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micropython-ulab/code/numpy/poly.c
Zoltán Vörös 8a6741b350 fix macro call in poly.c
2021-12-03 08:59:23 +01:00

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/*
* This file is part of the micropython-ulab project,
*
* https://github.com/v923z/micropython-ulab
*
* The MIT License (MIT)
*
* Copyright (c) 2019-2021 Zoltán Vörös
* 2020 Jeff Epler for Adafruit Industries
* 2020 Scott Shawcroft for Adafruit Industries
* 2020 Taku Fukada
*/
#include "py/obj.h"
#include "py/runtime.h"
#include "py/objarray.h"
#include "../ulab.h"
#include "linalg/linalg_tools.h"
#include "../ulab_tools.h"
#include "carray/carray_tools.h"
#include "poly.h"
#if ULAB_NUMPY_HAS_POLYFIT
mp_obj_t poly_polyfit(size_t n_args, const mp_obj_t *args) {
if(!ndarray_object_is_array_like(args[0])) {
mp_raise_ValueError(translate("input data must be an iterable"));
}
#if ULAB_SUPPORTS_COMPLEX
if(mp_obj_is_type(args[0], &ulab_ndarray_type)) {
ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(args[0]);
COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype)
}
#endif
size_t lenx = 0, leny = 0;
uint8_t deg = 0;
mp_float_t *x, *XT, *y, *prod;
if(n_args == 2) { // only the y values are supplied
// TODO: this is actually not enough: the first argument can very well be a matrix,
// in which case we are between the rock and a hard place
leny = (size_t)mp_obj_get_int(mp_obj_len_maybe(args[0]));
deg = (uint8_t)mp_obj_get_int(args[1]);
if(leny < deg) {
mp_raise_ValueError(translate("more degrees of freedom than data points"));
}
lenx = leny;
x = m_new(mp_float_t, lenx); // assume uniformly spaced data points
for(size_t i=0; i < lenx; i++) {
x[i] = i;
}
y = m_new(mp_float_t, leny);
fill_array_iterable(y, args[0]);
} else /* n_args == 3 */ {
if(!ndarray_object_is_array_like(args[1])) {
mp_raise_ValueError(translate("input data must be an iterable"));
}
lenx = (size_t)mp_obj_get_int(mp_obj_len_maybe(args[0]));
leny = (size_t)mp_obj_get_int(mp_obj_len_maybe(args[1]));
if(lenx != leny) {
mp_raise_ValueError(translate("input vectors must be of equal length"));
}
deg = (uint8_t)mp_obj_get_int(args[2]);
if(leny < deg) {
mp_raise_ValueError(translate("more degrees of freedom than data points"));
}
x = m_new(mp_float_t, lenx);
fill_array_iterable(x, args[0]);
y = m_new(mp_float_t, leny);
fill_array_iterable(y, args[1]);
}
// one could probably express X as a function of XT,
// and thereby save RAM, because X is used only in the product
XT = m_new(mp_float_t, (deg+1)*leny); // XT is a matrix of shape (deg+1, len) (rows, columns)
for(size_t i=0; i < leny; i++) { // column index
XT[i+0*lenx] = 1.0; // top row
for(uint8_t j=1; j < deg+1; j++) { // row index
XT[i+j*leny] = XT[i+(j-1)*leny]*x[i];
}
}
prod = m_new(mp_float_t, (deg+1)*(deg+1)); // the product matrix is of shape (deg+1, deg+1)
mp_float_t sum;
for(uint8_t i=0; i < deg+1; i++) { // column index
for(uint8_t j=0; j < deg+1; j++) { // row index
sum = 0.0;
for(size_t k=0; k < lenx; k++) {
// (j, k) * (k, i)
// Note that the second matrix is simply the transpose of the first:
// X(k, i) = XT(i, k) = XT[k*lenx+i]
sum += XT[j*lenx+k]*XT[i*lenx+k]; // X[k*(deg+1)+i];
}
prod[j*(deg+1)+i] = sum;
}
}
if(!linalg_invert_matrix(prod, deg+1)) {
// Although X was a Vandermonde matrix, whose inverse is guaranteed to exist,
// we bail out here, if prod couldn't be inverted: if the values in x are not all
// distinct, prod is singular
m_del(mp_float_t, XT, (deg+1)*lenx);
m_del(mp_float_t, x, lenx);
m_del(mp_float_t, y, lenx);
m_del(mp_float_t, prod, (deg+1)*(deg+1));
mp_raise_ValueError(translate("could not invert Vandermonde matrix"));
}
// at this point, we have the inverse of X^T * X
// y is a column vector; x is free now, we can use it for storing intermediate values
for(uint8_t i=0; i < deg+1; i++) { // row index
sum = 0.0;
for(size_t j=0; j < lenx; j++) { // column index
sum += XT[i*lenx+j]*y[j];
}
x[i] = sum;
}
// XT is no longer needed
m_del(mp_float_t, XT, (deg+1)*leny);
ndarray_obj_t *beta = ndarray_new_linear_array(deg+1, NDARRAY_FLOAT);
mp_float_t *betav = (mp_float_t *)beta->array;
// x[0..(deg+1)] contains now the product X^T * y; we can get rid of y
m_del(float, y, leny);
// now, we calculate beta, i.e., we apply prod = (X^T * X)^(-1) on x = X^T * y; x is a column vector now
for(uint8_t i=0; i < deg+1; i++) {
sum = 0.0;
for(uint8_t j=0; j < deg+1; j++) {
sum += prod[i*(deg+1)+j]*x[j];
}
betav[i] = sum;
}
m_del(mp_float_t, x, lenx);
m_del(mp_float_t, prod, (deg+1)*(deg+1));
for(uint8_t i=0; i < (deg+1)/2; i++) {
// We have to reverse the array, for the leading coefficient comes first.
SWAP(mp_float_t, betav[i], betav[deg-i]);
}
return MP_OBJ_FROM_PTR(beta);
}
MP_DEFINE_CONST_FUN_OBJ_VAR_BETWEEN(poly_polyfit_obj, 2, 3, poly_polyfit);
#endif
#if ULAB_NUMPY_HAS_POLYVAL
mp_obj_t poly_polyval(mp_obj_t o_p, mp_obj_t o_x) {
if(!ndarray_object_is_array_like(o_p) || !ndarray_object_is_array_like(o_x)) {
mp_raise_TypeError(translate("inputs are not iterable"));
}
#if ULAB_SUPPORTS_COMPLEX
ndarray_obj_t *input;
if(mp_obj_is_type(o_p, &ulab_ndarray_type)) {
input = MP_OBJ_TO_PTR(o_p);
COMPLEX_DTYPE_NOT_IMPLEMENTED(input->dtype)
}
if(mp_obj_is_type(o_x, &ulab_ndarray_type)) {
input = MP_OBJ_TO_PTR(o_x);
COMPLEX_DTYPE_NOT_IMPLEMENTED(input->dtype)
}
#endif
// p had better be a one-dimensional standard iterable
uint8_t plen = mp_obj_get_int(mp_obj_len_maybe(o_p));
mp_float_t *p = m_new(mp_float_t, plen);
mp_obj_iter_buf_t p_buf;
mp_obj_t p_item, p_iterable = mp_getiter(o_p, &p_buf);
uint8_t i = 0;
while((p_item = mp_iternext(p_iterable)) != MP_OBJ_STOP_ITERATION) {
p[i] = mp_obj_get_float(p_item);
i++;
}
// polynomials are going to be of type float, except, when both
// the coefficients and the independent variable are integers
ndarray_obj_t *ndarray;
if(mp_obj_is_type(o_x, &ulab_ndarray_type)) {
ndarray_obj_t *source = MP_OBJ_TO_PTR(o_x);
uint8_t *sarray = (uint8_t *)source->array;
ndarray = ndarray_new_dense_ndarray(source->ndim, source->shape, NDARRAY_FLOAT);
mp_float_t *array = (mp_float_t *)ndarray->array;
mp_float_t (*func)(void *) = ndarray_get_float_function(source->dtype);
// TODO: these loops are really nothing, but the re-impplementation of
// ITERATE_VECTOR from vectorise.c. We could pass a function pointer here
#if ULAB_MAX_DIMS > 3
size_t i = 0;
do {
#endif
#if ULAB_MAX_DIMS > 2
size_t j = 0;
do {
#endif
#if ULAB_MAX_DIMS > 1
size_t k = 0;
do {
#endif
size_t l = 0;
do {
mp_float_t y = p[0];
mp_float_t _x = func(sarray);
for(uint8_t m=0; m < plen-1; m++) {
y *= _x;
y += p[m+1];
}
*array++ = y;
sarray += source->strides[ULAB_MAX_DIMS - 1];
l++;
} while(l < source->shape[ULAB_MAX_DIMS - 1]);
#if ULAB_MAX_DIMS > 1
sarray -= source->strides[ULAB_MAX_DIMS - 1] * source->shape[ULAB_MAX_DIMS-1];
sarray += source->strides[ULAB_MAX_DIMS - 2];
k++;
} while(k < source->shape[ULAB_MAX_DIMS - 2]);
#endif
#if ULAB_MAX_DIMS > 2
sarray -= source->strides[ULAB_MAX_DIMS - 2] * source->shape[ULAB_MAX_DIMS-2];
sarray += source->strides[ULAB_MAX_DIMS - 3];
j++;
} while(j < source->shape[ULAB_MAX_DIMS - 3]);
#endif
#if ULAB_MAX_DIMS > 3
sarray -= source->strides[ULAB_MAX_DIMS - 3] * source->shape[ULAB_MAX_DIMS-3];
sarray += source->strides[ULAB_MAX_DIMS - 4];
i++;
} while(i < source->shape[ULAB_MAX_DIMS - 4]);
#endif
} else {
// o_x had better be a one-dimensional standard iterable
ndarray = ndarray_new_linear_array(mp_obj_get_int(mp_obj_len_maybe(o_x)), NDARRAY_FLOAT);
mp_float_t *array = (mp_float_t *)ndarray->array;
mp_obj_iter_buf_t x_buf;
mp_obj_t x_item, x_iterable = mp_getiter(o_x, &x_buf);
while ((x_item = mp_iternext(x_iterable)) != MP_OBJ_STOP_ITERATION) {
mp_float_t _x = mp_obj_get_float(x_item);
mp_float_t y = p[0];
for(uint8_t j=0; j < plen-1; j++) {
y *= _x;
y += p[j+1];
}
*array++ = y;
}
}
m_del(mp_float_t, p, plen);
return MP_OBJ_FROM_PTR(ndarray);
}
MP_DEFINE_CONST_FUN_OBJ_2(poly_polyval_obj, poly_polyval);
#endif
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