\documentclass[a4paper, 12pt]{article}

% a nice font
\usepackage{kpfonts}

% basic text stuff
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}

\usepackage{pgfplots}
\pgfplotsset{
    compat = 1.17, % to have the same coordinate system between axis and draw
}

\usepackage{tikz} % main tikz package
\usepackage{tikz-network} % provides graph / network utilities (Edge, Node, etc)

% for a nicer colorscheme
\input{colors.tex}

\begin{document}
    \begin{tikzpicture}[>=stealth']
        \begin{axis} [yscale=0.7,xscale=2.,domain=0:2.1,ymin=-1,samples=200,no markers,hide y axis,xtick=\empty,axis lines=middle,xlabel=$t$,]
         \addplot[color=darkblue, ultra thin] {0.5*cos(deg(5.0*x + 100.0))+0.25*cos(deg(9.0*x + 100.0))+0.1*cos(deg(10*x + 10))+0.2*cos(deg(20.0*x + 0))};
         \coordinate (p0) at (0.10,0.65);
         \coordinate (p0_orig) at (0.10,0.00);
         \draw[dotted, thin] (p0) -- (p0_orig);
         \definecolor{tempcolor_line_graph_0}{RGB}{ 182, 64, 45 };
         \node[ultra thick, color=tempcolor_line_graph_0] at (p0) {$\bullet$};
         \coordinate (p1) at (0.18,0.48);
         \coordinate (p1_orig) at (0.18,0.00);
         \draw[dotted, thin] (p1) -- (p1_orig);
         \definecolor{tempcolor_line_graph_1}{RGB}{ 190, 80, 51 };
         \node[ultra thick, color=tempcolor_line_graph_1] at (p1) {$\bullet$};
         \coordinate (p2) at (0.26,0.49);
         \coordinate (p2_orig) at (0.26,0.00);
         \draw[dotted, thin] (p2) -- (p2_orig);
         \definecolor{tempcolor_line_graph_2}{RGB}{ 190, 80, 51 };
         \node[ultra thick, color=tempcolor_line_graph_2] at (p2) {$\bullet$};
         \coordinate (p3) at (0.34,0.25);
         \coordinate (p3_orig) at (0.34,0.00);
         \draw[dotted, thin] (p3) -- (p3_orig);
         \definecolor{tempcolor_line_graph_3}{RGB}{ 203, 105, 62 };
         \node[ultra thick, color=tempcolor_line_graph_3] at (p3) {$\bullet$};
         \coordinate (p4) at (0.42,-0.34);
         \coordinate (p4_orig) at (0.42,0.00);
         \draw[dotted, thin] (p4) -- (p4_orig);
         \definecolor{tempcolor_line_graph_4}{RGB}{ 231, 162, 85 };
         \node[ultra thick, color=tempcolor_line_graph_4] at (p4) {$\bullet$};
         \coordinate (p5) at (0.50,-0.61);
         \coordinate (p5_orig) at (0.50,0.00);
         \draw[dotted, thin] (p5) -- (p5_orig);
         \definecolor{tempcolor_line_graph_5}{RGB}{ 244, 188, 95 };
         \node[ultra thick, color=tempcolor_line_graph_5] at (p5) {$\bullet$};
         \coordinate (p6) at (0.57,-0.37);
         \coordinate (p6_orig) at (0.57,0.00);
         \draw[dotted, thin] (p6) -- (p6_orig);
         \definecolor{tempcolor_line_graph_6}{RGB}{ 234, 167, 87 };
         \node[ultra thick, color=tempcolor_line_graph_6] at (p6) {$\bullet$};
         \coordinate (p7) at (0.65,-0.20);
         \coordinate (p7_orig) at (0.65,0.00);
         \draw[dotted, thin] (p7) -- (p7_orig);
         \definecolor{tempcolor_line_graph_7}{RGB}{ 224, 147, 78 };
         \node[ultra thick, color=tempcolor_line_graph_7] at (p7) {$\bullet$};
         \coordinate (p8) at (0.73,-0.35);
         \coordinate (p8_orig) at (0.73,0.00);
         \draw[dotted, thin] (p8) -- (p8_orig);
         \definecolor{tempcolor_line_graph_8}{RGB}{ 231, 162, 85 };
         \node[ultra thick, color=tempcolor_line_graph_8] at (p8) {$\bullet$};
         \coordinate (p9) at (0.81,-0.34);
         \coordinate (p9_orig) at (0.81,0.00);
         \draw[dotted, thin] (p9) -- (p9_orig);
         \definecolor{tempcolor_line_graph_9}{RGB}{ 231, 162, 85 };
         \node[ultra thick, color=tempcolor_line_graph_9] at (p9) {$\bullet$};
         \coordinate (p10) at (0.89,-0.06);
         \coordinate (p10_orig) at (0.89,0.00);
         \draw[dotted, thin] (p10) -- (p10_orig);
         \definecolor{tempcolor_line_graph_10}{RGB}{ 218, 136, 74 };
         \node[ultra thick, color=tempcolor_line_graph_10] at (p10) {$\bullet$};
         \coordinate (p11) at (0.97,-0.04);
         \coordinate (p11_orig) at (0.97,0.00);
         \draw[dotted, thin] (p11) -- (p11_orig);
         \definecolor{tempcolor_line_graph_11}{RGB}{ 216, 131, 72 };
         \node[ultra thick, color=tempcolor_line_graph_11] at (p11) {$\bullet$};
         \coordinate (p12) at (1.05,-0.33);
         \coordinate (p12_orig) at (1.05,0.00);
         \draw[dotted, thin] (p12) -- (p12_orig);
         \definecolor{tempcolor_line_graph_12}{RGB}{ 231, 162, 85 };
         \node[ultra thick, color=tempcolor_line_graph_12] at (p12) {$\bullet$};
         \coordinate (p13) at (1.13,-0.29);
         \coordinate (p13_orig) at (1.13,0.00);
         \draw[dotted, thin] (p13) -- (p13_orig);
         \definecolor{tempcolor_line_graph_13}{RGB}{ 229, 157, 83 };
         \node[ultra thick, color=tempcolor_line_graph_13] at (p13) {$\bullet$};
         \coordinate (p14) at (1.21,0.22);
         \coordinate (p14_orig) at (1.21,0.00);
         \draw[dotted, thin] (p14) -- (p14_orig);
         \definecolor{tempcolor_line_graph_14}{RGB}{ 203, 105, 62 };
         \node[ultra thick, color=tempcolor_line_graph_14] at (p14) {$\bullet$};
         \coordinate (p15) at (1.29,0.58);
         \coordinate (p15_orig) at (1.29,0.00);
         \draw[dotted, thin] (p15) -- (p15_orig);
         \definecolor{tempcolor_line_graph_15}{RGB}{ 185, 69, 47 };
         \node[ultra thick, color=tempcolor_line_graph_15] at (p15) {$\bullet$};
         \coordinate (p16) at (1.37,0.57);
         \coordinate (p16_orig) at (1.37,0.00);
         \draw[dotted, thin] (p16) -- (p16_orig);
         \definecolor{tempcolor_line_graph_16}{RGB}{ 185, 69, 47 };
         \node[ultra thick, color=tempcolor_line_graph_16] at (p16) {$\bullet$};
         \coordinate (p17) at (1.45,0.62);
         \coordinate (p17_orig) at (1.45,0.00);
         \draw[dotted, thin] (p17) -- (p17_orig);
         \definecolor{tempcolor_line_graph_17}{RGB}{ 182, 64, 45 };
         \node[ultra thick, color=tempcolor_line_graph_17] at (p17) {$\bullet$};
         \coordinate (p18) at (1.52,0.77);
         \coordinate (p18_orig) at (1.52,0.00);
         \draw[dotted, thin] (p18) -- (p18_orig);
         \definecolor{tempcolor_line_graph_18}{RGB}{ 177, 54, 41 };
         \node[ultra thick, color=tempcolor_line_graph_18] at (p18) {$\bullet$};
         \coordinate (p19) at (1.60,0.45);
         \coordinate (p19_orig) at (1.60,0.00);
         \draw[dotted, thin] (p19) -- (p19_orig);
         \definecolor{tempcolor_line_graph_19}{RGB}{ 193, 85, 53 };
         \node[ultra thick, color=tempcolor_line_graph_19] at (p19) {$\bullet$};
         \coordinate (p20) at (1.68,-0.27);
         \coordinate (p20_orig) at (1.68,0.00);
         \draw[dotted, thin] (p20) -- (p20_orig);
         \definecolor{tempcolor_line_graph_20}{RGB}{ 229, 157, 83 };
         \node[ultra thick, color=tempcolor_line_graph_20] at (p20) {$\bullet$};
         \coordinate (p21) at (1.76,-0.67);
         \coordinate (p21_orig) at (1.76,0.00);
         \draw[dotted, thin] (p21) -- (p21_orig);
         \definecolor{tempcolor_line_graph_21}{RGB}{ 247, 193, 97 };
         \node[ultra thick, color=tempcolor_line_graph_21] at (p21) {$\bullet$};
         \coordinate (p22) at (1.84,-0.57);
         \coordinate (p22_orig) at (1.84,0.00);
         \draw[dotted, thin] (p22) -- (p22_orig);
         \definecolor{tempcolor_line_graph_22}{RGB}{ 244, 188, 95 };
         \node[ultra thick, color=tempcolor_line_graph_22] at (p22) {$\bullet$};
         \coordinate (p23) at (1.92,-0.50);
         \coordinate (p23_orig) at (1.92,0.00);
         \draw[dotted, thin] (p23) -- (p23_orig);
         \definecolor{tempcolor_line_graph_23}{RGB}{ 239, 178, 91 };
         \node[ultra thick, color=tempcolor_line_graph_23] at (p23) {$\bullet$};
         \coordinate (p24) at (2.00,-0.57);
         \coordinate (p24_orig) at (2.00,0.00);
         \draw[dotted, thin] (p24) -- (p24_orig);
         \definecolor{tempcolor_line_graph_24}{RGB}{ 242, 183, 93 };
         \node[ultra thick, color=tempcolor_line_graph_24] at (p24) {$\bullet$};
        \end{axis}

        \Vertex[x=0.70,y=0.,size=0.2,color={182,64,45},RGB]{0}
        \Vertex[x=1.21,y=0.,size=0.2,color={190,80,51},RGB]{1}
        \Vertex[x=1.73,y=0.,size=0.2,color={190,80,51},RGB]{2}
        \Vertex[x=2.24,y=0.,size=0.2,color={203,105,62},RGB]{3}
        \Vertex[x=2.75,y=0.,size=0.2,color={231,162,85},RGB]{4}
        \Vertex[x=3.26,y=0.,size=0.2,color={244,188,95},RGB]{5}
        \Vertex[x=3.78,y=0.,size=0.2,color={234,167,87},RGB]{6}
        \Vertex[x=4.29,y=0.,size=0.2,color={224,147,78},RGB]{7}
        \Vertex[x=4.80,y=0.,size=0.2,color={231,162,85},RGB]{8}
        \Vertex[x=5.32,y=0.,size=0.2,color={231,162,85},RGB]{9}
        \Vertex[x=5.83,y=0.,size=0.2,color={218,136,74},RGB]{10}
        \Vertex[x=6.34,y=0.,size=0.2,color={216,131,72},RGB]{11}
        \Vertex[x=6.85,y=0.,size=0.2,color={231,162,85},RGB]{12}
        \Vertex[x=7.37,y=0.,size=0.2,color={229,157,83},RGB]{13}
        \Vertex[x=7.88,y=0.,size=0.2,color={203,105,62},RGB]{14}
        \Vertex[x=8.39,y=0.,size=0.2,color={185,69,47},RGB]{15}
        \Vertex[x=8.91,y=0.,size=0.2,color={185,69,47},RGB]{16}
        \Vertex[x=9.42,y=0.,size=0.2,color={182,64,45},RGB]{17}
        \Vertex[x=9.93,y=0.,size=0.2,color={177,54,41},RGB]{18}
        \Vertex[x=10.44,y=0.,size=0.2,color={193,85,53},RGB]{19}
        \Vertex[x=10.96,y=0.,size=0.2,color={229,157,83},RGB]{20}
        \Vertex[x=11.47,y=0.,size=0.2,color={247,193,97},RGB]{21}
        \Vertex[x=11.98,y=0.,size=0.2,color={244,188,95},RGB]{22}
        \Vertex[x=12.49,y=0.,size=0.2,color={239,178,91},RGB]{23}
        \Vertex[x=13.01,y=0.,size=0.2,color={242,183,93},RGB]{24}
        \Edge[lw=0.5,Direct](0)(1)
        \Edge[lw=0.5,Direct](1)(2)
        \Edge[lw=0.5,Direct](2)(3)
        \Edge[lw=0.5,Direct](3)(4)
        \Edge[lw=0.5,Direct](4)(5)
        \Edge[lw=0.5,Direct](5)(6)
        \Edge[lw=0.5,Direct](6)(7)
        \Edge[lw=0.5,Direct](7)(8)
        \Edge[lw=0.5,Direct](8)(9)
        \Edge[lw=0.5,Direct](9)(10)
        \Edge[lw=0.5,Direct](10)(11)
        \Edge[lw=0.5,Direct](11)(12)
        \Edge[lw=0.5,Direct](12)(13)
        \Edge[lw=0.5,Direct](13)(14)
        \Edge[lw=0.5,Direct](14)(15)
        \Edge[lw=0.5,Direct](15)(16)
        \Edge[lw=0.5,Direct](16)(17)
        \Edge[lw=0.5,Direct](17)(18)
        \Edge[lw=0.5,Direct](18)(19)
        \Edge[lw=0.5,Direct](19)(20)
        \Edge[lw=0.5,Direct](20)(21)
        \Edge[lw=0.5,Direct](21)(22)
        \Edge[lw=0.5,Direct](22)(23)
        \Edge[lw=0.5,Direct](23)(24)
    \end{tikzpicture}
\end{document}

# ---
# jupyter:
#   jupytext:
#     formats: ipynb,py:light
#     text_representation:
#       extension: .py
#       format_name: light
#       format_version: '1.5'
#       jupytext_version: 1.4.0
#   kernelspec:
#     display_name: Python 3
#     language: python
#     name: python3
# ---

import networkx as nx
import network2tikz as n2t
import numpy as np
import matplotlib.pyplot as plt

# +
# my colors

blue = 255 * np.array([0.38, 0.51,0.71])
darkblue = [17,42,60]
red = [175,49,39]
orange=[217, 156, 55]
green=[144, 169, 84]
palegreen=[197, 184, 104]
yellow=[250, 199, 100]
brokenwhite=[218, 192, 166]
brokengrey = 255 * np.array([0.77, 0.76, 0.82])


# +
# from https://bsou.io/posts/color-gradients-with-python
def hex_to_RGB(hex):
    ''' "#FFFFFF" -> [255,255,255] '''
    # Pass 16 to the integer function for change of base
    return [int(hex[i:i+2], 16) for i in range(1,6,2)]


def RGB_to_hex(RGB):
    ''' [255,255,255] -> "#FFFFFF" '''
    # Components need to be integers for hex to make sense
    RGB = [int(x) for x in RGB]
    return "#"+"".join(["0{0:x}".format(v) if v < 16 else
            "{0:x}".format(v) for v in RGB])

def color_dict(gradient):
    ''' Takes in a list of RGB sub-lists and returns dictionary of
    colors in RGB and hex form for use in a graphing function
    defined later on '''
    return {"hex":[RGB_to_hex(RGB) for RGB in gradient],
      "r":[RGB[0] for RGB in gradient],
      "g":[RGB[1] for RGB in gradient],
      "b":[RGB[2] for RGB in gradient]}


def linear_gradient(start_hex, finish_hex="#FFFFFF", n=10):
    ''' returns a gradient list of (n) colors between
    two hex colors. start_hex and finish_hex
    should be the full six-digit color string,
    inlcuding the number sign ("#FFFFFF") '''
    # Starting and ending colors in RGB form
    s = hex_to_RGB(start_hex)
    f = hex_to_RGB(finish_hex)
    # Initilize a list of the output colors with the starting color
    RGB_list = [s]
    # Calcuate a color at each evenly spaced value of t from 1 to n
    for t in range(1, n):
        # Interpolate RGB vector for color at the current value of t
        curr_vector = [int(s[j] + (float(t)/(n-1))*(f[j]-s[j])) for j in range(3)]
        # Add it to our list of output colors
        RGB_list.append(curr_vector)

    return color_dict(RGB_list)



# -

def s(t):
    coeffs = [0.5, 0.25, 0.1, 0.2]
    pulses = [5., 9., 10, 20.]
    phases = [100., 100., 10, 0]
    print("\t\\addplot[color=darkblue, ultra thin] {"+"+".join(["{}*cos(deg({}*x + {}))".format(c,w,p) for c,w,p in zip(coeffs,pulses,phases)]) + "};")
    return sum([c*np.cos(w*t+phi) for c,w,phi in zip(coeffs,pulses,phases)])


plt.plot(s(np.linspace(0,2,100)))

X = np.linspace(0.1,2,25)

# +
print("\\begin{axis} [domain=0:2.1,samples=200,no markers,hide y axis,xtick=\empty,axis lines=middle,xlabel=$t$,]")

low = yellow
high = red
bins_nb = 30
Y = s(X)
eps = 1e-6
bins = np.linspace(Y.min()-eps,Y.max()+eps,bins_nb-1)
colors = np.array([hex_to_RGB(linear_gradient(RGB_to_hex(low), RGB_to_hex(high), bins_nb)['hex'][i]) for i in range(bins_nb)])
colors_tuples = [(c[0],c[1], c[2]) for c in colors[np.digitize(Y,bins)]]


for i,(x,y, col) in enumerate(zip(X,Y, colors_tuples)):
    #print("{}: {},{}".format(i,x,y))
    print("\t\\coordinate (p{}) at ({:.2f},{:.2f});".format(i,x,y))
    print("\t\\coordinate (p{}_orig) at ({:.2f},{:.2f});".format(i,x,0.0))
    print("\t\\draw[dotted, thin] (p{}) -- (p{}_orig);".format(i,i))
    print("\t\definecolor{{tempcolor_line_graph_{}}}{{RGB}}{{ {}, {}, {} }};".format(i, *col))
    print("\t\\node[ultra thick, color=tempcolor_line_graph_{}] at (p{}) {{$\\bullet$}};".format(i,i))

print("\\end{axis}")
# -

# now print the corresponding line graph
import networkx as nx

n = X.shape[0]
G = nx.path_graph(25)

nx.draw_spring(G)

visual_style = {}
visual_style['vertex_color'] = colors_tuples
visual_style['vertex_size'] = 0.2
visual_style['edge_curved'] = 0.1

# +
layout = nx.spectral_layout(G)
#layout = {i:np.array([2*i, 0]) for i in range(n)}
#layout

n2t.plot(G, "test.tex", standalone=False, layout=layout, **visual_style)
# -

for i,c in enumerate(colors_tuples):
    print("\\Vertex[x={:.2f},y=0.,size=0.2,color={{{},{},{}}},RGB]{{{}}}".format(0.7+i/1.95,*c,i))
for i,c in enumerate(colors_tuples[:-1]):
    print("\\Edge[lw=0.5,Direct]({})({})".format(i, i+1))