Struct Spline2d 

pub struct Spline2d<I, T> {
    pub interp: I,
    pub xa: Vec<T>,
    pub ya: Vec<T>,
    pub za: Vec<T>,
    /* private fields */
}

2D Higher level interface.

A 2D Spline owns the data it is constructed with, and provides the same evalulation methods as the lower-level Interpolator object, without needing to provide the data arrays in every call.

Example

let mut xacc = Accelerator::new();
let mut yacc = Accelerator::new();

let xa = [0.0, 1.0, 2.0, 3.0];
let ya = [0.0, 2.0, 4.0, 6.0];
// z = x + y, in column-major order
let za = [
    0.0, 1.0, 2.0, 3.0,
    2.0, 3.0, 4.0, 5.0,
    4.0, 5.0, 6.0, 7.0,
    6.0, 7.0, 8.0, 9.0,
];

let interp = Bicubic.build(&xa, &ya, &za)?;

let typ = Bicubic;
let spline = Spline2d::build(typ, &xa, &ya, &za)?;

let (x, y) = (2.5, 4.1);
let y_interp = interp.eval(&xa, &ya, &za, x, y, &mut xacc, &mut yacc)?;
let y_spline = spline.eval(x, y, &mut xacc, &mut yacc)?;

assert_eq!(y_interp, y_spline);

Fields

interp: I

The lower-level 2D Interpolator.

xa: Vec<T>

The owned x data.

ya: Vec<T>

The owned y data.

za: Vec<T>

The owned z data.

Implementations

impl<I, T> Spline2d<I, T>

where I: Interpolation2d<T>, T: Num + Lapack,

pub fn build( typ: impl Interp2dType<T, Interpolator2d = I>, xa: &[T], ya: &[T], za: &[T], ) -> Result<Self, InterpolationError>

Constructs a 2D Spline of a 2D Interpolation type typ from the data arrays xa, ya and za.

Example

let mut xacc = Accelerator::new();
let mut yacc = Accelerator::new();

let xa = [0.0, 1.0, 2.0, 3.0];
let ya = [0.0, 2.0, 4.0, 6.0];
// z = x + y, in column-major order
let za = [
    0.0, 1.0, 2.0, 3.0,
    2.0, 3.0, 4.0, 5.0,
    4.0, 5.0, 6.0, 7.0,
    6.0, 7.0, 8.0, 9.0,
];

let typ = Bicubic;
let spline = Spline2d::build(typ, &xa, &ya, &za)?;

pub fn eval( &self, x: T, y: T, xacc: &mut Accelerator, yacc: &mut Accelerator, ) -> Result<T, DomainError>

Returns the interpolated value of z for a given point (x, y), using the Accelerators xacc and yacc.

Example

let mut xacc = Accelerator::new();
let mut yacc = Accelerator::new();

let xa = [0.0, 1.0, 2.0];
let ya = [0.0, 2.0, 4.0];
// z = x + y
let za = [
    0.0, 1.0, 2.0,
    2.0, 3.0, 4.0,
    4.0, 5.0, 6.0,
];

let typ = Bilinear;
let spline = Spline2d::build(typ, &xa, &ya, &za)?;

let z = spline.eval(1.5, 3.0, &mut xacc, &mut yacc)?;

assert_eq!(z, 4.5);

Errors

Returns a DomainError if x is outside the range of xa or y is outside the range of ya.

pub fn eval_extrap( &self, x: T, y: T, xacc: &mut Accelerator, yacc: &mut Accelerator, ) -> Result<T, DomainError>

Returns the interpolated value of z for a given point (x, y), using the Accelerators xaccandyacc`.

Note

This function performs no bound checking, so when x is outside the range of xa or y is outside the range of ya, extrapolation is performed.

Example

let mut xacc = Accelerator::new();
let mut yacc = Accelerator::new();

let xa = [0.0, 1.0, 2.0];
let ya = [0.0, 2.0, 4.0];
// z = x + y
let za = [
    0.0, 1.0, 2.0,
    2.0, 3.0, 4.0,
    4.0, 5.0, 6.0,
];

let typ = Bilinear;
let spline = Spline2d::build(typ, &xa, &ya, &za)?;

let z = spline.eval_extrap(3.0, 6.0, &mut xacc, &mut yacc)?;

assert_eq!(z, 9.0);

Errors

Returns a DomainError if x is outside the range of xa or y is outside the range of ya.

pub fn eval_deriv_x( &self, x: T, y: T, xacc: &mut Accelerator, yacc: &mut Accelerator, ) -> Result<T, DomainError>

Returns the interpolated value d = ∂z/∂x for a given point (x, y), using the Accelerators xacc and yacc.

Example

let mut xacc = Accelerator::new();
let mut yacc = Accelerator::new();

let xa = [0.0, 1.0, 2.0];
let ya = [0.0, 2.0, 4.0];
// z = x² + y²
let za = [
     0.0,  1.0,  4.0,
     4.0,  5.0,  8.0,
    16.0, 17.0, 20.0,
];

let typ = Bilinear;
let spline = Spline2d::build(typ, &xa, &ya, &za)?;

let dzdx = spline.eval_deriv_x(1.5, 3.0, &mut xacc, &mut yacc)?;

assert_eq!(dzdx, 3.0);

Errors

Returns a DomainError if x is outside the range of xa or y is outside the range of ya.

pub fn eval_deriv_y( &self, x: T, y: T, xacc: &mut Accelerator, yacc: &mut Accelerator, ) -> Result<T, DomainError>

Returns the interpolated value d = ∂z/∂y for a given point (x, y), using the Accelerators xacc and yacc.

Example

let mut xacc = Accelerator::new();
let mut yacc = Accelerator::new();

let xa = [0.0, 1.0, 2.0];
let ya = [0.0, 2.0, 4.0];
// z = x² + y²
let za = [
     0.0,  1.0,  4.0,
     4.0,  5.0,  8.0,
    16.0, 17.0, 20.0,
];

let typ = Bilinear;
let spline = Spline2d::build(typ, &xa, &ya, &za)?;

let dzdx = spline.eval_deriv_y(1.5, 3.0, &mut xacc, &mut yacc)?;

assert_eq!(dzdx, 6.0);

Errors

Returns a DomainError if x is outside the range of xa or y is outside the range of ya.

pub fn eval_deriv_xx( &self, x: T, y: T, xacc: &mut Accelerator, yacc: &mut Accelerator, ) -> Result<T, DomainError>

Returns the interpolated value d = 𝜕²z/𝜕x² for a given point (x, y), using the Accelerators xacc and yacc.

Example

let mut xacc = Accelerator::new();
let mut yacc = Accelerator::new();

let xa = [0.0, 1.0, 2.0];
let ya = [0.0, 2.0, 4.0];
// z = x² + y²
let za = [
     0.0,  1.0,  4.0,
     4.0,  5.0,  8.0,
    16.0, 17.0, 20.0,
];

let typ = Bilinear;
let spline = Spline2d::build(typ, &xa, &ya, &za)?;

let dzdx2 = spline.eval_deriv_xx(1.5, 3.0, &mut xacc, &mut yacc)?;

assert_eq!(dzdx2, 0.0); // Linear Interpolation!

Errors

Returns a DomainError if x is outside the range of xa or y is outside the range of ya.

pub fn eval_deriv_yy( &self, x: T, y: T, xacc: &mut Accelerator, yacc: &mut Accelerator, ) -> Result<T, DomainError>

Returns the interpolated value d = 𝜕²z/𝜕x² for a given point (x, y), using the Accelerators xacc and yacc.

Example

let mut xacc = Accelerator::new();
let mut yacc = Accelerator::new();

let xa = [0.0, 1.0, 2.0];
let ya = [0.0, 2.0, 4.0];
// z = x² + y²
let za = [

     0.0,  1.0,  4.0,
     4.0,  5.0,  8.0,
    16.0, 17.0, 20.0,
];
let typ = Bilinear;
let spline = Spline2d::build(typ, &xa, &ya, &za)?;

let dzdx2 = spline.eval_deriv_yy(1.5, 3.0, &mut xacc, &mut yacc)?;

assert_eq!(dzdx2, 0.0); // Linear Interpolation!

Errors

Returns a DomainError if x is outside the range of xa or y is outside the range of ya.

pub fn eval_deriv_xy( &self, x: T, y: T, xacc: &mut Accelerator, yacc: &mut Accelerator, ) -> Result<T, DomainError>

Returns the interpolated value d = 𝜕²z/𝜕x𝜕y for a given point (x, y), using the Accelerators xacc and yacc.

Example

let mut xacc = Accelerator::new();
let mut yacc = Accelerator::new();

let xa = [0.0, 1.0, 2.0];
let ya = [0.0, 2.0, 4.0];
// z = x² + y²
let za = [
     0.0,  1.0,  4.0,
     4.0,  5.0,  8.0,
    16.0, 17.0, 20.0,
];

let typ = Bilinear;
let spline = Spline2d::build(typ, &xa, &ya, &za)?;

let dzdxy = spline.eval_deriv_xy(1.5, 3.0, &mut xacc, &mut yacc)?;

assert_eq!(dzdxy, 0.0);

Errors

Returns a DomainError if x is outside the range of xa or y is outside the range of ya.

pub fn name(&self) -> String

Returns the name of the Interpolator.

pub fn min_size(&self) -> usize

Returns the minimum number of points required by the Interpolator.