統計解析R たぶんpart3くらい

統計解析R たぶんpart3くらい (587ﾚｽ)
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278: デフォルトの名無しさん [] 2019/06/09(日) 01:58:16.45 ID:wNZZZJ2C(1/3) AAS
[so]{#so}: [Showing existence of a diffeomorphism preserving volume forms](https://math.stackexchange.com/questions/2731058)

一次元だと積分表が使えるので絵を描いてみる [so-1]{#so-1}

``` {r}
big_data = list (`%>%` = purrr::`%>%`, add = rlist::list.append
, size = length, null = NULL, true = T, false = F, na = NA);
big_data = with (c (big_data, xa = 0, sa = 0.1, db = 1, sbm = 0.3
, sbp = 0.2), { pa = function (x) { dnorm (x, mean = xa, sd = sa); };
pb = function (x) { 0.5 * (dnorm (x, mean = - db, sd = sbm) + dnorm (x
, mean = db, sd = sbp)); }; Pa = function (x) { pnorm (x, mean = xa
, sd = sa); }; Pb = function (x) { 0.5 * (pnorm (x, mean = - db, sd = sbm)
+ pnorm (x, mean = db, sd = sbp)); }; ra = function (n) { rnorm (n
, mean = xa, sd = sa); }; rb = function (n) { sample (c (rnorm (n
, mean = - db, sd = sbm) , rnorm (n, mean = db, sd = sbp)), n); };
x = 3 * seq (- 1, 1, len = 1e+3); ya = pa (x); yb = pb (x); plot (range (x)
, range (ya, yb), type = 'n'); lines (x, ya, col = 'blue'); lines (x, yb
, col = 'red'); add (big_data, pa = pa, pb = pb, ra = ra, rb = rb, Pa = Pa
, Pb = Pb); }); no_plot = function (text = 'space') { plot (c (0, 1), c (0
, 1), ann = F, bty = 'n', type = 'n', xaxt = 'n', yaxt = 'n'); text (
x = 0.5, y = 0.5, text);};
```

279: デフォルトの名無しさん [] 2019/06/09(日) 01:59:10.30 ID:wNZZZJ2C(2/3) AAS
青の分布を赤の分布に連続的に変形させる [so-2]{#so-2}

``` {r}
big_data = with (c (big_data, nx = 2e+3, nt = 1e+3, alim = 2, blim = 4), {
vec = function (x, t) { (Pa (x) - Pb (x)) / ((1 - t) * pa (x) + t * pb (x));
}; t = seq (0, 1, len = nt); dt = diff (t) %>% mean; x = ra (nx); x = x0 =
x [which (abs (x) <= alim)]; x = purrr::map (t, function (t) { x <<- x +
dt * vec (x, t); }) %>% do.call (what = rbind); draw = function (t, x,
nbin = 20 , vector = null) { xlim = range (x, na.rm = true); plot ( xlim,
range (t), type = 'n', main = 'trajectories', xlab = 'x', ylab = 't');
purrr::map ( sample (1 : ncol (x), 50), function (j) { x = x [, j]; if (
all ( is.finite (x))) { lines (x, t); } else { points (x, t); }; }); if (
is.function (vector)) { no_plot (); }; doit = function (ind) { t = t [ind];
x = x [ind, ]; if (is.null (nbin)) { nbin = 'scott'; }; msg = sprintf (
'at the time %.1e', t); msg = c (msg, sprintf ('%d / %d', sum ( xlim [1] <=
abs (x) & abs (x) <= xlim [2], na.rm = true), size (x))); hist (x, breaks =
nbin, freq = false, xlim = xlim, main = msg); x = seq ( xlim [1], xlim [2],
len = 1e+3);
# lines (x, pa (x), col = 'blue');
lines (x, pb (x), col = 'red'); if (is.function (vector)) { x = seq (min (
xlim), max (xlim), len = 1e+5); plot (x, vector (t, x) %>% abs (), type =
'l', log = 'y', main = msg); }; }; for (i in c (1, size (t) / 2, size (
t))) { doit (i); } }; x = rbind (x0, x [- nrow (x), ]); x [which (blim <
abs (x))] = na; fix_bin = function (x, lim) { max (sum (abs (x [nrow (x)
, ]) <= lim , na.rm = true) / 50, 10) %>% as.integer (); }; draw (t, x
, nbin = fix_bin (x, blim), vector = vec); add (big_data, x0 = x0, t = t
, dt = dt , nt = nt, nx = nx, vec = vec, draw = draw, fix_bin = fix_bin
, alim = alim, blim = blim);});
```

280: デフォルトの名無しさん [] 2019/06/09(日) 02:00:21.38 ID:wNZZZJ2C(3/3) AAS
逆方向に変形させてみる [so-3]{#so-3}

``` {r}
with (c (big_data), {
wec = function (x, t) {
- vec (x, 1 - t);
};
x = rb (nx);
x = x0 = x [which (abs (x) <= blim)];
x = purrr::map (t, function (t) {
x <<- x + dt * wec (x, t);
}) %>% do.call (what = rbind);
x = rbind (x0, x [- nrow (x), ]);
x [which (blim < abs (x))] = na;
draw (t, x, nbin = fix_bin (x, blim), vector = wec);
});
```

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