Do anyone have any idea how can I rewrite `eig(A,B)`

from Matlab used to calculate generalized eigenvector/eigenvalues? I've been struggling with this problem lately. So far:

Matlab definition of `eig`

function I need:

```
[V,D] = eig(A,B) produces a diagonal matrix D of generalized
eigenvalues and a full matrix V whose columns are the corresponding
eigenvectors so that A*V = B*V*D.
```

- So far I tried the
`Eigen`

library (http://eigen.tuxfamily.org/dox/classEigen_1_1GeneralizedSelfAdjointEigenSolver.html)

My implementation looks like this:

```
std::pair<Matrix4cd, Vector4d> eig(const Matrix4cd& A, const Matrix4cd& B)
{
Eigen::GeneralizedSelfAdjointEigenSolver<Matrix4cd> solver(A, B);
Matrix4cd V = solver.eigenvectors();
Vector4d D = solver.eigenvalues();
return std::make_pair(V, D);
}
```

But first thing that comes to my mind is, that I can't use `Vector4cd`

as `.eigenvalues()`

doesn't return complex values where Matlab does. Furthermore results of `.eigenvectors()`

and `.eigenvalues()`

for the same matrices are not the same at all:

C++:

```
Matrix4cd x;
Matrix4cd y;
pair<Matrix4cd, Vector4d> result;
for (int i = 0; i < 4; i++)
{
for (int j = 0; j < 4; j++)
{
x.real()(i,j) = (double)(i+j+1+i*3);
y.real()(i,j) = (double)(17 - (i+j+1+i*3));
x.imag()(i,j) = (double)(i+j+1+i*3);
y.imag()(i,j) = (double)(17 - (i+j+1+i*3));
}
}
result = eig(x,y);
cout << result.first << endl << endl;
cout << result.second << endl << endl;
```

Matlab:

```
for i=1:1:4
for j=1:1:4
x(i,j) = complex((i-1)+(j-1)+1+((i-1)*3), (i-1)+(j-1)+1+((i-1)*3));
y(i,j) = complex(17 - ((i-1)+(j-1)+1+((i-1)*3)), 17 - ((i-1)+(j-1)+1+((i-1)*3)));
end
end
[A,B] = eig(x,y)
```

So I give `eig`

the same 4x4 matrices holding values 1-16 ascending (x) and descending (y). But I receive different results, furthermore `Eigen`

method returns double from eigenvalues while Matlab returns complex dobule. I also find out that there is other `Eigen`

solver named `GeneralizedEigenSolver`

. That one in the documentation (http://eigen.tuxfamily.org/dox/classEigen_1_1GeneralizedEigenSolver.html) has written that it solves `A*V = B*V*D`

but to be honest I tried it and results (matrix sizes) are not the same size as Matlab so I got quite lost how it works (examplary results are on the website I've linked). It also has only .eigenvector method.

C++ results:

```
(-0.222268,-0.0108754) (0.0803437,-0.0254809) (0.0383264,-0.0233819) (0.0995482,0.00682079)
(-0.009275,-0.0182668) (-0.0395551,-0.0582127) (0.0550395,0.03434) (-0.034419,-0.0287563)
(-0.112716,-0.0621061) (-0.010788,0.10297) (-0.0820552,0.0294896) (-0.114596,-0.146384)
(0.28873,0.257988) (0.0166259,-0.0529934) (0.0351645,-0.0322988) (0.405394,0.424698)
-1.66983
-0.0733194
0.0386832
3.97933
```

Matlab results:

```
[A,B] = eig(x,y)
A =
Columns 1 through 3
-0.9100 + 0.0900i -0.5506 + 0.4494i 0.3614 + 0.3531i
0.7123 + 0.0734i 0.4928 - 0.2586i -0.5663 - 0.4337i
0.0899 - 0.4170i -0.1210 - 0.3087i 0.0484 - 0.1918i
0.1077 + 0.2535i 0.1787 + 0.1179i 0.1565 + 0.2724i
Column 4
-0.3237 - 0.3868i
0.2338 + 0.7662i
0.5036 - 0.3720i
-0.4136 - 0.0074i
B =
Columns 1 through 3
-1.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i -1.0000 - 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i -4.5745 - 1.8929i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
Column 4
0.0000 + 0.0000i
0.0000 + 0.0000i
0.0000 + 0.0000i
-0.3317 + 1.1948i
```

- Second try was with Intel IPP but it seems that it solves only
`A*V = V*D`

and support told me that it's not supported anymore.

https://software.intel.com/en-us/node/505270 (list of constructors for Intel IPP)

- I got suggestion to move from Intel IPP to MKL. I did it and hit the wall again. I tried to check all algorithms for
`Eigen`

but it seems that there are only`A*V = V*D`

problems solved. I was checking`lapack95.lib`

. The list of algorithms used by this library is available there: https://software.intel.com/sites/products/documentation/doclib/mkl_sa/11/mkl_lapack_examples/index.htm#dsyev.htm

Somewhere on the web I could find topic on Mathworks when someone said that managed to solve my problem partially with usage of MKL:

Person said that he/she used `dsygv`

algorithm but I can't locate anything like that on the web. Maybe it's a typo.

Anyone has any other proposition/idea how can I implement it? Or maybe point my mistake. I'd appreciate that.

EDIT: In comments I've received a hint that I was using `Eigen`

solver wrong. My `A`

matrix wasn't self-adjoint and my `B`

matrix wasn't positive-definite. I took matrices from program I want to rewrite to C++ (from random iteration) and checked if they meet the requirements. They did:

```
Rj =
1.0e+02 *
Columns 1 through 3
0.1302 + 0.0000i -0.0153 + 0.0724i 0.0011 - 0.0042i
-0.0153 - 0.0724i 1.2041 + 0.0000i -0.0524 + 0.0377i
0.0011 + 0.0042i -0.0524 - 0.0377i 0.0477 + 0.0000i
-0.0080 - 0.0108i 0.0929 - 0.0115i -0.0055 + 0.0021i
Column 4
-0.0080 + 0.0108i
0.0929 + 0.0115i
-0.0055 - 0.0021i
0.0317 + 0.0000i
Rt =
Columns 1 through 3
4.8156 + 0.0000i -0.3397 + 1.3502i -0.2143 - 0.3593i
-0.3397 - 1.3502i 7.3635 + 0.0000i -0.5539 - 0.5176i
-0.2143 + 0.3593i -0.5539 + 0.5176i 1.7801 + 0.0000i
0.5241 + 0.9105i 0.9514 + 0.6572i -0.7302 + 0.3161i
Column 4
0.5241 - 0.9105i
0.9514 - 0.6572i
-0.7302 - 0.3161i
9.6022 + 0.0000i
```

As for `Rj`

which is now my `A`

- it is self-adjoint because `Rj = Rj'`

and `Rj = ctranspose(Rj)`

. (http://mathworld.wolfram.com/Self-AdjointMatrix.html)

As for `Rt`

which is now my `B`

- it is Positive-Definite what is checked with method linked to me. (http://www.mathworks.com/matlabcentral/answers/101132-how-do-i-determine-if-a-matrix-is-positive-definite-using-matlab). So

```
>> [~,p] = chol(Rt)
p =
0
```

I've rewritten matrices manually to C++ and performed `eig(A,B)`

again with matrices meeting requirements:

```
Matrix4cd x;
Matrix4cd y;
pair<Matrix4cd, Vector4d> result;
x.real()(0,0) = 13.0163601949795;
x.real()(0,1) = -1.53172561296005;
x.real()(0,2) = 0.109594869350436;
x.real()(0,3) = -0.804231869422614;
x.real()(1,0) = -1.53172561296005;
x.real()(1,1) = 120.406645675346;
x.real()(1,2) = -5.23758765476463;
x.real()(1,3) = 9.28686785230169;
x.real()(2,0) = 0.109594869350436;
x.real()(2,1) = -5.23758765476463;
x.real()(2,2) = 4.76648319080400;
x.real()(2,3) = -0.552823839520508;
x.real()(3,0) = -0.804231869422614;
x.real()(3,1) = 9.28686785230169;
x.real()(3,2) = -0.552823839520508;
x.real()(3,3) = 3.16510496622613;
x.imag()(0,0) = -0.00000000000000;
x.imag()(0,1) = 7.23946944213164;
x.imag()(0,2) = 0.419181335323979;
x.imag()(0,3) = 1.08441894337449;
x.imag()(1,0) = -7.23946944213164;
x.imag()(1,1) = -0.00000000000000;
x.imag()(1,2) = 3.76849276970080;
x.imag()(1,3) = 1.14635625342266;
x.imag()(2,0) = 0.419181335323979;
x.imag()(2,1) = -3.76849276970080;
x.imag()(2,2) = -0.00000000000000;
x.imag()(2,3) = 0.205129702522089;
x.imag()(3,0) = -1.08441894337449;
x.imag()(3,1) = -1.14635625342266;
x.imag()(3,2) = 0.205129702522089;
x.imag()(3,3) = -0.00000000000000;
y.real()(0,0) = 4.81562784930907;
y.real()(0,1) = -0.339731222392148;
y.real()(0,2) = -0.214319720979258;
y.real()(0,3) = 0.524107127885349;
y.real()(1,0) = -0.339731222392148;
y.real()(1,1) = 7.36354235698375;
y.real()(1,2) = -0.553927983436786;
y.real()(1,3) = 0.951404408649307;
y.real()(2,0) = -0.214319720979258;
y.real()(2,1) = -0.553927983436786;
y.real()(2,2) = 1.78008768533745;
y.real()(2,3) = -0.730246631850385;
y.real()(3,0) = 0.524107127885349;
y.real()(3,1) = 0.951404408649307;
y.real()(3,2) = -0.730246631850385;
y.real()(3,3) = 9.60215057284395;
y.imag()(0,0) = -0.00000000000000;
y.imag()(0,1) = 1.35016928394966;
y.imag()(0,2) = -0.359262708214312;
y.imag()(0,3) = -0.910512495060186;
y.imag()(1,0) = -1.35016928394966;
y.imag()(1,1) = -0.00000000000000;
y.imag()(1,2) = -0.517616473138836;
y.imag()(1,3) = -0.657235460367660;
y.imag()(2,0) = 0.359262708214312;
y.imag()(2,1) = 0.517616473138836;
y.imag()(2,2) = -0.00000000000000;
y.imag()(2,3) = -0.316090662865005;
y.imag()(3,0) = 0.910512495060186;
y.imag()(3,1) = 0.657235460367660;
y.imag()(3,2) = 0.316090662865005;
y.imag()(3,3) = -0.00000000000000;
result = eig(x,y);
cout << result.first << endl << endl;
cout << result.second << endl << endl;
```

And the results of C++:

```
(0.0295948,0.00562174) (-0.253532,0.0138373) (-0.395087,-0.0139696) (-0.0918132,-0.0788735)
(-0.00994614,-0.0213973) (-0.0118322,-0.0445976) (0.00993512,0.0127006) (0.0590018,-0.387949)
(0.0139485,-0.00832193) (0.363694,-0.446652) (-0.319168,0.376483) (-0.234447,-0.0859585)
(0.173697,0.268015) (0.0279387,-0.0103741) (0.0273701,0.0937148) (-0.055169,0.0295393)
0.244233
2.24309
3.24152
18.664
```

Results of MATLAB:

```
>> [A,B] = eig(Rj,Rt)
A =
Columns 1 through 3
0.0208 - 0.0218i 0.2425 + 0.0753i -0.1242 + 0.3753i
-0.0234 - 0.0033i -0.0044 + 0.0459i 0.0150 - 0.0060i
0.0006 - 0.0162i -0.4964 + 0.2921i 0.2719 + 0.4119i
0.3194 + 0.0000i -0.0298 + 0.0000i 0.0976 + 0.0000i
Column 4
-0.0437 - 0.1129i
0.2351 - 0.3142i
-0.1661 - 0.1864i
-0.0626 + 0.0000i
B =
0.2442 0 0 0
0 2.2431 0 0
0 0 3.2415 0
0 0 0 18.6640
```

`Eigenvalues`

are the same! Nice, but why `Eigenvectors`

are not similar at all?

Answer:

There is no problem here with Eigen.

In fact for the second example run, Matlab and Eigen produced the very same result. Please remember from basic linear algebra that eigenvector are determined up to an arbitrary scaling factor. (I.e. if v is an eigenvector the same holds for alpha*v, where alpha is a non zero complex scalar.)

It is quite common that different linear algebra libraries compute different eigenvectors, but this does not mean that one of the two codes is wrong: it simply means that they choose a different scaling of the eigenvectors.

EDIT

The main problem with exactly replicating the scaling chosen by matlab is that `eig(A,B)`

is a *driver* routine, which depending from the different properties of `A`

and `B`

may call different libraries/routines, and apply extra steps like balancing the matrices and so on. By quickly inspecting your example, I would say that in this case matlab is enforcing following condition:

`all(imag(V(end,:))==0)`

(the last component of each eigenvector is real)

but not imposing other constraints. This unfortunately means that the scaling is not unique, and probably depends on intermediate results of the generalised eigenvector algorithm used. In this case I'm not able to give you advice on how to *exactly* replicate matlab: knowledge of the internal working of matlab is required.

As a general remark, in linear algebra usually one does not care too much about eigenvector scaling, since this is usually completely irrelevant for the problem solved, when the eigenvectors are just used as intermediate results.

The only case in which the scaling has to be defined exactly, is when you are going to give a graphic representation of the eigenvalues.

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c++,arrays,string,qt,random

In my small Qt application, I want to pick a random string out of an array after I clicked on a button. I've read many threads but nothing works for me. So in my slot there's an array with several strings in it. I also implemented <string>, <time.h> and srand....

c++,arrays,pointers

I've been having bad luck with dynamic pointers when I want to close it. why the application wrote to memory after end of heap buffer? how can I close my array? int main() { . . int **W; W = new int* [n]; for (int i=1; i <= n; i++)...

c++,string,c++11,gcc

I know it sounds stupid, but I'm using MinGW32 on Windows7, and "to_string was not declared in this scope." It's an actual GCC Bug, and I've followed these instructions and they did not work. So, how can I convert an int to a string in C++11 without using to_string or...

c#,c++,marshalling

I have the following structures in C# and C++. C++: struct TestA { char* iu; }; struct TestB { int cycle1; int cycle2; }; struct MainStruct { TestA test; TestB test2; }; C#: [StructLayout(LayoutKind.Sequential, CharSet=CharSet.Ansi, Pack = 1)] internal struct TestA { [MarshalAs(UnmanagedType.ByValTStr, SizeConst = 36)] private string iu; public...

c++,boost,boost-filesystem

I have used boost::filesystem::directory_iterator in order to get a list of all the available files into a given folder. The problem is that I supposed this method would give me the files in alphabetical order, while the results seem pretty random. Is there any fancy way of alphabetically sorting them?...

c++,opencv

I am working on Traffic Surveillance System an OpenCv project, I need to detect moving cars and people. I am using background subtraction method to detect moving objects and thus drawing counters. I have a problem : When two car are moving on road closely them my system detects it...

matlab,plot,legend,movie

i have a question regarding legend for movies. This is my code: fig = figure(); for i = 1: 70000 plot(signal1) hold on; plot([i,i],[-5,5]) plot(signal2,'r') hold off; title('\fontsize{14} my data'); legend('signal1','signal2'); axis tight; f(i) = getframe(fig); end The legend shows the same colors for the first two things I plot....

c++,file,hdf5,dataformat

We aim at using HDF5 for our data format. HDF5 has been selected because it is a hierarchical filesystem-like cross-platform data format and it supports large amounts of data. The file will contain arrays and some parameters. The question is about how to store the parameters (which are not made...

c++,boost,boost-asio

I have a third-part server, and I'm writing a dll interface for it, my clients use my dll to communicate with the server. The protocol uses a long tcp connection, all traffic goes from this tcp connection. There could be sending/receiving multiple packets at the same time, like a send_msg...

c++,inline,private,member,protected

This is another question about inlining a function. But I will take possible comments and answers right away: Defining a function inside a class makes it inline automatically. The same behaviour can be achieved by marking a function with inline outside of the class. An inline function doesn't have to...

c++,polar-coordinates,cartesian-coordinates

I am getting incorrect conversions from polar to cartesian coordinates and vice versa. My code produces weird points like (1,-0). Im using this calculator to check my conversions. Also one of the conversions is completely wrong when I convert back to cartesian coordinates. Point b: (0,1) => (1,1.5708) => (0,0)...

c++,vector,heap-memory

I am creating a temporary vector of pointers to myObject objects. But I am wondering about what happens to the objects I created... { std::vector<myObject *> myVector; myVector.reserve(5); for (int i = 0 ; i < 5 ; ++i){ myVector[i] = new myObject(); } } I assume that at the...

c++

As a continuation of a: Thread, I came across a problem with writing a method of a class which returns: std::vector<std::unique_ptr<Object>> I get compiler errors when such a return type is written. There is some problem with delete operand or something ... Generally, I've wanted to write a method which...

c++,string

Here a basic code I'm trying to run But I'm having trouble with stoi (it's c++) I keep getting error: ‘stoi’ was not declared in this scope I tried atoi and strtol with this error .cpp:23: error: cannot convert ‘std::string’ to ‘const char*’ for argument ‘1’ to ‘int atoi(const char*)’...

c++,templates

I'm trying to understand C++ template templates by implementing a generic container class. Here is the code: using namespace std; template <typename T, template <typename STORETYPE> class Container> class Store { public: ~Store() {}; Store() {}; void someFunc( const T & ) {}; //... private: Container<T> storage; }; int main(int...