diff -r 000000000000 -r eb3c7813b67a src/plot.rs
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/plot.rs	Thu Dec 01 23:07:35 2022 +0200
@@ -0,0 +1,413 @@
+//! 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;
+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
+    );
+}
+
+/// 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;
+        }
+    }
+}