horner

Calling sequence

Parameters

• P: polynomial matrix
• Q: a polynomial or numerical matrix
• vdim, ttmode: optional named boolean arguments.
• R: a cell whose elements are polynomial or numerical matrices if ttmode is false and a polynomial or a numerical matrix if ttmode is true.

Description

For a polynomial matrix P returns P(Q). The evaluation is performed using the Horner algorithm. When Q is a numerical matrix the Horner algorithm is a builtin function and when Q is a polynomial matrix the computation is performed with a library nsp function.

When ttmode is false the returned value is a cell matrix

• if vdim is false the cell matrix has same dimension as P and the cell element (i,j) is the polynomial matrix P(i,j)(Q).
• if vdim is true the cell matrix has same dimension as Q and the cell element (i,j) is the polynomial matrix P(Q(i,j)).

When ttmode is true then the operation is a term to term horner which implies that both matrices have same dimensions (with the usual convention that 1x1 matrices are promoted to any dimensions). The returned result is then a polynomial matrix.

Examples

• ttmode=%f
          p=m2p(1:3);
          q=m2p(1:2);
          r=testmatrix('magic',3);
          R=horner([p,q],r); // a 1x2 cell
          R1=horner([p,q],r,vdim=%t); // a 3x3 cell
          A=ce2m(R1,indice=1); // a 3x3 matrix
          B=ce2m(R1,indice=2); // a 3x3 matrix
          R.equal[{A,B}]  // recovering R from R1.
• ttmode=%t
          p=m2p(1:3);
          q=m2p(1:2);
          r=[1,2;3,7];
          R=horner([p,q;q,p],r,ttmode=%t);