micropython-ulab/code/approx.c
2020-05-18 19:44:26 +02:00

396 lines
16 KiB
C

/*
* This file is part of the micropython-ulab project,
*
* https://github.com/v923z/micropython-ulab
*
* The MIT License (MIT)
*
* Copyright (c) 2020 Zoltán Vörös
*/
#include <math.h>
#include <stdlib.h>
#include <string.h>
#include "py/obj.h"
#include "py/runtime.h"
#include "py/misc.h"
#include "linalg.h"
#include "approx.h"
#if ULAB_APPROX_MODULE
const mp_obj_float_t xtolerance = {{&mp_type_float}, 2.4e-7};
const mp_obj_float_t rtolerance = {{&mp_type_float}, 0.0};
mp_float_t approx_python_call(const mp_obj_type_t *type, mp_obj_t fun, mp_float_t x, mp_obj_t *fargs, uint8_t nparams) {
// Helper function for calculating the value of f(x, a, b, c, ...),
// where f is defined in python. Takes a float, returns a float.
// The array of mp_obj_t type must be supplied, as must the number of parameters (a, b, c...) in nparams
fargs[0] = mp_obj_new_float(x);
return mp_obj_get_float(type->call(fun, nparams+1, 0, fargs));
}
mp_obj_t approx_bisect(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
// Simple bisection routine
static const mp_arg_t allowed_args[] = {
{ MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
{ MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
{ MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none} },
{ MP_QSTR_xtol, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = MP_ROM_PTR(&xtolerance)} },
{ MP_QSTR_maxiter, MP_ARG_KW_ONLY | MP_ARG_INT, {.u_int = 100} },
};
mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)];
mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args);
mp_obj_t fun = args[0].u_obj;
const mp_obj_type_t *type = mp_obj_get_type(fun);
if(type->call == NULL) {
mp_raise_TypeError(translate("first argument must be a function"));
}
mp_float_t xtol = mp_obj_get_float(args[3].u_obj);
mp_obj_t *fargs = m_new(mp_obj_t, 1);
mp_float_t left, right;
mp_float_t x_mid;
mp_float_t a = mp_obj_get_float(args[1].u_obj);
mp_float_t b = mp_obj_get_float(args[2].u_obj);
left = approx_python_call(type, fun, a, fargs, 0);
right = approx_python_call(type, fun, b, fargs, 0);
if(left * right > 0) {
mp_raise_ValueError(translate("function has the same sign at the ends of interval"));
}
mp_float_t rtb = left < 0.0 ? a : b;
mp_float_t dx = left < 0.0 ? b - a : a - b;
for(uint16_t i=0; i < args[4].u_int; i++) {
dx *= 0.5;
x_mid = rtb + dx;
if(approx_python_call(type, fun, x_mid, fargs, 0) < 0.0) {
rtb = x_mid;
}
if(MICROPY_FLOAT_C_FUN(fabs)(dx) < xtol) break;
}
return mp_obj_new_float(rtb);
}
MP_DEFINE_CONST_FUN_OBJ_KW(approx_bisect_obj, 3, approx_bisect);
mp_obj_t approx_newton(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
// this is actually the secant method, as the first derivative of the function
// is not accepted as an argument. The function whose root we want to solve for
// must depend on a single variable without parameters, i.e., f(x)
static const mp_arg_t allowed_args[] = {
{ MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
{ MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
{ MP_QSTR_tol, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = MP_ROM_PTR(&xtolerance)} },
{ MP_QSTR_rtol, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = MP_ROM_PTR(&rtolerance)} },
{ MP_QSTR_maxiter, MP_ARG_KW_ONLY | MP_ARG_INT, {.u_int = 50} },
};
mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)];
mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args);
mp_obj_t fun = args[0].u_obj;
const mp_obj_type_t *type = mp_obj_get_type(fun);
if(type->call == NULL) {
mp_raise_TypeError(translate("first argument must be a function"));
}
mp_float_t x = mp_obj_get_float(args[1].u_obj);
mp_float_t tol = mp_obj_get_float(args[2].u_obj);
mp_float_t rtol = mp_obj_get_float(args[3].u_obj);
mp_float_t dx, df, fx;
dx = x > 0.0 ? APPROX_EPS * x : -APPROX_EPS * x;
mp_obj_t *fargs = m_new(mp_obj_t, 1);
for(uint16_t i=0; i < args[4].u_int; i++) {
fx = approx_python_call(type, fun, x, fargs, 0);
df = (approx_python_call(type, fun, x + dx, fargs, 0) - fx) / dx;
dx = fx / df;
x -= dx;
if(MICROPY_FLOAT_C_FUN(fabs)(dx) < (tol + rtol * MICROPY_FLOAT_C_FUN(fabs)(x))) break;
}
return mp_obj_new_float(x);
}
MP_DEFINE_CONST_FUN_OBJ_KW(approx_newton_obj, 2, approx_newton);
mp_obj_t approx_fmin(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
// downhill simplex method in 1D
static const mp_arg_t allowed_args[] = {
{ MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
{ MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
{ MP_QSTR_xatol, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = MP_ROM_PTR(&xtolerance)} },
{ MP_QSTR_fatol, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = MP_ROM_PTR(&xtolerance)} },
{ MP_QSTR_maxiter, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = mp_const_none} },
};
mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)];
mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args);
mp_obj_t fun = args[0].u_obj;
const mp_obj_type_t *type = mp_obj_get_type(fun);
if(type->call == NULL) {
mp_raise_TypeError(translate("first argument must be a function"));
}
// parameters controlling convergence conditions
mp_float_t xatol = mp_obj_get_float(args[2].u_obj);
mp_float_t fatol = mp_obj_get_float(args[3].u_obj);
uint16_t maxiter = args[4].u_obj == mp_const_none ? 200 : mp_obj_get_int(args[4].u_obj);
mp_float_t x0 = mp_obj_get_float(args[1].u_obj);
mp_float_t x1 = x0 != 0.0 ? (1.0 + APPROX_NONZDELTA) * x0 : APPROX_ZDELTA;
mp_obj_t *fargs = m_new(mp_obj_t, 1);
mp_float_t f0 = approx_python_call(type, fun, x0, fargs, 0);
mp_float_t f1 = approx_python_call(type, fun, x1, fargs, 0);
if(f1 < f0) {
SWAP(mp_float_t, x0, x1);
SWAP(mp_float_t, f0, f1);
}
for(uint16_t i=0; i < maxiter; i++) {
uint8_t shrink = 0;
f0 = approx_python_call(type, fun, x0, fargs, 0);
f1 = approx_python_call(type, fun, x1, fargs, 0);
// reflection
mp_float_t xr = (1.0 + APPROX_ALPHA) * x0 - APPROX_ALPHA * x1;
mp_float_t fr = approx_python_call(type, fun, xr, fargs, 0);
if(fr < f0) { // expansion
mp_float_t xe = (1 + APPROX_ALPHA * APPROX_BETA) * x0 - APPROX_ALPHA * APPROX_BETA * x1;
mp_float_t fe = approx_python_call(type, fun, xe, fargs, 0);
if(fe < fr) {
x1 = xe;
f1 = fe;
} else {
x1 = xr;
f1 = fr;
}
} else {
if(fr < f1) { // contraction
mp_float_t xc = (1 + APPROX_GAMMA * APPROX_ALPHA) * x0 - APPROX_GAMMA * APPROX_ALPHA * x1;
mp_float_t fc = approx_python_call(type, fun, xc, fargs, 0);
if(fc < fr) {
x1 = xc;
f1 = fc;
} else {
shrink = 1;
}
} else { // inside contraction
mp_float_t xc = (1.0 - APPROX_GAMMA) * x0 + APPROX_GAMMA * x1;
mp_float_t fc = approx_python_call(type, fun, xc, fargs, 0);
if(fc < f1) {
x1 = xc;
f1 = fc;
} else {
shrink = 1;
}
}
if(shrink == 1) {
x1 = x0 + APPROX_DELTA * (x1 - x0);
f1 = approx_python_call(type, fun, x1, fargs, 0);
}
if((MICROPY_FLOAT_C_FUN(fabs)(f1 - f0) < fatol) ||
(MICROPY_FLOAT_C_FUN(fabs)(x1 - x0) < xatol)) {
break;
}
if(f1 < f0) {
SWAP(mp_float_t, x0, x1);
SWAP(mp_float_t, f0, f1);
}
}
}
return mp_obj_new_float(x0);
}
MP_DEFINE_CONST_FUN_OBJ_KW(approx_fmin_obj, 2, approx_fmin);
#if 0
static void approx_jacobi(const mp_obj_type_t *type, mp_obj_t fun, mp_float_t *x, mp_float_t *y, uint16_t len, mp_float_t *params, uint8_t nparams, mp_float_t *jacobi, mp_float_t *grad) {
/* Calculates the Jacobian and the gradient of the cost function
*
* The entries in the Jacobian are
* J(m, n) = de_m/da_n,
*
* where
*
* e_m = (f(x_m, a1, a2, ...) - y_m)/sigma_m is the error at x_m,
*
* and
*
* a1, a2, ..., a_n are the free parameters
*/
mp_obj_t *fargs0 = m_new(mp_obj_t, lenp+1);
mp_obj_t *fargs1 = m_new(mp_obj_t, lenp+1);
for(uint8_t p=0; p < nparams; p++) {
fargs0[p+1] = mp_obj_new_float(params[p]);
fargs1[p+1] = mp_obj_new_float(params[p]);
}
for(uint8_t p=0; p < nparams; p++) {
mp_float_t da = params[p] != 0.0 ? (1.0 + APPROX_NONZDELTA) * params[p] : APPROX_ZDELTA;
fargs1[p+1] = mp_obj_new_float(params[p] + da);
grad[p] = 0.0;
for(uint16_t i=0; i < len; i++) {
mp_float_t f0 = approx_python_call(type, fun, x[i], fargs0, nparams);
mp_float_t f1 = approx_python_call(type, fun, x[i], fargs1, nparams);
jacobi[i*nparamp+p] = (f1 - f0) / da;
grad[p] += (f0 - y[i]) * jacobi[i*nparamp+p];
}
fargs1[p+1] = fargs0[p+1]; // set back to the original value
}
}
static void approx_delta(mp_float_t *jacobi, mp_float_t *grad, uint16_t len, uint8_t nparams, mp_float_t lambda) {
//
}
mp_obj_t approx_curve_fit(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
// Levenberg-Marquardt non-linear fit
// The implementation follows the introductory discussion in Mark Tanstrum's paper, https://arxiv.org/abs/1201.5885
static const mp_arg_t allowed_args[] = {
{ MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
{ MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
{ MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
{ MP_QSTR_p0, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
{ MP_QSTR_xatol, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = MP_ROM_PTR(&xtolerance)} },
{ MP_QSTR_fatol, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = MP_ROM_PTR(&xtolerance)} },
{ MP_QSTR_maxiter, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = mp_const_none} },
};
mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)];
mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args);
mp_obj_t fun = args[0].u_obj;
const mp_obj_type_t *type = mp_obj_get_type(fun);
if(type->call == NULL) {
mp_raise_TypeError(translate("first argument must be a function"));
}
mp_obj_t x_obj = args[1].u_obj;
mp_obj_t y_obj = args[2].u_obj;
mp_obj_t p0_obj = args[3].u_obj;
if(!ndarray_object_is_nditerable(x_obj) || !ndarray_object_is_nditerable(y_obj)) {
mp_raise_TypeError(translate("data must be iterable"));
}
if(!ndarray_object_is_nditerable(p0_obj)) {
mp_raise_TypeError(translate("initial values must be iterable"));
}
uint16_t len = (uint16_t)mp_obj_get_int(mp_obj_len_maybe(x_obj));
uint8_t lenp = (uint8_t)mp_obj_get_int(mp_obj_len_maybe(p0_obj));
if(len != (uint16_t)mp_obj_get_int(mp_obj_len_maybe(y_obj))) {
mp_raise_ValueError(translate("data must be of equal length"));
}
mp_float_t *x = m_new(mp_float_t, len);
fill_array_iterable(x, x_obj);
mp_float_t *y = m_new(mp_float_t, len);
fill_array_iterable(y, y_obj);
mp_float_t *p0 = m_new(mp_float_t, lenp);
fill_array_iterable(p0, p0_obj);
mp_float_t *grad = m_new(mp_float_t, len);
mp_float_t *jacobi = m_new(mp_float_t, len*len);
mp_obj_t *fargs = m_new(mp_obj_t, lenp+1);
m_del(mp_float_t, p0, lenp);
// parameters controlling convergence conditions
//mp_float_t xatol = mp_obj_get_float(args[2].u_obj);
//mp_float_t fatol = mp_obj_get_float(args[3].u_obj);
// this has finite binary representation; we will multiply/divide by 4
//mp_float_t lambda = 0.0078125;
//linalg_invert_matrix(mp_float_t *data, size_t N)
m_del(mp_float_t, x, len);
m_del(mp_float_t, y, len);
m_del(mp_float_t, grad, len);
m_del(mp_float_t, jacobi, len*len);
m_del(mp_obj_t, fargs, lenp+1);
return mp_const_none;
}
MP_DEFINE_CONST_FUN_OBJ_KW(approx_curve_fit_obj, 2, approx_curve_fit);
#endif
mp_obj_t approx_interp(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
static const mp_arg_t allowed_args[] = {
{ MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
{ MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
{ MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
{ MP_QSTR_left, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = mp_const_none} },
{ MP_QSTR_right, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = mp_const_none} },
};
mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)];
mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args);
ndarray_obj_t *x = ndarray_from_mp_obj(args[0].u_obj);
ndarray_obj_t *xp = ndarray_from_mp_obj(args[1].u_obj); // xp must hold an increasing sequence of independent values
ndarray_obj_t *fp = ndarray_from_mp_obj(args[2].u_obj);
// TODO: check if the shape is (1, n), or (m, 1)
if(((xp->m != 1) && (xp->n != 1)) || ((fp->m != 1) && (fp->n != 1)) ||
(xp->array->len < 2) || (fp->array->len < 2) || (xp->array->len != fp->array->len)) {
mp_raise_ValueError(translate("interp is defined for 1D arrays of equal length"));
}
ndarray_obj_t *y = create_new_ndarray(x->m, x->n, NDARRAY_FLOAT);
mp_float_t left_value, right_value;
mp_float_t xp_left = ndarray_get_float_value(xp->array->items, xp->array->typecode, 0);
mp_float_t xp_right = ndarray_get_float_value(xp->array->items, xp->array->typecode, xp->array->len-1);
if(args[3].u_obj == mp_const_none) {
left_value = ndarray_get_float_value(fp->array->items, fp->array->typecode, 0);
} else {
left_value = mp_obj_get_float(args[3].u_obj);
}
if(args[4].u_obj == mp_const_none) {
right_value = ndarray_get_float_value(fp->array->items, fp->array->typecode, fp->array->len-1);
} else {
right_value = mp_obj_get_float(args[4].u_obj);
}
mp_float_t *yarray = (mp_float_t *)y->array->items;
for(size_t i=0; i < x->array->len; i++, yarray++) {
mp_float_t x_value = ndarray_get_float_value(x->array->items, x->array->typecode, i);
if(x_value <= xp_left) {
*yarray = left_value;
} else if(x_value >= xp_right) {
*yarray = right_value;
} else { // do the binary search here
mp_float_t xp_left_, xp_right_;
mp_float_t fp_left, fp_right;
size_t left_index = 0, right_index = xp->array->len - 1, middle_index;
while(right_index - left_index > 1) {
middle_index = left_index + (right_index - left_index) / 2;
mp_float_t xp_middle = ndarray_get_float_value(xp->array->items, xp->array->typecode, middle_index);
if(x_value <= xp_middle) {
right_index = middle_index;
} else {
left_index = middle_index;
}
}
xp_left_ = ndarray_get_float_value(xp->array->items, xp->array->typecode, left_index);
xp_right_ = ndarray_get_float_value(xp->array->items, xp->array->typecode, right_index);
fp_left = ndarray_get_float_value(fp->array->items, fp->array->typecode, left_index);
fp_right = ndarray_get_float_value(fp->array->items, fp->array->typecode, right_index);
*yarray = fp_left + (x_value - xp_left_) * (fp_right - fp_left) / (xp_right_ - xp_left_);
}
}
return MP_OBJ_FROM_PTR(y);
}
MP_DEFINE_CONST_FUN_OBJ_KW(approx_interp_obj, 2, approx_interp);
STATIC const mp_rom_map_elem_t ulab_approx_globals_table[] = {
{ MP_OBJ_NEW_QSTR(MP_QSTR___name__), MP_OBJ_NEW_QSTR(MP_QSTR_approx) },
{ MP_OBJ_NEW_QSTR(MP_QSTR_bisect), (mp_obj_t)&approx_bisect_obj },
{ MP_OBJ_NEW_QSTR(MP_QSTR_newton), (mp_obj_t)&approx_newton_obj },
{ MP_OBJ_NEW_QSTR(MP_QSTR_fmin), (mp_obj_t)&approx_fmin_obj },
// { MP_OBJ_NEW_QSTR(MP_QSTR_curve_fit), (mp_obj_t)&approx_curve_fit_obj },
{ MP_OBJ_NEW_QSTR(MP_QSTR_interp), (mp_obj_t)&approx_interp_obj },
};
STATIC MP_DEFINE_CONST_DICT(mp_module_ulab_approx_globals, ulab_approx_globals_table);
mp_obj_module_t ulab_approx_module = {
.base = { &mp_type_module },
.globals = (mp_obj_dict_t*)&mp_module_ulab_approx_globals,
};
#endif