rowcomp

Scilab Function
Last update : 06/04/2006

rowcomp - row compression, range

### Calling Sequence

  `[W,rk]=rowcomp(A [,flag [,tol]])`

### Parameters

- `A`: real or complex matrix
- `flag`: optionnal character string, with possible values `'svd'` or `'qr'`. The default value is `'svd'`.
- `tol`: optionnal real non negative number. The default value is `sqrt(%eps)*norm(A,1)`.
- `W`: square non-singular matrix (change of basis)
- `rk`: integer (rank of `A`)

### Description

Row compression of `A`. `Ac = W*A` is a row compressed matrix: i.e. `Ac=[Af;0]` with `Af` full row rank.

`flag` and `tol` are optional parameters: `flag='qr'` or `'svd'` (default `'svd'`).

`tol` is a tolerance parameter.

The `rk` first columns of `W'` span the range of `A`.

The `rk` first (top) rows of `W` span the row range of `A`.

A non zero vector `x` belongs to range(`A`) iff `W*x` is row compressed in accordance with `Ac` i.e the norm of its last components is small w.r.t its first components.

### Examples

        A=rand(5,2)*rand(2,4);              // 4 col. vectors, 2 independent.
        [X,dim]=rowcomp(A);Xp=X';
        svd([Xp(:,1:dim),A])                //span(A) = span(Xp(:,1:dim)
        x=A*rand(4,1);                      //x belongs to span(A)
        y=X*x
        norm(y(dim+1:$))/norm(y(1:dim))     // small

### See Also

`colcomp`, `fullrf`, `fullrfk`,

### Author

F. D.; INRIA

### Used Function

The `rowcomp` function is based on the `svd` or `qr` decompositions.