Mat

Mat – matrix data type

Calling sequence

A=[a11, a12, ..., a1n;
   a21, a22, ..., a2n;
   ...
   am1, am2, ...; amn]

Parameters

a11 ...: real or complex numbers.

Description
The Mat data type is the basic matrix numerical object. More generally, matrices are two dimensional arrays which contains scalar objects (real or complex numbers, boolean numbers, strings, polynomials). The Mat data type is built from real or complex numbers.

Column vectors are considered as m x 1 matrices and row vectors as 1 x n matrices.

Internally numerical matrices Mat type are stored by default as arrays of double.

Operations on matrices

Matrix methods

A.add[B] add matrix B to matrix A.
A.blas_axpy[alpha, x [i1,i2 [,j1,j2]]] constant times a vector plus a vector i.e A = A + alpha*X
A.blas_ger[alpha, x, y [,i1,i2,j1,j2]] rank one update A = A + alpha*x*y’ on a submatrix of A.
A.scale_rows[x] multiplies each row i of A with a scalar: A(i,:) = x(i) A(i,:).
A.scale_cols[x] multiplies each column j of A with a scalar: A(:,j) = x(j) A(:,j).

Methods from the matint interface

A.redim[m,n] reshape matrix to size mxn. m or n can be set to -1
A.concatr[B] A = [A,B]
A.concatd[B] A = [A;B]
A.perm_elem[p,q[,dim]] permute p and q: elements (default or dim=0), rows (dim=1) or columns (dim=2).

Extraction, insertion, deletion

If I and is J are respectively row and column indices A(I,J) is the submatrix of A with entries in I and j.
A(I,:) is the submatrix of A with row indices in I.
A(:,J) is the submatrix of A with comumn indices in I.
A(:,:) is A
A(:) is the column matrix obtained by stacking the columns of A.

If I and is J are row and column indices A(I,J)=B inserts matrix B into matrix A in rows I and columns J.
A(I,:)=[] removes the rows of A with indices in J.
A(:,J)=[] removes the columns of A with indices in J.

Empty matrices

Empty matrices are matrices with zero rows or zero columns. Operations with empty matrices are compatible with linear algebra operations. The m x n zero matrix can be factorized as the empty m x 0 matrix * the 0 x n matrix.

For loop control

With a matrix A:

     for col=A
       ....
     end

is a loop with size(A,2) iterations, the loop variable col being equal to the ith column of A at the i-th iteration.

Some functions

length(A) returns the number of entries in A.
size(A) returns in a 1 x 2 vector the dimensions (rows, columns) of A. size(A,1) (resp. size(A,2)) retuns the number of rows (resp. columns) of A.