Interpolate Matrix(x,y,z)

Return interpolated matrix for given inputs

• 

Libraries:
Aerospace Blockset / GNC / Control

Description

The Interpolate Matrix(x,y,z) block interpolates a three-dimensional array of matrices.

This three-dimensional case assumes the matrix is defined as a function of three independent variables:

x = [ x ₁ x ₂ x ₃ ... x _i x _i+1 ... x _n ]

y = [ y ₁ y ₂ y ₃ ... y _j y _j+1 ... y _m ]

z = [ z ₁ z ₂ z ₃ ... z _k z _k+1 ... z _p ]

For given values of x, y, and z, eight matrices are interpolated. Then for

x _i < x < x _i+1

y _j < y < y _j+1

z _k < z < z _k+1

the output matrix is given by

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

where the three interpolation fractions are denoted by

$$\begin{array}{l}{\lambda }_x=\left(x-x_i\right)/\left(x_{i+1}-x_i\right)\\ i_y=(y-y_j)/\left(y_{j+1}-y_j\right)\\ {\lambda }_z=\left(z-z_k\right)/\left(z_{k+1}-z_k\right)\end{array}$$

In the three-dimensional case, the interpolation is carried out first on x, then y, and finally z.

The matrix to be interpolated should be five-dimensional, the first two dimensions corresponding to the matrix at each value of x, y, and z. For example, if you have eight matrices A, B, C, D, E, F, G, and H defined at the following values of x, y, and z, then the corresponding input matrix is given by

(x = 0.0,y = 1.0,z = 0.1)	matrix(:,:,1,1,1) = A;
(x = 0.0,y = 1.0,z = 0.5)	matrix(:,:,1,1,2) = B;
(x = 0.0,y = 3.0,z = 0.1)	matrix(:,:,1,2,1) = C;
(x = 0.0,y = 3.0,z = 0.5)	matrix(:,:,1,2,2) = D;
(x = 1.0,y = 1.0,z = 0.1)	matrix(:,:,2,1,1) = E;
(x = 1.0,y = 1.0,z = 0.5)	matrix(:,:,2,1,2) = F;
(x = 1.0,y = 3.0,z = 0.1)	matrix(:,:,2,2,1) = G;
(x = 1.0,y = 3.0,z = 0.5)	matrix(:,:,2,2,2) = H;

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.

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

z_k — Third interpolation index

scalar

Third interpolation index k, specified as a scalar.

Data Types: double

z_f — Third interpolation fraction

scalar

Third interpolation fraction λ _z, specified as a scalar.

Data Types: double

Output

Matrix(x,y,z) — Interpolated matrix

matrix

Interpolated matrix, specified as a matrix.

Data Types: double

Parameters

Matrix to interpolate — Matrix to interpolate

matrix (default)

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

Programmatic Use

Block Parameter: matrix

Type: character vector

Values: matrix

Default: 'matrix'

Extended Capabilities

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

Version History

Introduced before R2006a