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// Copyright (c) 2017-2023 California Institute of Technology ("Caltech"). U.S.
// Government sponsorship acknowledged. All rights reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
#pragma once
/*
Automatic differentiation routines. Used in poseutils-uses-autodiff.cc. See
that file for usage examples
*/
// Apparently I need this in MSVC to get constants
#define _USE_MATH_DEFINES
#include <math.h>
#include <string.h>
#include "strides.h"
template<int NGRAD, int NVEC> struct vec_withgrad_t;
template<int NGRAD>
struct val_withgrad_t
{
double x;
double j[NGRAD];
__attribute__ ((visibility ("hidden")))
val_withgrad_t(double _x = 0.0) : x(_x)
{
for(int i=0; i<NGRAD; i++) j[i] = 0.0;
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> operator+( const val_withgrad_t<NGRAD>& b ) const
{
val_withgrad_t<NGRAD> y = *this;
y.x += b.x;
for(int i=0; i<NGRAD; i++)
y.j[i] += b.j[i];
return y;
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> operator+( double b ) const
{
val_withgrad_t<NGRAD> y = *this;
y.x += b;
return y;
}
__attribute__ ((visibility ("hidden")))
void operator+=( const val_withgrad_t<NGRAD>& b )
{
*this = (*this) + b;
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> operator-( const val_withgrad_t<NGRAD>& b ) const
{
val_withgrad_t<NGRAD> y = *this;
y.x -= b.x;
for(int i=0; i<NGRAD; i++)
y.j[i] -= b.j[i];
return y;
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> operator-( double b ) const
{
val_withgrad_t<NGRAD> y = *this;
y.x -= b;
return y;
}
__attribute__ ((visibility ("hidden")))
void operator-=( const val_withgrad_t<NGRAD>& b )
{
*this = (*this) - b;
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> operator-() const
{
return (*this) * (-1);
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> operator*( const val_withgrad_t<NGRAD>& b ) const
{
val_withgrad_t<NGRAD> y;
y.x = x * b.x;
for(int i=0; i<NGRAD; i++)
y.j[i] = j[i]*b.x + x*b.j[i];
return y;
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> operator*( double b ) const
{
val_withgrad_t<NGRAD> y;
y.x = x * b;
for(int i=0; i<NGRAD; i++)
y.j[i] = j[i]*b;
return y;
}
__attribute__ ((visibility ("hidden")))
void operator*=( const val_withgrad_t<NGRAD>& b )
{
*this = (*this) * b;
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> operator/( const val_withgrad_t<NGRAD>& b ) const
{
val_withgrad_t<NGRAD> y;
y.x = x / b.x;
for(int i=0; i<NGRAD; i++)
y.j[i] = (j[i]*b.x - x*b.j[i]) / (b.x*b.x);
return y;
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> operator/( double b ) const
{
return (*this) * (1./b);
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> sqrt(void) const
{
val_withgrad_t<NGRAD> y;
y.x = ::sqrt(x);
for(int i=0; i<NGRAD; i++)
y.j[i] = j[i] / (2. * y.x);
return y;
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> square(void) const
{
val_withgrad_t<NGRAD> s;
s.x = x*x;
for(int i=0; i<NGRAD; i++)
s.j[i] = 2. * x * j[i];
return s;
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> sin(void) const
{
const double s = ::sin(x);
const double c = ::cos(x);
val_withgrad_t<NGRAD> y;
y.x = s;
for(int i=0; i<NGRAD; i++)
y.j[i] = c*j[i];
return y;
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> cos(void) const
{
const double s = ::sin(x);
const double c = ::cos(x);
val_withgrad_t<NGRAD> y;
y.x = c;
for(int i=0; i<NGRAD; i++)
y.j[i] = -s*j[i];
return y;
}
__attribute__ ((visibility ("hidden")))
vec_withgrad_t<NGRAD, 2> sincos(void) const
{
const double s = ::sin(x);
const double c = ::cos(x);
vec_withgrad_t<NGRAD, 2> sc;
sc.v[0].x = s;
sc.v[1].x = c;
for(int i=0; i<NGRAD; i++)
{
sc.v[0].j[i] = c*j[i];
sc.v[1].j[i] = -s*j[i];
}
return sc;
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> tan(void) const
{
const double s = ::sin(x);
const double c = ::cos(x);
val_withgrad_t<NGRAD> y;
y.x = s/c;
for(int i=0; i<NGRAD; i++)
y.j[i] = j[i] / (c*c);
return y;
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> atan2(val_withgrad_t<NGRAD>& x) const
{
val_withgrad_t<NGRAD> th;
const val_withgrad_t<NGRAD>& y = *this;
th.x = ::atan2(y.x, x.x);
// dth/dv = d/dv atan2(y,x)
// = d/dv atan(y/x)
// = 1 / (1 + y^2/x^2) d/dv (y/x)
// = x^2 / (x^2 + y^2) / x^2 * (dy/dv x - y dx/dv)
// = 1 / (x^2 + y^2) * (dy/dv x - y dx/dv)
double norm2 = y.x*y.x + x.x*x.x;
for(int i=0; i<NGRAD; i++)
th.j[i] = (y.j[i]*x.x - y.x*x.j[i]) / norm2;
return th;
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> acos(void) const
{
val_withgrad_t<NGRAD> th;
th.x = ::acos(x);
double dacos_dx = -1. / ::sqrt( 1. - x*x );
for(int i=0; i<NGRAD; i++)
th.j[i] = dacos_dx * j[i];
return th;
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> sinx_over_x(// To avoid recomputing it
const val_withgrad_t<NGRAD>& sinx) const
{
// For small x I need special-case logic. In the limit as x->0 I have
// sin(x)/x -> 1. But I'm propagating gradients, so I need to capture
// that. I have
//
// d(sin(x)/x)/dx =
// (x cos(x) - sin(x))/x^2
//
// As x -> 0 this is
//
// (cos(x) - x sin(x) - cos(x)) / (2x) =
// (- x sin(x)) / (2x) =
// -sin(x) / 2 =
// 0
//
// So for small x the gradient is 0
if(fabs(x) < 1e-8)
return val_withgrad_t<NGRAD>(1.0);
return sinx / (*this);
}
};
template<int NGRAD, int NVEC>
struct vec_withgrad_t
{
val_withgrad_t<NGRAD> v[NVEC];
vec_withgrad_t() {}
__attribute__ ((visibility ("hidden")))
void init_vars(const double* x_in, int ivar0, int Nvars, int i_gradvec0 = -1,
int stride = sizeof(double))
{
// Initializes vector entries ivar0..ivar0+Nvars-1 inclusive using the
// data in x_in[]. x_in[0] corresponds to vector entry ivar0. If
// i_gradvec0 >= 0 then vector ivar0 corresponds to gradient index
// i_gradvec0, with all subsequent entries being filled-in
// consecutively. It's very possible that NGRAD > Nvars. Initially the
// subset of the gradient array corresponding to variables
// i_gradvec0..i_gradvec0+Nvars-1 is an identity, with the rest being 0
memset((char*)&v[ivar0], 0, Nvars*sizeof(v[0]));
for(int i=ivar0; i<ivar0+Nvars; i++)
{
v[i].x = _P1(x_in,stride, i-ivar0);
if(i_gradvec0 >= 0)
v[i].j[i_gradvec0+i-ivar0] = 1.0;
}
}
__attribute__ ((visibility ("hidden")))
vec_withgrad_t(const double* x_in, int i_gradvec0 = -1,
int stride = sizeof(double))
{
init_vars(x_in, 0, NVEC, i_gradvec0, stride);
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD>& operator[](int i)
{
return v[i];
}
__attribute__ ((visibility ("hidden")))
const val_withgrad_t<NGRAD>& operator[](int i) const
{
return v[i];
}
__attribute__ ((visibility ("hidden")))
void operator+=( const vec_withgrad_t<NGRAD,NVEC>& x )
{
(*this) = (*this) + x;
}
__attribute__ ((visibility ("hidden")))
vec_withgrad_t<NGRAD,NVEC> operator+( const vec_withgrad_t<NGRAD,NVEC>& x ) const
{
vec_withgrad_t<NGRAD,NVEC> p;
for(int i=0; i<NVEC; i++)
p[i] = v[i] + x.v[i];
return p;
}
__attribute__ ((visibility ("hidden")))
void operator+=( const val_withgrad_t<NGRAD>& x )
{
(*this) = (*this) + x;
}
__attribute__ ((visibility ("hidden")))
vec_withgrad_t<NGRAD,NVEC> operator+( const val_withgrad_t<NGRAD>& x ) const
{
vec_withgrad_t<NGRAD,NVEC> p;
for(int i=0; i<NVEC; i++)
p[i] = v[i] + x;
return p;
}
__attribute__ ((visibility ("hidden")))
void operator+=( double x )
{
(*this) = (*this) + x;
}
__attribute__ ((visibility ("hidden")))
vec_withgrad_t<NGRAD,NVEC> operator+( double x ) const
{
vec_withgrad_t<NGRAD,NVEC> p;
for(int i=0; i<NVEC; i++)
p[i] = v[i] + x;
return p;
}
__attribute__ ((visibility ("hidden")))
void operator-=( const vec_withgrad_t<NGRAD,NVEC>& x )
{
(*this) = (*this) - x;
}
__attribute__ ((visibility ("hidden")))
vec_withgrad_t<NGRAD,NVEC> operator-( const vec_withgrad_t<NGRAD,NVEC>& x ) const
{
vec_withgrad_t<NGRAD,NVEC> p;
for(int i=0; i<NVEC; i++)
p[i] = v[i] - x.v[i];
return p;
}
__attribute__ ((visibility ("hidden")))
void operator-=( const val_withgrad_t<NGRAD>& x )
{
(*this) = (*this) - x;
}
__attribute__ ((visibility ("hidden")))
vec_withgrad_t<NGRAD,NVEC> operator-( const val_withgrad_t<NGRAD>& x ) const
{
vec_withgrad_t<NGRAD,NVEC> p;
for(int i=0; i<NVEC; i++)
p[i] = v[i] - x;
return p;
}
__attribute__ ((visibility ("hidden")))
void operator-=( double x )
{
(*this) = (*this) - x;
}
__attribute__ ((visibility ("hidden")))
vec_withgrad_t<NGRAD,NVEC> operator-( double x ) const
{
vec_withgrad_t<NGRAD,NVEC> p;
for(int i=0; i<NVEC; i++)
p[i] = v[i] - x;
return p;
}
__attribute__ ((visibility ("hidden")))
void operator*=( const vec_withgrad_t<NGRAD,NVEC>& x )
{
(*this) = (*this) * x;
}
__attribute__ ((visibility ("hidden")))
vec_withgrad_t<NGRAD,NVEC> operator*( const vec_withgrad_t<NGRAD,NVEC>& x ) const
{
vec_withgrad_t<NGRAD,NVEC> p;
for(int i=0; i<NVEC; i++)
p[i] = v[i] * x.v[i];
return p;
}
__attribute__ ((visibility ("hidden")))
void operator*=( const val_withgrad_t<NGRAD>& x )
{
(*this) = (*this) * x;
}
__attribute__ ((visibility ("hidden")))
vec_withgrad_t<NGRAD,NVEC> operator*( const val_withgrad_t<NGRAD>& x ) const
{
vec_withgrad_t<NGRAD,NVEC> p;
for(int i=0; i<NVEC; i++)
p[i] = v[i] * x;
return p;
}
__attribute__ ((visibility ("hidden")))
void operator*=( double x )
{
(*this) = (*this) * x;
}
__attribute__ ((visibility ("hidden")))
vec_withgrad_t<NGRAD,NVEC> operator*( double x ) const
{
vec_withgrad_t<NGRAD,NVEC> p;
for(int i=0; i<NVEC; i++)
p[i] = v[i] * x;
return p;
}
__attribute__ ((visibility ("hidden")))
void operator/=( const vec_withgrad_t<NGRAD,NVEC>& x )
{
(*this) = (*this) / x;
}
__attribute__ ((visibility ("hidden")))
vec_withgrad_t<NGRAD,NVEC> operator/( const vec_withgrad_t<NGRAD,NVEC>& x ) const
{
vec_withgrad_t<NGRAD,NVEC> p;
for(int i=0; i<NVEC; i++)
p[i] = v[i] / x.v[i];
return p;
}
__attribute__ ((visibility ("hidden")))
void operator/=( const val_withgrad_t<NGRAD>& x )
{
(*this) = (*this) / x;
}
__attribute__ ((visibility ("hidden")))
vec_withgrad_t<NGRAD,NVEC> operator/( const val_withgrad_t<NGRAD>& x ) const
{
vec_withgrad_t<NGRAD,NVEC> p;
for(int i=0; i<NVEC; i++)
p[i] = v[i] / x;
return p;
}
__attribute__ ((visibility ("hidden")))
void operator/=( double x )
{
(*this) = (*this) / x;
}
__attribute__ ((visibility ("hidden")))
vec_withgrad_t<NGRAD,NVEC> operator/( double x ) const
{
vec_withgrad_t<NGRAD,NVEC> p;
for(int i=0; i<NVEC; i++)
p[i] = v[i] / x;
return p;
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> dot( const vec_withgrad_t<NGRAD,NVEC>& x) const
{
val_withgrad_t<NGRAD> d; // initializes to 0
for(int i=0; i<NVEC; i++)
{
val_withgrad_t<NGRAD> e = x.v[i]*v[i];
d += e;
}
return d;
}
__attribute__ ((visibility ("hidden")))
vec_withgrad_t<NGRAD,NVEC> cross( const vec_withgrad_t<NGRAD,NVEC>& x) const
{
vec_withgrad_t<NGRAD,NVEC> c;
c[0] = v[1]*x.v[2] - v[2]*x.v[1];
c[1] = v[2]*x.v[0] - v[0]*x.v[2];
c[2] = v[0]*x.v[1] - v[1]*x.v[0];
return c;
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> norm2(void) const
{
return dot(*this);
}
__attribute__ ((visibility ("hidden")))
val_withgrad_t<NGRAD> mag(void) const
{
val_withgrad_t<NGRAD> l2 = norm2();
return l2.sqrt();
}
__attribute__ ((visibility ("hidden")))
void extract_value(double* out,
int stride = sizeof(double),
int ivar0 = 0, int Nvars = NVEC) const
{
for(int i=ivar0; i<ivar0+Nvars; i++)
_P1(out,stride, i-ivar0) = v[i].x;
}
__attribute__ ((visibility ("hidden")))
void extract_grad(double* J,
int i_gradvec0, int N_gradout,
int ivar0,
int J_stride0, int J_stride1,
int Nvars = NVEC) const
{
for(int i=ivar0; i<ivar0+Nvars; i++)
for(int j=0; j<N_gradout; j++)
_P2(J,J_stride0,J_stride1, i-ivar0,j) = v[i].j[i_gradvec0+j];
}
};
template<int NGRAD>
static
vec_withgrad_t<NGRAD, 3>
cross( const vec_withgrad_t<NGRAD, 3>& a,
const vec_withgrad_t<NGRAD, 3>& b )
{
vec_withgrad_t<NGRAD, 3> c;
c.v[0] = a.v[1]*b.v[2] - a.v[2]*b.v[1];
c.v[1] = a.v[2]*b.v[0] - a.v[0]*b.v[2];
c.v[2] = a.v[0]*b.v[1] - a.v[1]*b.v[0];
return c;
}
template<int NGRAD>
static
val_withgrad_t<NGRAD>
cross_norm2( const vec_withgrad_t<NGRAD, 3>& a,
const vec_withgrad_t<NGRAD, 3>& b )
{
vec_withgrad_t<NGRAD, 3> c = cross(a,b);
return c.norm2();
}
template<int NGRAD>
static
val_withgrad_t<NGRAD>
cross_mag( const vec_withgrad_t<NGRAD, 3>& a,
const vec_withgrad_t<NGRAD, 3>& b )
{
vec_withgrad_t<NGRAD, 3> c = cross(a,b);
return c.mag();
}
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