems

public class AnalyticProblems
extends Object

Constructor Summary

AnalyticProblems()

Method Summary

static void

marquardt(int m, int n, float[] parameter, float[] rv, float[][] v, Function function, float[] out) The standard deviation of each parameter in the fit is sqrt(v[j][j] / m) and the correlation between parameter i and parameter j is v[i][j]/ sqrt(v[i][i]*v[j][j]) where i=1,...,n and j=i+1,...,n.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

AnalyticProblems

public AnalyticProblems()

Method Detail

marquardt

public static void marquardt(int m,
                             int n,
                             float[] parameter,
                             float[] rv,
                             float[][] v,
                             Function function,
                             float[] out)

The standard deviation of each parameter in the fit is sqrt(v[j][j] / m) and the correlation between parameter i and parameter j is v[i][j]/ sqrt(v[i][i]*v[j][j]) where i=1,...,n and j=i+1,...,n. // http://www.crcpress.com/shopping_cart/products/product_detail.asp?sku=C4304

Output values
• out[1] information about the termination of the process
• 0 : normal termination
• 1 : number of invocations of Function.computeResidualVector(int, int, float[], float[]) exceeded Function.getInvocations()
• 2 : Function.computeResidualVector(int, int, float[], float[]) returned false
• 3 : Function.computeResidualVector(int, int, float[], float[]) returned false when called with the initial estimates of parameter[1:n]; the iteration process was not started and so v[1:n][1:n] can't be used
• 4 : precision asked for can't be attained; this precision is possibly chosen too high, relative to the precision in which the residual vector is calculated (see Function.getRelativeTolerance()
• out[2] the Euclidean norm of the residual vector calculated with values of the unknowns delivered
• out[3] the Euclidean norm of the residual vector calculated with the initial values of the unknown variables
• out[4] the number of calls of Function.computeResidualVector(int, int, float[], float[]) necessary to attain the calculated results
• out[5] the total number of iterations performed; note that in each iteration one call to Function.computeJacobian(int, int, float[], float[], float[][]) had to be made
• out[6] the improvement vector in the last iteration
• out[7] the condition number of J^T J, i.e., the ratio of its largest to smallest eigenvalues

Dependencies: Basic.mulcol(int, int, int, int, float[][], float[][], float), Basic.dupvec(int, int, int, float[], float[]), Basic.vecvec(int, int, int, float[], float[]), Basic.matvec(int, int, int, float[][], float[]), Basic.tamvec(int, int, int, float[][], float[]), Basic.mattam(int, int, int, int, float[][], float[][]), LinearAlgebra.qrisngvaldec(float[][], int, int, float[], float[][], float[]).

Parameters:

m - sample points used in the fitting

n - number of parameters, must be less than or equal to m

parameter - input: initial approximation to the set of parameters output: parameters producing a least square fit

rv - 1xm vector output : residual vector obtained with current value of unknowns

v - nxn matrix output : inverse of matrix J^T J where J denotes the transpose of the matrix of partial derivatives dg[1..m]/dp[1..n]

function - residual vector of a given function, jacobian and options such as precision and maximum number of iterations

out - an array of 7 output values (see description above)