xs: A vector of Float64 values representing the x-coordinates (must be monotonically increasing)
fs: A vector or matrix of Float64/ComplexF64 values representing the function values at the x-coordinates
bctype: An integer specifying the boundary condition type (default is 1):
- 1: Natural spline (zero second derivative at endpoints)
- 2: Periodic spline
- 3: Extrapolated spline
- 4: Not-a-knot spline

Returns

A CubicSplineType object that can be used for evaluation

Examples

# 1D spline
xs = collect(range(0.0; stop=2π, length=21))
fs = sin.(xs)
spline = spline_setup(xs, fs, 1)

# Multi-quantity spline
fs_matrix = hcat(sin.(xs), cos.(xs))
spline = spline_setup(xs, fs_matrix, 1)

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spline_eval

JPEC.SplinesMod.CubicSpline.spline_eval — Function

spline_eval(spline, x, derivs=0)

Evaluate a cubic spline at given points.

Arguments

spline: A CubicSplineType object created by spline_setup
x: A Float64 value or vector of Float64 values representing the x-coordinates to evaluate
derivs: Integer specifying derivative level (default is 0):
- 0: Function values only
- 1: Function values and first derivatives
- 2: Function values, first and second derivatives

Returns

If derivs=0: Matrix of function values (length(x) × nqty)
If derivs=1: Tuple of (values, first_derivatives)
If derivs=2: Tuple of (values, firstderivatives, secondderivatives)

Examples

# Evaluate at single point
spline = spline_setup(xs, fs, 1)
f_vals = spline_eval(spline, π / 2)

# Evaluate at multiple points
x_eval = [π / 4, π / 2, 3π / 4]
f_vals = spline_eval(spline, x_eval)

# Get derivatives
f_vals, f_derivs = spline_eval(spline, x_eval, 1)

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bicube_setup

JPEC.SplinesMod.BicubicSpline.bicube_setup — Function

bicube_setup(xs, ys, fs, bctypex=1, bctypey=1)

Set up a bicubic spline interpolation for 2D data.

Arguments

xs: Vector of Float64 values representing the x-coordinates (must be monotonically increasing)
ys: Vector of Float64 values representing the y-coordinates (must be monotonically increasing)
fs: 3D array of Float64 values with dimensions (nx, ny, nqty) representing function values
bctypex: Boundary condition type for x-direction (default is 1)
bctypey: Boundary condition type for y-direction (default is 1)
- 1: Natural spline (zero second derivative at boundaries)
- 2: Periodic spline
- 3: Extrapolated spline
- 4: Not-a-knot spline

Returns

A BicubicSplineType object that can be used for 2D evaluation

Examples

# Create 2D grid
xs = collect(range(0.0; stop=2π, length=20))
ys = collect(range(0.0; stop=2π, length=20))

# Create 3D function data array
fs = zeros(20, 20, 1)
for i in 1:20, j in 1:20
    fs[i, j, 1] = sin(xs[i]) * cos(ys[j])
end

# Set up bicubic spline
bcspline = bicube_setup(xs, ys, fs, 1, 1)

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bicube_eval

JPEC.SplinesMod.BicubicSpline.bicube_eval — Function

bicube_eval(bicube, x, y, derivs=0)

Evaluate a bicubic spline at given 2D points.

Arguments

bicube: A BicubicSplineType object created by bicube_setup
x: Float64 value or vector of x-coordinates to evaluate
y: Float64 value or vector of y-coordinates to evaluate
derivs: Integer specifying derivative level (default is 0):
- 0: Function values only
- 1: Function values and first derivatives (∂f/∂x, ∂f/∂y)
- 2: Function values, first and second derivatives (∂f/∂x, ∂f/∂y, ∂²f/∂x², ∂²f/∂x∂y, ∂²f/∂y²)

Returns

If derivs=0: 3D array of function values (length(x) × length(y) × nqty)
If derivs=1: Tuple of (values, xderivatives, yderivatives)
If derivs=2: Tuple of (values, xderivatives, yderivatives, xxderivatives, xyderivatives, yy_derivatives)

Examples

# Evaluate at single point
bcspline = bicube_setup(xs, ys, fs, 1, 1)
f_vals = bicube_eval(bcspline, π / 2, π / 4)

# Evaluate on grid
x_eval = collect(range(0, 2π; length=50))
y_eval = collect(range(0, 2π; length=50))
f_vals = bicube_eval(bcspline, x_eval, y_eval)

# Get derivatives
f_vals, fx, fy = bicube_eval(bcspline, x_eval, y_eval, 1)

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Example Usage

1D Cubic Spline

using JPEC

# Create data points
xs = collect(range(0.0, stop=2π, length=21))
fs = sin.(xs)

# Set up spline (1 quantity)
spline = JPEC.SplinesMod.spline_setup(xs, hcat(fs), 1)

# Evaluate at new points
xs_fine = collect(range(0.0, stop=2π, length=100))
fs_fine = JPEC.SplinesMod.spline_eval(spline, xs_fine)

2D Bicubic Spline

# Create 2D grid
xs = collect(range(0.0, stop=2π, length=20))
ys = collect(range(0.0, stop=2π, length=20))

# Create 2D function data
fs = zeros(20, 20, 1)
for i in 1:20, j in 1:20
    fs[i, j, 1] = sin(xs[i]) * cos(ys[j])
end

# Set up bicubic spline
bcspline = JPEC.SplinesMod.bicube_setup(xs, ys, fs, 1, 1)

# Evaluate with derivatives
x_eval, y_eval = π/2, π/4
f, fx, fy = JPEC.SplinesMod.bicube_eval(bcspline, x_eval, y_eval, 1)