fixed.interpn
Interpolation for 1D, 2D, 3D, and ND gridded data in
ndgrid
format
Since R2024a
Syntax
Description
returns interpolated values of a function of n variables at specific
query points using linear interpolation. The results always pass through the original
sampling of the function. Vq
= fixed.interpn(X1,X2,...,Xn
,V
,Xq1,Xq2,...,Xqn
)X1,X2,...,Xn
contain the coordinates of the
sample points. V
contains the corresponding function values at each
sample point. Xq1,Xq2,...,Xqn
contain the coordinates of the query
points.
assumes a default grid of sample points. The default grid consists of the points,
1,2,3,...n_{i} in each dimension. The value of
n_{i} is the length of the ith dimension in Vq
= fixed.interpn(V
,Xq1,Xq2,...,Xqn
)V
.
Use this syntax when you want to conserve memory and are not concerned about the absolute
distances between points.
Examples
Implement ND FixedPoint Lookup Tables Using Interpolation
This example shows how to implement an Ndimensional fixedpoint lookup table using fixed.interpn
.
Run the example multiple times to see the approximation over different query points.
Create Lookup Table for Function
Define a function f(x,y)
to replace with a lookup table approximation.
clearvars f = @(x,y) sin(x)+sin(y)(x.^2+y.^2)/20;
Define breakpoints x
and y
for the lookup table. Note that m
and n
do not have to be equal and x
and y
do not have to be linearly spaced.
m = 16; n = 16; x = linspace(5,5,n); y = linspace(5,5,m); [X,Y] = ndgrid(x,y);
Generate lookup table values V
, corresponding to the breakpoints.
V = f(X,Y);
Query Lookup Table
Choose a random query point (xq,yq)
in the ranges of x
and y
.
xq = fixed.example.realUniformRandomArray(x(1),x(end),1); yq = fixed.example.realUniformRandomArray(y(1),y(end),1);
Cast the inputs to 16bit fixedpoint.
x = fi(x); y = fi(y); V = fi(V); xq = fi(xq); yq = fi(yq);
The fixed.interpn
function computes vq
, the lookup table approximation of f(xq,yq)
.
vq = fixed.interpn(x,y,V,xq,yq)
vq = 2.0808 DataTypeMode: Fixedpoint: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 12
Compare Lookup Approximation to Actual Function Value
Compare vq
to the actual function evaluation f(xq,yq)
.
vq_expected = f(double(xq),double(yq))
vq_expected = 2.1175
err = double(vq)  vq_expected
err = 0.0367
Plot f(x,y)
.
clf mesh(x,y,V,'EdgeAlpha',0.8,'FaceAlpha',0); xlabel('x') ylabel('y') zlabel('v') hold on
Plot vq
, the lookup table approximation of f(xq,vq)
, using a red stem plot.
stem3(xq,yq,vq,'Filled','red') legend('f(x)','vq = Fixedpoint lookuptable approximation of f(xq)','location','best')
Input Arguments
X1,X2,...,Xn
— Sample grid points
arrays  vectors
Sample grid points, specified as real arrays or vectors. The sample grid points must be strictly monotonically increasing in each dimension.
If
X1,X2,...,Xn
are arrays, then they contain the coordinates of a full grid (inndgrid
format). Use thengrid
function to create theX1,X2,...,Xn
arrays together. These arrays must be the same size.If
X1,X2,...,Xn
are vectors, then they are treated as grid vectors. The values in these vectors must be strictly monotonically increasing.
The inputs [X1,X2,...,Xn]
, V
, and
[Xq1,Xq2,...,Xqn]
must be the same data type:
fi
, half
, single
, or
double
. When using fi
data, you can use the
shortened function name interpn
.
Example: [X1,X2,X3,X4] =
fi(ndgrid(1:30,10:10,1:5,10:13))
Example: [X1,X2,X3,X4] =
half(ndgrid(1:30,10:10,1:5,10:13))
Data Types: fi
 single
 double
V
— Sample values
array
Sample values, specified as a real or complex array. The size requirements for
V
depend on the size of the grid of sample points defined by
X1,X2,...,Xn
. The sample points X1,X2,...,Xn
can
be arrays or grid vectors, but in both cases they define an
ndimensional grid. V
must be an array that at
least has the same n dimension sizes, but it also can have extra
dimensions beyond n:
If
V
also hasn
dimensions, then the size ofV
must match the size of the ndimensional grid defined byX1,X2,...,Xn
. In this case,V
contains one set of sample values at the sample points. For example, ifX1,X2,X3
are 3by3by3 arrays, thenV
can also be a 3by3by3 array.If
V
has more thann
dimensions, then the firstn
dimensions ofV
must match the size of the ndimensional grid defined byX1,X2,...,Xn
. The extra dimensions inV
define extra sets of sample values at the sample points. For example, ifX1,X2,X3
are 3by3by3 arrays, thenV
can be a 3by3by3by2 array that defines two sets of sample values at the sample points.
If V
contains complex numbers, then
fixed.interpn
interpolates the real and imaginary parts
separately.
The inputs [X1,X2,...,Xn]
, V
, and
[Xq1,Xq2,...,Xqn]
must be the same data type:
fi
, half
, single
, or
double
. When using fi
data, you can use the
shortened function name interpn
.
Example: fi(rand(10,5,3,2))
Example: half(rand(10,5,3,2))
Data Types: fi
 single
 double
Complex Number Support: Yes
Xq1,Xq2,...,Xqn
— Query points
scalars  vectors  arrays
Query points, specified as real scalars, vectors, or arrays.
If
Xq1,Xq2,...,Xqn
are scalars, then they are the coordinates of a single query point in R^{n}.If
Xq1,Xq2,...,Xqn
are vectors of different orientations, thenXq1,Xq2,...,Xqn
are treated as grid vectors in R^{n}.If
Xq1,Xq2,...,Xqn
are vectors of the same size and orientation, thenXq1,Xq2,...,Xqn
are treated as scattered points in R^{n}.If
Xq1,Xq2,...,Xqn
are arrays of the same size, then they represent either a full grid of query points (inndgrid
format) or scattered points in R^{n}.
The inputs [X1,X2,...,Xn]
, V
, and
[Xq1,Xq2,...,Xqn]
must be the same data type:
fi
, half
, single
, or
double
. When using fi
data, you can use the
shortened function name interpn
.
Example: [X1,X2,X3,X4] =
fi(ndgrid(1:10,1:5,7:9,10:11))
Example: [X1,X2,X3,X4] =
half(ndgrid(1:10,1:5,7:9,10:11))
Data Types: fi
 single
 double
method
— Interpolation method
"linear"
(default)  "nearest"
Interpolation method, specified as one of the options in this table.
Method  Description  Continuity  Comments 

"linear"  The interpolated value at a query point is based on linear interpolation of the values at neighboring grid points in each respective dimension. This method is the default interpolation method.  C^{0} 

"nearest"  The interpolated value at a query point is the value at the nearest sample grid point.  Discontinuous 

extrapval
— Function value outside domain of X1,X2,...,Xn
scalar
Function value outside the domain of X1,X2,...,Xn
, specified as a
real or complex scalar. interpn
returns this constant value for all
points outside the domain of X1,X2,...,Xn
. If the scalar value is
nonzero and outside the range of the sample values v
, then this value
is set to the minimum or maximum value of v
, whichever is
closer.
The data type of extrapval
must be the same as
[X1,X2,...,Xn]
, V
, and
[Xq1,Xq2,...,Xqn]
.
The default behavior with fi
input data is to return
0
for query points outside the domain. The default behavior with
half
, single
, or double
input
data is to return NaN
for query points outside the domain.
Example: fi(5)
Example: half(5+1i)
Data Types: fi
 single
 double
Complex Number Support: Yes
Note
The default behavior of the interpn
function is to return
NaN
when a query point is outside the domain. The
fixed.interpn
function with fi
input data is not
consistent with this behavior because fi
casts NaN
to 0
.
Output Arguments
Vq
— Interpolated values
scalar  vector  array
Interpolated values, returned as a real or complex scalar, vector, or array. The
size and shape of Vq
depends on the syntax you use and, in some
cases, the size and value of the input arguments. The data type of Vq
is the same as that of the sample values V
.
If you specify sample points with
X1,X2,...,Xn
, or use the default grid, andV
has the same number of dimensions as the ndimensional grid of sample points, thenVq
contains a single set of interpolated values at the query points defined byXq1,Xq2,...,Xqn
.If
Xq1,Xq2,...,Xqn
are scalars, thenVq
is a scalar.If
Xq1,Xq2,...,Xqn
are vectors of the same size and orientation, thenVq
is a vector with the same size and orientation.If
Xq1,Xq2,...,Xqn
are grid vectors of mixed orientation, thenVq
is an array with the same size as the grid implicitly defined by the grid vectors.If
Xq1,Xq2,...,Xqn
are arrays of the same size, thenVq
is an array with the same size.
If you specify sample points with
X1,X2,...,Xn
, or use the default grid, andV
has more dimensions than the ndimensional grid of sample points, thenVq
contains multiple sets of interpolated values at the query points defined byXq1,Xq2,...,Xqn
. In this case, the first n dimensions ofVq
follow the size rules for a single set of interpolated values above, butVq
also has the same extra dimensions asV
with the same sizes.With the syntax
fixed.interpn(V)
,Vq
is an array with the same number of dimensions asV
, where the size of the ith dimension is2 * (size(V,i)1)+1
.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.
Version History
Introduced in R2024a
See Also
fixed.interp1
 fixed.interp2
 fixed.interp3
 ndgrid
 interpn
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