src/plot.rs

//! Plotting helper utilities

use numeric_literals::replace_float_literals;
use std::io::Write;
use image::{
    ImageFormat,
    ImageBuffer,
    Rgb
};
use itertools::izip;
use colorbrewer::Palette as CbPalette;

use alg_tools::types::*;
use alg_tools::lingrid::LinGrid;
use alg_tools::mapping::{
    RealMapping,
    DifferentiableRealMapping,
    SliceCodomain
};
use alg_tools::loc::Loc;
use alg_tools::bisection_tree::Bounds;
use alg_tools::maputil::map4;
use alg_tools::tabledump::write_csv;
use crate::measures::*;

/// Default RGB ramp from [`colorbrewer`].
///
/// This is a tuple of parameters to [`colorbrewer::get_color_ramp`].
const RAMP : (CbPalette, u32) = (CbPalette::RdBu, 11);

/// Helper trait for implementing dimension-dependent plotting routines.
pub trait Plotting<const N : usize> {
    /// Plot several mappings and a discrete measure into a file.
    fn plot_into_file_spikes<
        F : Float,
        T1 : RealMapping<F, N>,
        T2 : RealMapping<F, N>
    > (
        g_explanation : String,
        g : &T1,
        ω_explanation : String,
        ω : Option<&T2>,
        grid : LinGrid<F, N>,
        bnd : Option<Bounds<F>>,
        μ : &DiscreteMeasure<Loc<F, N>, F>,
        filename : String,
    );

    /// Plot a mapping into a file, sampling values on a given grid.
    fn plot_into_file<
        F : Float,
        T1 : RealMapping<F, N>,
    > (
        g : &T1,
        grid : LinGrid<F, N>,
        filename : String,
        explanation : String
    );

    /// Plot a differentiable mapping into several file, sampling values on a given grid.
    fn plot_into_file_diff<
        F : Float,
        T1 : DifferentiableRealMapping<F, N>,
    > (
        g : &T1,
        grid : LinGrid<F, N>,
        base_filename : String,
        explanation : String
    ) {
        Self::plot_into_file(g, grid, base_filename.clone(), explanation.clone());
        let d = g.diff_ref();
        for i in 0..N {
            Self::plot_into_file(&d.slice_codomain_ref(i),
                                 grid,
                                 format!("{base_filename}_diff{i}"),
                                 format!("{explanation} differential, dimension {i}"));
        }
    }
}

/// Helper type for looking up a [`Plotting`] based on dimension.
pub struct PlotLookup;

impl Plotting<1> for PlotLookup {
    fn plot_into_file_spikes<
        F : Float,
        T1 : RealMapping<F, 1>,
        T2 : RealMapping<F, 1>
    > (
        g_explanation : String,
        g : &T1,
        ω_explanation : String,
        ω0 : Option<&T2>,
        grid : LinGrid<F, 1>,
        bnd0 : Option<Bounds<F>>,
        μ : &DiscreteMeasure<Loc<F, 1>, F>,
        filename : String,
    ) {
        let start = grid.start[0].as_();
        let end = grid.end[0].as_();
        let m = μ.iter_masses().fold(F::ZERO, |m, α| m.max(α));
        let s = μ.iter_masses().fold(F::ZERO, |m, α| m.add(α));
        let mut spike_scale = F::ONE;

        let mut plotter = poloto::plot(
            "f", "x",
            format!("f(x); spike max={:.4}, n={}, ∑={:.4}", m, μ.len(), s)
        ).move_into();

        if let Some(ω) = ω0 {
            let graph_ω = grid.into_iter().map(|x@Loc([x0]) : Loc<F, 1>| {
                [x0.as_(), ω.apply(&x).as_()]
            });
            plotter.line(ω_explanation.as_str(), graph_ω.clone());
            // let csv_f = format!("{}.txt", filename);
            // write_csv(graph_ω, csv_f).expect("CSV save error");
        }

        let graph_g = grid.into_iter().map(|x@Loc([x0]) : Loc<F, 1>| {
            [x0.as_(), g.apply(&x).as_()]
        });
        plotter.line(g_explanation.as_str(), graph_g.clone());
        // let csv_f = format!("{}.txt", filename);
        // write_csv(graph_g, csv_f).expect("CSV save error");

        bnd0.map(|bnd| {
            let upperb = bnd.upper().as_();
            let lowerb =  bnd.lower().as_();
            let upper : [[f64; 2]; 2] = [[start, upperb], [end, upperb]];
            let lower = [[start, lowerb], [end, lowerb]];
            spike_scale *= bnd.upper();

            plotter.line("upper bound", upper)
                   .line("lower bound", lower)
                   .ymarker(lowerb)
                   .ymarker(upperb);
        });

        for &DeltaMeasure{ α, x : Loc([x]) } in μ.iter_spikes() {
            let spike = [[x.as_(), 0.0], [x.as_(), (α/m * spike_scale).as_()]];
            plotter.line("", spike);
        }

        let svg = format!("{}", poloto::disp(|a| poloto::simple_theme(a, plotter)));

        std::fs::File::create(filename + ".svg").and_then(|mut file|
            file.write_all(svg.as_bytes())
        ).expect("SVG save error");
    }

    fn plot_into_file<
        F : Float,
        T1 : RealMapping<F, 1>,
    > (
        g : &T1,
        grid : LinGrid<F, 1>,
        filename : String,
        explanation : String
    ) {
        let graph_g = grid.into_iter().map(|x@Loc([x0]) : Loc<F, 1>| {
            [x0.as_(), g.apply(&x).as_()]
        });

        let plotter: poloto::Plotter<'_, float, float> = poloto::plot("f", "x", "f(x)")
            .line(explanation.as_str(), graph_g.clone())
            .move_into();

        let svg = format!("{}", poloto::disp(|a| poloto::simple_theme(a, plotter)));

        let svg_f = format!("{}.svg", filename);
        std::fs::File::create(svg_f).and_then(|mut file|
            file.write_all(svg.as_bytes())
        ).expect("SVG save error");

        let csv_f = format!("{}.txt", filename);
        write_csv(graph_g, csv_f).expect("CSV save error");
    }

}

/// Convert $[0, 1] ∈ F$ to $\\\{0, …, M\\\} ∈ F$ where $M=$`F::RANGE_MAX`.
#[inline]
fn scale_uint<F, U>(v : F) -> U
where F : Float + CastFrom<U> + num_traits::cast::AsPrimitive<U>,
      U : Unsigned {
    (v*F::cast_from(U::RANGE_MAX)).as_()
}

/// Convert $[a, b] ∈ F$ to $\\\{0, …, M\\\} ∈ F$ where $M=$`F::RANGE_MAX`.
#[replace_float_literals(F::cast_from(literal))]
#[inline]
fn scale_range_uint<F, U>(v : F, &Bounds(a, b) : &Bounds<F>) -> U
where F : Float + CastFrom<U> + num_traits::cast::AsPrimitive<U>,
      U : Unsigned {
    debug_assert!(a < b);
    scale_uint(((v - a)/(b - a)).max(0.0).min(1.0))
}


/// Sample a mapping on a grid.
///
/// Returns a vector of values as well as upper and lower bounds of the values.
fn rawdata_and_range<F, T>(grid : &LinGrid<F, 2>, g :&T) -> (Vec<F>, Bounds<F>)
where F : Float,
      T : RealMapping<F, 2> {
    let rawdata : Vec<F> = grid.into_iter().map(|x| g.apply(&x)).collect();
    let range = rawdata.iter()
                        .map(|&v| Bounds(v, v))
                        .reduce(|b1, b2| b1.common(&b2))
                        .unwrap();
    (rawdata, range)
}

/*fn to_range<'a, F, U>(rawdata : &'a Vec<F>,  range : &'a Bounds<F>)
-> std::iter::Map<std::slice::Iter<'a, F>, impl FnMut(&'a F) -> U>
where F : Float + CastFrom<U> + num_traits::cast::AsPrimitive<U>,
      U : Unsigned {
    rawdata.iter().map(move |&v| scale_range_uint(v, range))
}*/

/// Convert a scalar value to an RGB triplet.
///
/// Converts the value `v` supposed to be within the range `[a, b]` to an rgb value according
/// to the given `ramp` of equally-spaced rgb interpolation points.
#[replace_float_literals(F::cast_from(literal))]
fn one_to_ramp<F, U>(
    &Bounds(a, b) : &Bounds<F>,
    ramp : &Vec<Loc<F, 3>>,
    v : F,
) -> Rgb<U>
where F : Float + CastFrom<U> + num_traits::cast::AsPrimitive<U>,
      U : Unsigned {

    let n = ramp.len() - 1;
    let m = F::cast_from(U::RANGE_MAX);
    let ramprange = move |v : F| {let m : usize = v.as_(); m.min(n).max(0) };

    let w = F::cast_from(n) * (v - a) / (b - a);  // convert [0, 1] to [0, n]
    let (l, u) = (w.floor(), w.ceil());           // Find closest integers
    let (rl, ru) = (ramprange(l), ramprange(u));
    let (cl, cu) = (ramp[rl], ramp[ru]);          // Get corresponding colours
    let λ = match rl==ru {                        // Interpolation factor
        true => 0.0,
        false => (u - w) / (u - l),
    };
    let Loc(rgb) = cl * λ + cu * (1.0 - λ);       // Interpolate

    Rgb(rgb.map(|v| (v * m).round().min(m).max(0.0).as_()))
}

/// Convert a an iterator over scalar values to an iterator over RGB triplets.
///
/// The conversion is that performed by [`one_to_ramp`].
#[replace_float_literals(F::cast_from(literal))]
fn to_ramp<'a, F, U, I>(
    bounds : &'a Bounds<F>,
    ramp : &'a Vec<Loc<F, 3>>,
    iter : I,
) -> std::iter::Map<I, impl FnMut(F) -> Rgb<U> + 'a>
where F : Float + CastFrom<U> + num_traits::cast::AsPrimitive<U>,
      U : Unsigned,
      I : Iterator<Item = F> + 'a {
    iter.map(move |v| one_to_ramp(bounds, ramp, v))
}

/// Convert a [`colorbrewer`] sepcification to a ramp of rgb triplets.
fn get_ramp<F : Float>((palette, nb) : (CbPalette, u32)) -> Vec<Loc<F, 3>> {
    let m = F::cast_from(u8::MAX);
    colorbrewer::get_color_ramp(palette, nb)
                 .expect("Invalid colorbrewer ramp")
                 .into_iter()
                 .map(|rgb::RGB{r, g, b}| {
                    [r, g, b].map(|c| F::cast_from(c) / m).into()
                 }).collect()
}

/// Perform hue shifting of an RGB value.
///
// The hue `ω` is in radians.
#[replace_float_literals(F::cast_from(literal))]
fn hueshift<F, U>(ω : F, Rgb([r_in, g_in, b_in]) : Rgb<U>) -> Rgb<U>
where F : Float + CastFrom<U>,
      U : Unsigned {
    let m = F::cast_from(U::RANGE_MAX);
    let r = F::cast_from(r_in) / m;
    let g = F::cast_from(g_in) / m;
    let b = F::cast_from(b_in) / m;
    let u = ω.cos();
    let w = ω.sin();

    let nr = (0.299 + 0.701*u + 0.168*w) * r
              + (0.587 - 0.587*u + 0.330*w) * g
              + (0.114 - 0.114*u - 0.497*w) * b;
    let ng = (0.299 - 0.299*u - 0.328*w) * r
              + (0.587 + 0.413*u + 0.035*w) * g
              + (0.114 - 0.114*u + 0.292*w) *b;
    let nb = (0.299 - 0.3*u + 1.25*w) * r
              + (0.587 - 0.588*u - 1.05*w) * g
              + (0.114 + 0.886*u - 0.203*w) * b;

    Rgb([nr, ng, nb].map(scale_uint))
}


impl Plotting<2> for PlotLookup {
    #[replace_float_literals(F::cast_from(literal))]
    fn plot_into_file_spikes<
        F : Float,
        T1 : RealMapping<F, 2>,
        T2 : RealMapping<F, 2>
    > (
        _g_explanation : String,
        g : &T1,
        _ω_explanation : String,
        ω0 : Option<&T2>,
        grid : LinGrid<F, 2>,
        _bnd0 : Option<Bounds<F>>,
        μ : &DiscreteMeasure<Loc<F, 2>, F>,
        filename : String,
    ) {
        let [w, h] = grid.count;
        let (rawdata_g, range_g) = rawdata_and_range(&grid, g);
        let (rawdata_ω, range) = match ω0 {
            Some(ω) => {
                let (rawdata_ω, range_ω) = rawdata_and_range(&grid, ω);
                (rawdata_ω, range_g.common(&range_ω))
            },
            None => {
                let mut zeros = Vec::new();
                zeros.resize(rawdata_g.len(), 0.0);
                (zeros, range_g)
            }
        };
        let ramp = get_ramp(RAMP);
        let base_im_iter = to_ramp::<F, u16, _>(&range_g, &ramp, rawdata_g.iter().cloned());
        let im_iter = izip!(base_im_iter, rawdata_g.iter(), rawdata_ω.iter())
            .map(|(rgb, &v, &w)| {
                hueshift(2.0 * F::PI * (v - w).abs() / range.upper(), rgb)
            });
        let mut img = ImageBuffer::new(w as u32, h as u32);
        img.pixels_mut()
           .zip(im_iter)
           .for_each(|(p, v)| *p = v);

        // Add spikes
        let m = μ.iter_masses().fold(F::ZERO, |m, α| m.max(α));
        let μ_range = Bounds(F::ZERO, m);
        for &DeltaMeasure{ ref x, α } in μ.iter_spikes() {
            let [a, b] = map4(x, &grid.start, &grid.end, &grid.count, |&ξ, &a, &b, &n| {
                ((ξ-a)/(b-a)*F::cast_from(n)).as_()
            });
            if a < w.as_() && b < h.as_() {
                let sc : u16 = scale_range_uint(α, &μ_range);
                // TODO: use max of points that map to this pixel.
                img[(a, b)] = Rgb([u16::MAX, u16::MAX, sc/2]);
            }
        }

        img.save_with_format(filename + ".png", ImageFormat::Png)
           .expect("Image save error");
    }

    fn plot_into_file<
        F : Float,
        T1 : RealMapping<F, 2>,
    > (
        g : &T1,
        grid : LinGrid<F, 2>,
        filename : String,
        _explanation : String
    ) {
        let [w, h] = grid.count;
        let (rawdata, range) = rawdata_and_range(&grid, g);
        let ramp = get_ramp(RAMP);
        let im_iter = to_ramp::<F, u16, _>(&range, &ramp, rawdata.iter().cloned());
        let mut img = ImageBuffer::new(w as u32, h as u32);
        img.pixels_mut()
           .zip(im_iter)
           .for_each(|(p, v)| *p = v);
        img.save_with_format(filename.clone() + ".png", ImageFormat::Png)
           .expect("Image save error");
        
        let csv_iter = grid.into_iter().zip(rawdata.iter()).map(|(Loc(x), &v)| (x, v));
        let csv_f = filename + ".txt";
        write_csv(csv_iter, csv_f).expect("CSV save error");
    }

}

/// A helper structure for plotting a sequence of images.
#[derive(Clone,Debug)]
pub struct SeqPlotter<F : Float, const N : usize> {
    /// File name prefix
    prefix : String,
    /// Maximum number of plots to perform
    max_plots : usize,
    /// Sampling grid
    grid : LinGrid<F, N>,
    /// Current plot count
    plot_count : usize,
}

impl<F : Float, const N : usize> SeqPlotter<F, N>
where PlotLookup : Plotting<N> {
    /// Creates a new sequence plotter instance
    pub fn new(prefix : String, max_plots : usize, grid : LinGrid<F, N>) -> Self {
        SeqPlotter { prefix, max_plots, grid, plot_count : 0 }
    }

    /// This calls [`PlotLookup::plot_into_file_spikes`] with a sequentially numbered file name.
    pub fn plot_spikes<T1, T2>(
        &mut self,
        g_explanation : String,
        g : &T1,
        ω_explanation : String,
        ω : Option<&T2>,
        tol : Option<Bounds<F>>,
        μ : &DiscreteMeasure<Loc<F, N>, F>,
    ) where T1 : RealMapping<F, N>,
            T2 : RealMapping<F, N>
    {
        if self.plot_count == 0 && self.max_plots > 0 {
            std::fs::create_dir_all(&self.prefix).expect("Unable to create plot directory");
        }
        if self.plot_count < self.max_plots {
            PlotLookup::plot_into_file_spikes(
                g_explanation, g,
                ω_explanation, ω,
                self.grid,
                tol,
                μ,
                format!("{}out{:03}", self.prefix, self.plot_count)
            );
            self.plot_count += 1;
        }
    }
}