Install Ocatve on Ubuntu

Update your apt-get first. 

1. $ sudo apt-get update
   
2. $ sudo apt-get install octave
   

Miss the first step, you may not find octave package when type step 2 command.

After updating, then input command of step 2.

Then system will ask you to agree the download process and upgrade process.

Press "y" and wait.

If you meet a problem, like 

ldconfig deferred processing tkaing place

dpkg: status database area is locked by another process

Just running step 2 again.

At least, I install it successfully.

Install gcc on Ubuntu

Before install any package, update apt-get is important.

$ sudo apt-get update

$ sudo apt-get install build-essential

from http://ubuntuforums.org/archive/index.php/t-7527.html

from http://fontignie.blogspot.com/2006/04/install-gcc-on-ubuntu.html

from http://www.linuxforums.org/forum/ubuntu-help/104156-gcc-installation-ubuntu.html

Octave and C/C++

Reference for using Octave and C/C++

參考這幾個網站，

http://octave.sourceforge.net/coda/

http://pagesperso-orange.fr/prthomas/intro.html

Please confirm that Dynamic Linking feature is ont or off.

先確認Octave是否有支援或是開啟Dynamic Linking，

Typing,

輸入

$ octave_config_info ("ENABLE_DYNAMIC_LINKING")

if

若

ans = true

That means ON.

表示有開啟。

因為Octave要用gcc compiler，所以勢必得換開發環境了。

至少我不知道怎麼用VisualCompiler去使用。

所以我改用Cygwin和Ubuntu，Cygwin因為我缺少了一些packages，所以花了點工夫。請參考HERE。

Ubuntu只要安裝好Octave和Octave-header後，就OK了。請參考HERE1 and HERE2。

程式要inlcude

然後告訴compile正確的octave library位置，但是通常都會用make來完成compile動作。下載範例Makefile。

內容大致如前面連結提供的範例相同，

makefile:

all:test

clean:

-rm test.o test

test: test.o

mkoctfile --link-stand-alone -o test hello.o

test.o: hello.cpp

g++ -c -I /usr/include/octave-3.0.3/ -o hello.o hello.cpp

指令輸入make all，就會完成Makefile裡指定的動作了。

The method of solving least-squares problems

Linear least squares problems

• Newton's Method
  

Non-Linear least squares problems

• Gauss-Newton Method
  
• Quasi-Newton Method
  
• Gauss-Raphson Method
  
• Levenberg-Marguardt Method
  
• Powell's Dog Leg Method
  
• Hybrid Method: L-M and Quasi-Newton
  

Good references:

• 1999, Poul E. Frandsen, http://www2.imm.dtu.dk/documents/ftp/publlec/lec2_99.pdf
  

Descent method

Conjugate Gradient mehod

Newton-based method, included Quasi-Newton

• 1999, Hans B. Nielsen: http://www2.imm.dtu.dk/documents/ftp/tr99/tr05_99.pdf
  

Descent method

Gauss-Newton method

Levenberg-Marquardt method

Powell's Dog Leg method

Hybrid: LMA+QN

Newton's Method, NM

Also called Newton-Raphson Method.  It uses the first few terms of the Taylor series (Taylor expansion) of a function  in the vicinity of a suspected root.  

• http://mathworld.wolfram.com/NewtonsMethod.html
  
• http://en.wikipedia.org/wiki/Newton's_method
  

Relationship between Newton's method, Halley method, and Householder's method.

• Newton's method is 1st in the class of Householder's method.
  
• Halley's method is 2nd in the class of Householder's method.
  
• http://en.wikipedia.org/wiki/Householder's_method
  
• http://en.wikipedia.org/wiki/Halley's_method
  

• Levenberg-Marquardt Algorithm, LMA
  
• http://en.wikipedia.org/wiki/Levenberg-Marquardt_algorithm
  
• http://mathworld.wolfram.com/Levenberg-MarquardtMethod.html
  
• http://homepages.inf.ed.ac.uk/cgi/rbf/CVONLINE/entries.pl?TAG49
  
• Nov. 1996, Sam Roweis: http://www.cs.toronto.edu/~roweis/notes/lm.pdf
  
• Good Introduction to talk about the LM from Newton's method, modefied by Levenberg, then modefied by Marquardt to become LM algorithm.
  

1999, Hans B. Nielsen: http://www2.imm.dtu.dk/documents/ftp/tr99/tr05_99.pdf

Apr. 2004, Hans B. Nielsen: http://www.imm.dtu.dk/pubdb/views/edoc_download.php/3215/pdf/imm3215.pdf

• Above two articles are refered by LEVMAR.
  

June 2004, Ananth R.: http://www.cc.gatech.edu/~ananth/docs/lmtut.pdf

• A good article also to talk about the LM from Newton's, Levenberg, and Marquardt to become LMA.
  

Feb. 2005, Manolis L.: http://www.ics.forth.gr/~lourakis/levmar/levmar.pdf

• The article talking about source code LEVMAR. A pseudocode provided.
  

Nov. 2006, Pradit M.: http://cobweb.ecn.purdue.edu/~kak/courses-i-teach/ECE661.08/homework/HW5_LM_handout.pdf

• Simple example and Matlab code provided.
  

http://www.cse.ucsd.edu/classes/fa04/cse252c/vrabaud1.pdf

• Matlab code, thanks for Pradit Mittrapiyanuruk.
  

Gauss-Newton Method, GNM

• http://en.wikipedia.org/wiki/Gauss-Newton_algorithm
  
• http://reference.wolfram.com/mathematica/tutorial/UnconstrainedOptimizationGaussNewtonMethods.html
  
• 1999, Hans B. Nielsen: http://www2.imm.dtu.dk/documents/ftp/tr99/tr05_99.pdf
  

Gauss-Raphson Method, GRM

Continue..

Quasi-Netwon Method, QNM

• http://reference.wolfram.com/mathematica/tutorial/UnconstrainedOptimizationQuasiNewtonMethods.html
  
• 1999, Poul E. Frandsen, http://www2.imm.dtu.dk/documents/ftp/publlec/lec2_99.pdf
  

Powell's Dog Leg Method, PDLM

• 1999, Hans B. Nielsen: http://www2.imm.dtu.dk/documents/ftp/tr99/tr05_99.pdf
  

Hybrid Method: L-M and Quasi-Newton, H:LM+QN

• 1999, Hans B. Nielsen: http://www2.imm.dtu.dk/documents/ftp/tr99/tr05_99.pdf
  

LMA for linear convergence

QN for superlinear convergence

Papers:

• Yao Jianchao, Chia Tien Chern, COMPARISON OF NEWTON-GAUSS WITH LEVENBERG-MARQUARDT ALGORITHM FOR SPACE RESECTION, Proc. ACRS 2001 - 22nd Asian Conference on Remote Sensing, 5-9 November 2001, Singapore. Vol. 1, pp. 256-261.
  
• C. Kanzow, N. Yamashita and M. Fukushima, Levenberg–Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints, J. Comput. Appl. Math.172 (2004), pp. 375–397.
  
• Kanzow, C., Yamashita, N., and Fukushima, M. 2004. Levenberg-Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints. J. Comput. Appl. Math. 172, 2 (Dec. 2004), 375-397. DOI= http://dx.doi.org/10.1016/j.cam.2004.02.013
  
• Lourakis, M. I. and Argyros, A. A. 2005. Is Levenberg-Marquardt the Most Efficient Optimization Algorithm for Implementing Bundle Adjustment?. In Proceedings of the Tenth IEEE international Conference on Computer Vision - Volume 2 (October 17 - 20, 2005). ICCV. IEEE Computer Society, Washington, DC, 1526-1531. DOI= http://dx.doi.org/10.1109/ICCV.2005.128
  

Source codes:

levmar: Levenberg-Marquardt nonlinear least squares algorithms in C/C++

lmfit — a C/C++ routine for Levenberg-Marquardt minimization with wrapper for least-squares curve fitting

lmfit is easy to install it because it is without the dependency problem.

Levenberg-Marquardt for Visual C++ 2005

Levenberg-Marquardt algorithm for multivariate optimization in C#/C++/Delphi/VB6/Zonnon

Continue....

Pointer in C

A simple example to using pointer in C.

we claim a pointer in main function, and hope to pass it to subroutin to allocate the memory.

How to use it?

Solution 1, return the address back.

=======================

#include

#include

int array_size =10;

int fill_array( float *ptr)

 {

    int i;

printf("Address %d\n", &ptr);

    ptr = (float *) malloc(array_size *sizeof(float));

    for(i=0; i<>

    {

         

      ptr[i] = (float)i;

    }

    

   for(i=0; i

   {

 printf("In function\n");

 

      printf("%d - %f ", &ptr[i],ptr[i]);

   }

   printf("\n");

   printf("ptr = %d\n", &ptr);

   return(ptr);

 }

main()

{

float *ptr = NULL;

int i;

printf("Address %d\n", &ptr);

ptr=fill_array(&ptr);

printf("Out function\n");

printf("Address %d\n", &ptr);

for(i=0; i

{

printf("Out function\n");

printf("%d - %f ", &ptr[i], ptr[i]);

}

}

=======================

The result will be

-------------------------------------

Address 1245052 //ptr in main( )

Address 1244968 //ptr in fill_array( )

In function

4397824 - 0.000000 In function

4397828 - 1.000000 In function

4397832 - 2.000000 In function

4397836 - 3.000000 In function

4397840 - 4.000000 In function

4397844 - 5.000000 In function

4397848 - 6.000000 In function

4397852 - 7.000000 In function

4397856 - 8.000000 In function

4397860 - 9.000000

ptr = 1244968  //ptr in fill_array( )

Out function

Address 1245052

Out function

4397824 - 0.000000 Out function

4397828 - 1.000000 Out function

4397832 - 2.000000 Out function

4397836 - 3.000000 Out function

4397840 - 4.000000 Out function

4397844 - 5.000000 Out function

4397848 - 6.000000 Out function

4397852 - 7.000000 Out function

4397856 - 8.000000 Out function

4397860 - 9.000000 Press any key to continue

-------------------------------------

Solution 2 , call by address.

=======================

#include

#include

void function(float ** ptrf)

{

int i;

printf("address of *ptrf = %d\n", &*ptrf);

*ptrf = (float *) malloc(5*sizeof(float*));

printf("address of *ptrf = %d\n", &*ptrf);

for(i=0; i<5;>

{

(*ptrf)[i] =i;

}

}

int main()

{

float *ptr=NULL;

int i;

printf("address of *ptr = %d\n", &ptr);

function(&ptr);

for(i=0; i<5;>

{

printf("%f ", ptr[i]);

}

printf("\nAddress ponited to by the ptr out function \nptr=%d, &ptr=%d\n", ptr, &ptr);

}

=======================

The result will be

---------------------------------

address of *ptr = 1245052

address of *ptrf = 1245052

address of *ptrf = 1245052

0.000000 1.000000 2.000000 3.000000 4.000000

Address ponited to by the ptr out function

ptr=4397856, &ptr=1245052

Press any key to continue

---------------------------------