## Tuesday, 12 July 2016

### chol/qz and matrix/vector flags

In the past weeks I worked on implementing the chol/qz and matrix/vector flags. My work can be found at my repository:

#### chol/qz flag

In case of a generalized eigenvalue problem the chol/qz flag can be used in Matlab. The aim of this task was to introduce this functionality to Octave.
The chol/qz flag only matters if your matrices are symmetric as:
Regardless of the algorithm you specify, the eig function always uses the QZ algorithm when A or B are not symmetric. 

If you omit the chol/qz flag it works as it worked before:
The algorithm used depends on whether there are one or two input matrices, if they are real or complex, and if they are symmetric (Hermitian if complex) or non-symmetric. 
Which is the same as in Matlab:
When you omit the algorithm argument, the eig function selects an algorithm based on the properties of A and B. It uses the 'chol' algorithm for symmetric (Hermitian) A and symmetric (Hermitian) positive definite B. Otherwise, it uses the 'qz' algorithm. 
So if it is a symmetric problem than the chol method is used otherwise the qz method is used.

#### matrix/vector flag

The matrix/vector flag can be used in every previous call forms. With it you can specify the format of the eigenvalues.
If you use the “vector” flag the eigenvalues will be returned in a column vector.
If you use the “matrix” flag the eigenvalues will be returned in a diagonal matrix.
If you omit this flag than the eigenvalues will be returned in the same format as before, which is the same as in Matlab:
The default behavior varies according to the number of outputs specified:
If you specify one output, such as e = eig(A), then the eigenvalues are returned as a column vector by default.
If you specify two or three outputs, such as [V,D] = eig(A), then the eigenvalues are returned as a diagonal matrix, D, by default. 

 http://www.mathworks.com/help/matlab/ref/eig.html#inputarg_algorithm