Interpolate Matrix(x,y)

Return interpolated matrix for given inputs

• 

Libraries:
Aerospace Blockset / GNC / Control

Description

The Interpolate Matrix(x,y) block interpolates a two-dimensional array of matrices. In two-dimensional cases, the interpolation is carried out first on x and then y. For more information, see Algorithms.

The matrix to be interpolated must be four-dimensional, the first two dimensions corresponding to the matrix at each value of x and y. For example, if you have four matrices A, B, C, and D defined at (x = 0.0,y = 1.0), (x = 0.0,y = 3.0), (x = 1.0,y = 1.0) and (x = 1.0,y = 3.0), then the input matrix is given by

matrix(:,:,1,1) = A;

matrix(:,:,1,2) = B;

matrix(:,:,2,1) = C;

matrix(:,:,2,2) = D;

Limitations

This block must be driven from the Prelookup block.

Ports

Input

x_k — First interpolation index

scalar

First interpolation index i, specified as a scalar and vector.

Data Types: double

x_f — First interpolation fraction

scalar

First interpolation fraction λ _x, specified as a scalar

Data Types: double

y_k — Second interpolation index

scalar

Second interpolation index j, specified as a scalar.

Data Types: double

y_f — Second interpolation fraction

scalar

Second interpolation fraction λ _y, specified as a scalar.

Data Types: double

Output

Matrix(x,y) — Interpolated matrix

matrix

Interpolated matrix, specified as a matrix.

Data Types: double

Parameters

Matrix to interpolate — Matrix

matrix (default)

Matrix to be interpolated, with four indices and the third and fourth indices labeling the interpolating values of x and y.

Programmatic Use

Block Parameter: matrix

Type: character vector

Values: matrix

Default: 'matrix'

Algorithms

This two-dimensional case assumes the matrix is defined as a function of two independent variables, x = [ x₁x₂x₃... x_ix_i+1 ... x_n] and y = [ y₁y₂y₃ ... y_jy_j+1 ... y_m]. For given values of x and y, four matrices are interpolated. Then for x_i < x < x_i+1 and y_j < y < y_j+1, the output matrix is given by

$$\begin{array}{l}(1-{\lambda }_y)[(1-{\lambda }_x)M(x_i,y_j)+{\lambda }_{x}M(x_{i+1},y_j)]+\\ {\lambda }_y[(1-{\lambda }_x)M(x_i,y_{j+1})+{\lambda }_{x}M(x_{i+1},y_{j+1})]\end{array}$$

where the two interpolation fractions are denoted by

$${\lambda }_x=(x-x_i)/(x_{i+1}-x_i)$$

and

$${\lambda }_y=(y-y_j)/(y_{j+1}-y_j)$$

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a