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check_gradient_rigid_body.c
1068 lines (881 loc) · 36.9 KB
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check_gradient_rigid_body.c
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/*
This file is part of the FlightSim project
Author: Alex Gorodetsky
email: goroda@umich.edu
Copyright (c) 2020 Alex Gorodetsky
License: GPL3
*/
//------------------------------------------
//------------------------------------------
//--------- Gradient Checkers --------------
//------------------------------------------
//------------------------------------------
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <assert.h>
#include <time.h>
#include <getopt.h>
#include "flight_sim.h"
#include "vehicles.h"
int check(real tol, real a, real b)
{
if (pow(a - b, 2) / pow(a, 2) > tol){
return 1;
}
return 0;
}
int check_grad_ac_to_e(real h, real tol)
{
struct EulerAngles ea;
ea.roll = M_PI/9.0;
ea.pitch = M_PI/8.0;
ea.yaw = M_PI/6.0;
euler_angles_g(&ea);
struct Vec3 ac = {120.0, 150.0, 80.0};
struct Vec3 e;
struct StateGrad sg[3];
// reference
orient_ac_to_e(&ea, &ac, &e);
struct Vec3 e_ref = {e.v1, e.v2, e.v3};
printf("Checking value computation\n");
printf("Numerical %3.5E %3.5E %3.5E\n", e_ref.v1, e_ref.v2, e_ref.v3);
// compute analytic gradient
orient_ac_to_e_g(&ea, &ac, &e, sg);
printf("Analytic %3.5E %3.5E %3.5E\n", e.v1, e.v2, e.v3);
printf("\n\n\n");
real grad_U[3];
ac.v1 += h;
orient_ac_to_e(&ea, &ac, &e);
grad_U[0] = (e.v1 - e_ref.v1) / h;
grad_U[1] = (e.v2 - e_ref.v2) / h;
grad_U[2] = (e.v3 - e_ref.v3) / h;
printf("Checking Gradient with respect to U\n");
printf("Numerical: %3.5E, %3.5E, %3.5E\n", grad_U[0], grad_U[1], grad_U[2]);
printf("Analytic: %3.5E, %3.5E, %3.5E\n", sg[0].U_g, sg[1].U_g, sg[2].U_g);
printf("\n\n");
real grad_V[3];
ac.v1 -= h;
ac.v2 += h;
orient_ac_to_e(&ea, &ac, &e);
grad_V[0] = (e.v1 - e_ref.v1) / h;
grad_V[1] = (e.v2 - e_ref.v2) / h;
grad_V[2] = (e.v3 - e_ref.v3) / h;
printf("Checking Gradient with respect to V\n");
printf("Numerical: %3.5E, %3.5E, %3.5E\n", grad_V[0], grad_V[1], grad_V[2]);
printf("Analytic: %3.5E, %3.5E, %3.5E\n", sg[0].V_g, sg[1].V_g, sg[2].V_g);
printf("\n\n");
real grad_W[3];
ac.v2 -= h;
ac.v3 += h;
orient_ac_to_e(&ea, &ac, &e);
grad_W[0] = (e.v1 - e_ref.v1) / h;
grad_W[1] = (e.v2 - e_ref.v2) / h;
grad_W[2] = (e.v3 - e_ref.v3) / h;
printf("Checking Gradient with respect to W\n");
printf("Numerical: %3.5E, %3.5E, %3.5E\n", grad_W[0], grad_W[1], grad_W[2]);
printf("Analytic: %3.5E, %3.5E, %3.5E\n", sg[0].W_g, sg[1].W_g, sg[2].W_g);
printf("\n\n");
real grad_R[3];
ac.v3 -= h;
ea.roll += h;
euler_angles(&ea);
orient_ac_to_e(&ea, &ac, &e);
grad_R[0] = (e.v1 - e_ref.v1) / h;
grad_R[1] = (e.v2 - e_ref.v2) / h;
grad_R[2] = (e.v3 - e_ref.v3) / h;
printf("Checking Gradient with respect to Roll\n");
printf("Numerical: %3.5E, %3.5E, %3.5E\n", grad_R[0], grad_R[1], grad_R[2]);
printf("Analytic: %3.5E, %3.5E, %3.5E\n", sg[0].Roll_g, sg[1].Roll_g, sg[2].Roll_g);
printf("\n\n");
real grad_P[3];
ea.roll -= h;
ea.pitch += h;
euler_angles(&ea);
orient_ac_to_e(&ea, &ac, &e);
grad_P[0] = (e.v1 - e_ref.v1) / h;
grad_P[1] = (e.v2 - e_ref.v2) / h;
grad_P[2] = (e.v3 - e_ref.v3) / h;
printf("Checking Gradient with respect to Pitch\n");
printf("Numerical: %3.5E, %3.5E, %3.5E\n", grad_P[0], grad_P[1], grad_P[2]);
printf("Analytic: %3.5E, %3.5E, %3.5E\n", sg[0].Pitch_g, sg[1].Pitch_g, sg[2].Pitch_g);
printf("\n\n");
real grad_Y[3];
ea.pitch -= h;
ea.yaw += h;
euler_angles(&ea);
orient_ac_to_e(&ea, &ac, &e);
grad_Y[0] = (e.v1 - e_ref.v1) / h;
grad_Y[1] = (e.v2 - e_ref.v2) / h;
grad_Y[2] = (e.v3 - e_ref.v3) / h;
printf("Checking Gradient with respect to Yaw\n");
printf("Numerical: %3.5E, %3.5E, %3.5E\n", grad_Y[0], grad_Y[1], grad_Y[2]);
printf("Analytic: %3.5E, %3.5E, %3.5E\n", sg[0].Yaw_g, sg[1].Yaw_g, sg[2].Yaw_g);
return 0;
}
int check_grad_rkin(real h, real tol)
{
struct EulerAngles ea;
ea.roll = M_PI/9.0;
ea.pitch = M_PI/8.0;
ea.yaw = M_PI/6.0;
euler_angles_g(&ea);
struct Vec3 pqr = {120.0, 150.0, 80.0};
struct Vec3 rates;
struct StateGrad sg[3];
// reference
rkin(&ea, &pqr, &rates);
struct Vec3 e_ref = {rates.v1, rates.v2, rates.v3};
printf("Checking value computation\n");
printf("Numerical %3.5E %3.5E %3.5E\n", rates.v1, rates.v2, rates.v3);
// compute analytic gradient
rkin_g(&ea, &pqr, &rates, sg);
printf("Analytic %3.5E %3.5E %3.5E\n", rates.v1, rates.v2, rates.v3);
printf("\n\n\n");
real grad_P[3];
pqr.v1 += h;
rkin(&ea, &pqr, &rates);
grad_P[0] = (rates.v1 - e_ref.v1) / h;
grad_P[1] = (rates.v2 - e_ref.v2) / h;
grad_P[2] = (rates.v3 - e_ref.v3) / h;
printf("Checking Gradient with respect to P\n");
printf("Numerical: %3.5E, %3.5E, %3.5E\n", grad_P[0], grad_P[1], grad_P[2]);
printf("Analytic: %3.5E, %3.5E, %3.5E\n", sg[0].P_g, sg[1].P_g, sg[2].P_g);
printf("\n\n");
real grad_Q[3];
pqr.v1 -= h;
pqr.v2 += h;
rkin(&ea, &pqr, &rates);
grad_Q[0] = (rates.v1 - e_ref.v1) / h;
grad_Q[1] = (rates.v2 - e_ref.v2) / h;
grad_Q[2] = (rates.v3 - e_ref.v3) / h;
printf("Checking Gradient with respect to Q\n");
printf("Numerical: %3.5E, %3.5E, %3.5E\n", grad_Q[0], grad_Q[1], grad_Q[2]);
printf("Analytic: %3.5E, %3.5E, %3.5E\n", sg[0].Q_g, sg[1].Q_g, sg[2].Q_g);
printf("\n\n");
real grad_R[3];
pqr.v2 -= h;
pqr.v3 += h;
rkin(&ea, &pqr, &rates);
grad_R[0] = (rates.v1 - e_ref.v1) / h;
grad_R[1] = (rates.v2 - e_ref.v2) / h;
grad_R[2] = (rates.v3 - e_ref.v3) / h;
printf("Checking Gradient with respect to R\n");
printf("Numerical: %3.5E, %3.5E, %3.5E\n", grad_R[0], grad_R[1], grad_R[2]);
printf("Analytic: %3.5E, %3.5E, %3.5E\n", sg[0].R_g, sg[1].R_g, sg[2].R_g);
printf("\n\n");
real grad_Roll[3];
pqr.v3 -= h;
ea.roll += h;
euler_angles(&ea);
rkin(&ea, &pqr, &rates);
grad_Roll[0] = (rates.v1 - e_ref.v1) / h;
grad_Roll[1] = (rates.v2 - e_ref.v2) / h;
grad_Roll[2] = (rates.v3 - e_ref.v3) / h;
printf("Checking Gradient with respect to Roll\n");
printf("Numerical: %3.5E, %3.5E, %3.5E\n", grad_Roll[0], grad_Roll[1], grad_Roll[2]);
printf("Analytic: %3.5E, %3.5E, %3.5E\n", sg[0].Roll_g, sg[1].Roll_g, sg[2].Roll_g);
printf("\n\n");
real grad_Pitch[3];
ea.roll -= h;
ea.pitch += h;
euler_angles(&ea);
rkin(&ea, &pqr, &rates);
grad_Pitch[0] = (rates.v1 - e_ref.v1) / h;
grad_Pitch[1] = (rates.v2 - e_ref.v2) / h;
grad_Pitch[2] = (rates.v3 - e_ref.v3) / h;
printf("Checking Gradient with respect to Pitch\n");
printf("Numerical: %3.5E, %3.5E, %3.5E\n", grad_Pitch[0], grad_Pitch[1], grad_Pitch[2]);
printf("Analytic: %3.5E, %3.5E, %3.5E\n", sg[0].Pitch_g, sg[1].Pitch_g, sg[2].Pitch_g);
printf("\n\n");
real grad_Yaw[3];
ea.pitch -= h;
ea.yaw += h;
euler_angles(&ea);
rkin(&ea, &pqr, &rates);
grad_Yaw[0] = (rates.v1 - e_ref.v1) / h;
grad_Yaw[1] = (rates.v2 - e_ref.v2) / h;
grad_Yaw[2] = (rates.v3 - e_ref.v3) / h;
printf("Checking Gradient with respect to Yaw\n");
printf("Numerical: %3.5E, %3.5E, %3.5E\n", grad_Yaw[0], grad_Yaw[1], grad_Yaw[2]);
printf("Analytic: %3.5E, %3.5E, %3.5E\n", sg[0].Yaw_g, sg[1].Yaw_g, sg[2].Yaw_g);
return 0;
}
int check_grad_aero_forces(real h, real tol)
{
struct Vec3 uvw = {120, 90, 60};
real vac = sqrt(pow(uvw.v1, 2) + pow(uvw.v2, 2) + pow(uvw.v3, 2));
struct StateGrad vac_g;
vac_g.U_g = uvw.v1 / vac;
vac_g.V_g = uvw.v2 / vac;
vac_g.W_g = uvw.v3 / vac;
struct Vec3 pqr = {10, -2.0, 8.0};
struct Vec3 aero_con = {3.0, 1.0, 2.5};
real rho = 0.002376892406675; // slug / ft^3
struct Aircraft aircraft;
pioneer_uav(&aircraft);
struct Vec3 DEL_ref;
struct Vec3 LMN_ref;
struct Vec3 DEL;
struct Vec3 LMN;
struct StateGrad sg[6];
struct ControlGrad cg[6];
struct AeroAngles aero;
// Reference
aero_angles(&uvw, vac, &aero);
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL_ref, &LMN_ref);
// Analytic
aero_angles_g(&uvw, vac, &vac_g, &aero);
aero_forces_g(&aero, &pqr, &aero_con, &aircraft, rho, vac, &vac_g, &DEL, &LMN, sg, cg);
printf("Checking value computation\n");
printf("Numerical %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", DEL_ref.v1, DEL_ref.v2, DEL_ref.v3, LMN_ref.v1, LMN_ref.v2, LMN_ref.v3);
printf("Analytic %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", DEL.v1, DEL.v2, DEL.v3, LMN.v1, LMN.v2, LMN.v3);
printf("\n\n\n");
real grad_U[6];
uvw.v1 += h;
vac = sqrt(pow(uvw.v1, 2) + pow(uvw.v2, 2) + pow(uvw.v3, 2));
vac_g.U_g = uvw.v1 / vac;
vac_g.V_g = uvw.v2 / vac;
vac_g.W_g = uvw.v3 / vac;
aero_angles(&uvw, vac, &aero);
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
grad_U[0] = (DEL.v1 - DEL_ref.v1) / h;
grad_U[1] = (DEL.v2 - DEL_ref.v2) / h;
grad_U[2] = (DEL.v3 - DEL_ref.v3) / h;
grad_U[3] = (LMN.v1 - LMN_ref.v1) / h;
grad_U[4] = (LMN.v2 - LMN_ref.v2) / h;
grad_U[5] = (LMN.v3 - LMN_ref.v3) / h;
printf("Checking Gradient with respect to U\n");
printf("Numerical %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", grad_U[0], grad_U[1], grad_U[2], grad_U[3], grad_U[4], grad_U[5]);
printf("Analytic %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", sg[0].U_g, sg[1].U_g, sg[2].U_g, sg[3].U_g, sg[4].U_g, sg[5].U_g);
printf("\n\n");
uvw.v1 -= h;
real grad_V[6];
uvw.v2 += h;
vac = sqrt(pow(uvw.v1, 2) + pow(uvw.v2, 2) + pow(uvw.v3, 2));
vac_g.U_g = uvw.v1 / vac;
vac_g.V_g = uvw.v2 / vac;
vac_g.W_g = uvw.v3 / vac;
aero_angles(&uvw, vac, &aero);
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
grad_V[0] = (DEL.v1 - DEL_ref.v1) / h;
grad_V[1] = (DEL.v2 - DEL_ref.v2) / h;
grad_V[2] = (DEL.v3 - DEL_ref.v3) / h;
grad_V[3] = (LMN.v1 - LMN_ref.v1) / h;
grad_V[4] = (LMN.v2 - LMN_ref.v2) / h;
grad_V[5] = (LMN.v3 - LMN_ref.v3) / h;
printf("Checking Gradient with respect to V\n");
printf("Numerical %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", grad_V[0], grad_V[1], grad_V[2], grad_V[3], grad_V[4], grad_V[5]);
printf("Analytic %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", sg[0].V_g, sg[1].V_g, sg[2].V_g, sg[3].V_g, sg[4].V_g, sg[5].V_g);
printf("\n\n");
uvw.v2 -= h;
real grad_W[6];
uvw.v3 += h;
vac = sqrt(pow(uvw.v1, 2) + pow(uvw.v2, 2) + pow(uvw.v3, 2));
vac_g.U_g = uvw.v1 / vac;
vac_g.V_g = uvw.v2 / vac;
vac_g.W_g = uvw.v3 / vac;
aero_angles(&uvw, vac, &aero);
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
grad_W[0] = (DEL.v1 - DEL_ref.v1) / h;
grad_W[1] = (DEL.v2 - DEL_ref.v2) / h;
grad_W[2] = (DEL.v3 - DEL_ref.v3) / h;
grad_W[3] = (LMN.v1 - LMN_ref.v1) / h;
grad_W[4] = (LMN.v2 - LMN_ref.v2) / h;
grad_W[5] = (LMN.v3 - LMN_ref.v3) / h;
printf("Checking Gradient with respect to W\n");
printf("Numerical %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", grad_W[0], grad_W[1], grad_W[2], grad_W[3], grad_W[4], grad_W[5]);
printf("Analytic %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", sg[0].W_g, sg[1].W_g, sg[2].W_g, sg[3].W_g, sg[4].W_g, sg[5].W_g);
printf("\n\n");
uvw.v3 -= h;
// reset
vac = sqrt(pow(uvw.v1, 2) + pow(uvw.v2, 2) + pow(uvw.v3, 2));
vac_g.U_g = uvw.v1 / vac;
vac_g.V_g = uvw.v2 / vac;
vac_g.W_g = uvw.v3 / vac;
aero_angles(&uvw, vac, &aero);
real grad_P[6];
pqr.v1 += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
grad_P[0] = (DEL.v1 - DEL_ref.v1) / h;
grad_P[1] = (DEL.v2 - DEL_ref.v2) / h;
grad_P[2] = (DEL.v3 - DEL_ref.v3) / h;
grad_P[3] = (LMN.v1 - LMN_ref.v1) / h;
grad_P[4] = (LMN.v2 - LMN_ref.v2) / h;
grad_P[5] = (LMN.v3 - LMN_ref.v3) / h;
printf("Checking Gradient with respect to P\n");
printf("Numerical %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", grad_P[0], grad_P[1], grad_P[2], grad_P[3], grad_P[4], grad_P[5]);
printf("Analytic %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", sg[0].P_g, sg[1].P_g, sg[2].P_g, sg[3].P_g, sg[4].P_g, sg[5].P_g);
printf("\n\n");
pqr.v1 -= h;
real grad_Q[6];
pqr.v2 += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
grad_Q[0] = (DEL.v1 - DEL_ref.v1) / h;
grad_Q[1] = (DEL.v2 - DEL_ref.v2) / h;
grad_Q[2] = (DEL.v3 - DEL_ref.v3) / h;
grad_Q[3] = (LMN.v1 - LMN_ref.v1) / h;
grad_Q[4] = (LMN.v2 - LMN_ref.v2) / h;
grad_Q[5] = (LMN.v3 - LMN_ref.v3) / h;
printf("Checking Gradient with respect to Q\n");
printf("Numerical %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", grad_Q[0], grad_Q[1], grad_Q[2], grad_Q[3], grad_Q[4], grad_Q[5]);
printf("Analytic %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", sg[0].Q_g, sg[1].Q_g, sg[2].Q_g, sg[3].Q_g, sg[4].Q_g, sg[5].Q_g);
printf("\n\n");
pqr.v2 -= h;
real grad_R[6];
pqr.v3 += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
grad_R[0] = (DEL.v1 - DEL_ref.v1) / h;
grad_R[1] = (DEL.v2 - DEL_ref.v2) / h;
grad_R[2] = (DEL.v3 - DEL_ref.v3) / h;
grad_R[3] = (LMN.v1 - LMN_ref.v1) / h;
grad_R[4] = (LMN.v2 - LMN_ref.v2) / h;
grad_R[5] = (LMN.v3 - LMN_ref.v3) / h;
printf("Checking Gradient with respect to R\n");
printf("Numerical %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", grad_R[0], grad_R[1], grad_R[2], grad_R[3], grad_R[4], grad_R[5]);
printf("Analytic %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", sg[0].R_g, sg[1].R_g, sg[2].R_g, sg[3].R_g, sg[4].R_g, sg[5].R_g);
printf("\n\n");
pqr.v3 -= h;
real grad_el[6];
aero_con.v1 += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
grad_el[0] = (DEL.v1 - DEL_ref.v1) / h;
grad_el[1] = (DEL.v2 - DEL_ref.v2) / h;
grad_el[2] = (DEL.v3 - DEL_ref.v3) / h;
grad_el[3] = (LMN.v1 - LMN_ref.v1) / h;
grad_el[4] = (LMN.v2 - LMN_ref.v2) / h;
grad_el[5] = (LMN.v3 - LMN_ref.v3) / h;
printf("Checking Gradient with respect to Elevator\n");
printf("Numerical %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", grad_el[0], grad_el[1], grad_el[2], grad_el[3], grad_el[4], grad_el[5]);
printf("Analytic %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", cg[0].elev_g, cg[1].elev_g, cg[2].elev_g, cg[3].elev_g, cg[4].elev_g, cg[5].elev_g);
printf("\n\n");
aero_con.v1 -= h;
real grad_ail[6];
aero_con.v2 += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
grad_ail[0] = (DEL.v1 - DEL_ref.v1) / h;
grad_ail[1] = (DEL.v2 - DEL_ref.v2) / h;
grad_ail[2] = (DEL.v3 - DEL_ref.v3) / h;
grad_ail[3] = (LMN.v1 - LMN_ref.v1) / h;
grad_ail[4] = (LMN.v2 - LMN_ref.v2) / h;
grad_ail[5] = (LMN.v3 - LMN_ref.v3) / h;
printf("Checking Gradient with respect to Aileron\n");
printf("Numerical %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", grad_ail[0], grad_ail[1], grad_ail[2], grad_ail[3], grad_ail[4], grad_ail[5]);
printf("Analytic %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", cg[0].aileron_g, cg[1].aileron_g, cg[2].aileron_g, cg[3].aileron_g, cg[4].aileron_g, cg[5].aileron_g);
printf("\n\n");
aero_con.v2 -= h;
real grad_rud[6];
aero_con.v3 += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
grad_rud[0] = (DEL.v1 - DEL_ref.v1) / h;
grad_rud[1] = (DEL.v2 - DEL_ref.v2) / h;
grad_rud[2] = (DEL.v3 - DEL_ref.v3) / h;
grad_rud[3] = (LMN.v1 - LMN_ref.v1) / h;
grad_rud[4] = (LMN.v2 - LMN_ref.v2) / h;
grad_rud[5] = (LMN.v3 - LMN_ref.v3) / h;
printf("Checking Gradient with respect to Rudder\n");
printf("Numerical %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", grad_rud[0], grad_rud[1], grad_rud[2], grad_rud[3], grad_rud[4], grad_rud[5]);
printf("Analytic %3.5E %3.5E %3.5E %3.5E %3.5E %3.5E\n", cg[0].rudder_g, cg[1].rudder_g, cg[2].rudder_g, cg[3].rudder_g, cg[4].rudder_g, cg[5].rudder_g);
printf("\n\n");
aero_con.v3 -= h;
return 0;
}
int check_grad_tdyn(real h, real tol)
{
struct Vec3 uvw = {120, 90, 60};
real vac = sqrt(pow(uvw.v1, 2) + pow(uvw.v2, 2) + pow(uvw.v3, 2));
struct StateGrad vac_g;
vac_g.U_g = uvw.v1 / vac;
vac_g.V_g = uvw.v2 / vac;
vac_g.W_g = uvw.v3 / vac;
struct Vec3 pqr = {10, -2.0, 8.0};
struct Vec3 aero_con = {3.0, 1.0, 2.5};
real Ft = 48.0; // force
real rho = 0.002376892406675; // slug / ft^3
struct Aircraft aircraft;
pioneer_uav(&aircraft);
struct Vec3 DEL_ref;
struct Vec3 LMN_ref;
struct Vec3 rates_ref;
struct Vec3 DEL;
struct Vec3 LMN;
struct Vec3 rates;
struct StateGrad sg_f[6];
struct ControlGrad cg_f[6];
struct StateGrad sg[3];
struct ControlGrad cg[3];
struct AeroAngles aero;
struct EulerAngles ea;
ea.roll = M_PI/9.0;
ea.pitch = M_PI/8.0;
ea.yaw = M_PI/6.0;
euler_angles_g(&ea);
// Reference
aero_angles(&uvw, vac, &aero);
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac,
&DEL_ref, &LMN_ref);
tdyn(&ea, &aero, &uvw, &pqr, &DEL_ref, Ft, &aircraft, &rates_ref);
// Analytic
aero_angles_g(&uvw, vac, &vac_g, &aero);
aero_forces_g(&aero, &pqr, &aero_con, &aircraft, rho, vac,
&vac_g, &DEL, &LMN, sg_f, cg_f);
tdyn_g(&ea, &aero, &vac_g, &uvw, &pqr, &DEL, sg_f, cg_f, Ft, &aircraft, &rates, sg, cg);
printf("Checking value computation\n");
printf("Numerical %3.5E %3.5E %3.5E\n", rates_ref.v1, rates_ref.v2, rates_ref.v3);
printf("Analytic %3.5E %3.5E %3.5E\n", rates.v1, rates.v2, rates.v3);
printf("\n\n\n");
real grad_U[3];
uvw.v1 += h;
vac = sqrt(pow(uvw.v1, 2) + pow(uvw.v2, 2) + pow(uvw.v3, 2));
vac_g.U_g = uvw.v1 / vac;
vac_g.V_g = uvw.v2 / vac;
vac_g.W_g = uvw.v3 / vac;
aero_angles(&uvw, vac, &aero);
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
tdyn(&ea, &aero, &uvw, &pqr, &DEL, Ft, &aircraft, &rates);
grad_U[0] = (rates.v1 - rates_ref.v1) / h;
grad_U[1] = (rates.v2 - rates_ref.v2) / h;
grad_U[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to U\n");
printf("Numerical %3.5E %3.5E %3.5E \n", grad_U[0], grad_U[1], grad_U[2]);
printf("Analytic %3.5E %3.5E %3.5E \n", sg[0].U_g, sg[1].U_g, sg[2].U_g);
printf("\n\n");
uvw.v1 -= h;
real grad_V[3];
uvw.v2 += h;
vac = sqrt(pow(uvw.v1, 2) + pow(uvw.v2, 2) + pow(uvw.v3, 2));
vac_g.U_g = uvw.v1 / vac;
vac_g.V_g = uvw.v2 / vac;
vac_g.W_g = uvw.v3 / vac;
aero_angles(&uvw, vac, &aero);
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
tdyn(&ea, &aero, &uvw, &pqr, &DEL, Ft, &aircraft, &rates);
grad_V[0] = (rates.v1 - rates_ref.v1) / h;
grad_V[1] = (rates.v2 - rates_ref.v2) / h;
grad_V[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to V\n");
printf("Numerical %3.5E %3.5E %3.5E \n", grad_V[0], grad_V[1], grad_V[2]);
printf("Analytic %3.5E %3.5E %3.5E \n", sg[0].V_g, sg[1].V_g, sg[2].V_g);
printf("\n\n");
uvw.v2 -= h;
real grad_W[3];
uvw.v3 += h;
vac = sqrt(pow(uvw.v1, 2) + pow(uvw.v2, 2) + pow(uvw.v3, 2));
vac_g.U_g = uvw.v1 / vac;
vac_g.V_g = uvw.v2 / vac;
vac_g.W_g = uvw.v3 / vac;
aero_angles(&uvw, vac, &aero);
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
tdyn(&ea, &aero, &uvw, &pqr, &DEL, Ft, &aircraft, &rates);
grad_W[0] = (rates.v1 - rates_ref.v1) / h;
grad_W[1] = (rates.v2 - rates_ref.v2) / h;
grad_W[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to W\n");
printf("Numerical %3.5E %3.5E %3.5E \n", grad_W[0], grad_W[1], grad_W[2]);
printf("Analytic %3.5E %3.5E %3.5E \n", sg[0].W_g, sg[1].W_g, sg[2].W_g);
printf("\n\n");
uvw.v3 -= h;
vac = sqrt(pow(uvw.v1, 2) + pow(uvw.v2, 2) + pow(uvw.v3, 2));
vac_g.U_g = uvw.v1 / vac;
vac_g.V_g = uvw.v2 / vac;
vac_g.W_g = uvw.v3 / vac;
aero_angles(&uvw, vac, &aero);
real grad_P[3];
pqr.v1 += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
tdyn(&ea, &aero, &uvw, &pqr, &DEL, Ft, &aircraft, &rates);
grad_P[0] = (rates.v1 - rates_ref.v1) / h;
grad_P[1] = (rates.v2 - rates_ref.v2) / h;
grad_P[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to P\n");
printf("Numerical %3.5E %3.5E %3.5E \n", grad_P[0], grad_P[1], grad_P[2]);
printf("Analytic %3.5E %3.5E %3.5E \n", sg[0].P_g, sg[1].P_g, sg[2].P_g);
printf("\n\n");
pqr.v1 -= h;
real grad_Q[3];
pqr.v2 += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
tdyn(&ea, &aero, &uvw, &pqr, &DEL, Ft, &aircraft, &rates);
grad_Q[0] = (rates.v1 - rates_ref.v1) / h;
grad_Q[1] = (rates.v2 - rates_ref.v2) / h;
grad_Q[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to Q\n");
printf("Numerical %3.5E %3.5E %3.5E \n", grad_Q[0], grad_Q[1], grad_Q[2]);
printf("Analytic %3.5E %3.5E %3.5E \n", sg[0].Q_g, sg[1].Q_g, sg[2].Q_g);
printf("\n\n");
pqr.v2 -= h;
real grad_R[3];
pqr.v3 += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
tdyn(&ea, &aero, &uvw, &pqr, &DEL, Ft, &aircraft, &rates);
grad_R[0] = (rates.v1 - rates_ref.v1) / h;
grad_R[1] = (rates.v2 - rates_ref.v2) / h;
grad_R[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to R\n");
printf("Numerical %3.5E %3.5E %3.5E \n", grad_R[0], grad_R[1], grad_R[2]);
printf("Analytic %3.5E %3.5E %3.5E \n", sg[0].R_g, sg[1].R_g, sg[2].R_g);
printf("\n\n");
pqr.v3 -= h;
real grad_Roll[3];
ea.roll += h;
euler_angles(&ea);
aero_angles(&uvw, vac, &aero);
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
tdyn(&ea, &aero, &uvw, &pqr, &DEL, Ft, &aircraft, &rates);
grad_Roll[0] = (rates.v1 - rates_ref.v1) / h;
grad_Roll[1] = (rates.v2 - rates_ref.v2) / h;
grad_Roll[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to Roll\n");
printf("Numerical %3.5E %3.5E %3.5E \n", grad_Roll[0], grad_Roll[1], grad_Roll[2]);
printf("Analytic %3.5E %3.5E %3.5E \n", sg[0].Roll_g, sg[1].Roll_g, sg[2].Roll_g);
printf("\n\n");
ea.roll -= h;
real grad_Pitch[3];
ea.pitch += h;
euler_angles(&ea);
aero_angles(&uvw, vac, &aero);
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
tdyn(&ea, &aero, &uvw, &pqr, &DEL, Ft, &aircraft, &rates);
grad_Pitch[0] = (rates.v1 - rates_ref.v1) / h;
grad_Pitch[1] = (rates.v2 - rates_ref.v2) / h;
grad_Pitch[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to Pitch\n");
printf("Numerical %3.5E %3.5E %3.5E \n", grad_Pitch[0], grad_Pitch[1], grad_Pitch[2]);
printf("Analytic %3.5E %3.5E %3.5E \n", sg[0].Pitch_g, sg[1].Pitch_g, sg[2].Pitch_g);
printf("\n\n");
ea.pitch -= h;
real grad_Yaw[3];
ea.yaw += h;
euler_angles(&ea);
aero_angles(&uvw, vac, &aero);
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
tdyn(&ea, &aero, &uvw, &pqr, &DEL, Ft, &aircraft, &rates);
grad_Yaw[0] = (rates.v1 - rates_ref.v1) / h;
grad_Yaw[1] = (rates.v2 - rates_ref.v2) / h;
grad_Yaw[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to Yaw\n");
printf("Numerical %3.5E %3.5E %3.5E \n", grad_Yaw[0], grad_Yaw[1], grad_Yaw[2]);
printf("Analytic %3.5E %3.5E %3.5E \n", sg[0].Yaw_g, sg[1].Yaw_g, sg[2].Yaw_g);
printf("\n\n");
ea.yaw -= h;
euler_angles(&ea);
real grad_el[6];
aero_con.v1 += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
tdyn(&ea, &aero, &uvw, &pqr, &DEL, Ft, &aircraft, &rates);
grad_el[0] = (rates.v1 - rates_ref.v1) / h;
grad_el[1] = (rates.v2 - rates_ref.v2) / h;
grad_el[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to Elevator\n");
printf("Numerical %3.5E %3.5E %3.5E \n", grad_el[0], grad_el[1], grad_el[2]);
printf("Analytic %3.5E %3.5E %3.5E \n", cg[0].elev_g, cg[1].elev_g, cg[2].elev_g);
printf("\n\n");
aero_con.v1 -= h;
real grad_ail[6];
aero_con.v2 += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
tdyn(&ea, &aero, &uvw, &pqr, &DEL, Ft, &aircraft, &rates);
grad_ail[0] = (rates.v1 - rates_ref.v1) / h;
grad_ail[1] = (rates.v2 - rates_ref.v2) / h;
grad_ail[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to Aileron\n");
printf("Numerical %3.5E %3.5E %3.5E\n", grad_ail[0], grad_ail[1], grad_ail[2]);
printf("Analytic %3.5E %3.5E %3.5E\n", cg[0].aileron_g, cg[1].aileron_g, cg[2].aileron_g);
printf("\n\n");
aero_con.v2 -= h;
real grad_rud[6];
aero_con.v3 += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
tdyn(&ea, &aero, &uvw, &pqr, &DEL, Ft, &aircraft, &rates);
grad_rud[0] = (rates.v1 - rates_ref.v1) / h;
grad_rud[1] = (rates.v2 - rates_ref.v2) / h;
grad_rud[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to Rudder\n");
printf("Numerical %3.5E %3.5E %3.5E\n", grad_rud[0], grad_rud[1], grad_rud[2]);
printf("Analytic %3.5E %3.5E %3.5E\n", cg[0].rudder_g, cg[1].rudder_g, cg[2].rudder_g);
printf("\n\n");
aero_con.v3 -= h;
real grad_thrust[6];
Ft += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
tdyn(&ea, &aero, &uvw, &pqr, &DEL, Ft, &aircraft, &rates);
grad_thrust[0] = (rates.v1 - rates_ref.v1) / h;
grad_thrust[1] = (rates.v2 - rates_ref.v2) / h;
grad_thrust[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to Thrust\n");
printf("Numerical %3.5E %3.5E %3.5E\n", grad_thrust[0], grad_thrust[1], grad_thrust[2]);
printf("Analytic %3.5E %3.5E %3.5E\n", cg[0].thrust_g, cg[1].thrust_g, cg[2].thrust_g);
printf("\n\n");
Ft -= h;
return 0;
}
int check_grad_rdyn(real h, real tol)
{
struct Vec3 uvw = {120, 90, 60};
real vac = sqrt(pow(uvw.v1, 2) + pow(uvw.v2, 2) + pow(uvw.v3, 2));
struct StateGrad vac_g;
vac_g.U_g = uvw.v1 / vac;
vac_g.V_g = uvw.v2 / vac;
vac_g.W_g = uvw.v3 / vac;
struct Vec3 pqr = {10, -2.0, 8.0};
struct Vec3 aero_con = {3.0, 1.0, 2.5};
real rho = 0.002376892406675; // slug / ft^3
struct Aircraft aircraft;
pioneer_uav(&aircraft);
struct Vec3 DEL_ref;
struct Vec3 LMN_ref;
struct Vec3 rates_ref;
struct Vec3 DEL;
struct Vec3 LMN;
struct Vec3 rates;
struct StateGrad sg_f[6];
struct ControlGrad cg_f[6];
struct StateGrad sg[3];
struct ControlGrad cg[3];
struct AeroAngles aero;
// Reference
aero_angles(&uvw, vac, &aero);
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac,
&DEL_ref, &LMN_ref);
rdyn(&pqr, &LMN_ref, &aircraft, &rates_ref);
// Analytic
aero_angles_g(&uvw, vac, &vac_g, &aero);
aero_forces_g(&aero, &pqr, &aero_con, &aircraft, rho, vac,
&vac_g, &DEL, &LMN, sg_f, cg_f);
rdyn_g(&pqr, &LMN, sg_f + 3, cg_f + 3, &aircraft, &rates, sg, cg);
printf("Checking value computation\n");
printf("Numerical %3.5E %3.5E %3.5E\n", rates_ref.v1, rates_ref.v2, rates_ref.v3);
printf("Analytic %3.5E %3.5E %3.5E\n", rates.v1, rates.v2, rates.v3);
printf("\n\n\n");
real grad_U[3];
uvw.v1 += h;
vac = sqrt(pow(uvw.v1, 2) + pow(uvw.v2, 2) + pow(uvw.v3, 2));
vac_g.U_g = uvw.v1 / vac;
vac_g.V_g = uvw.v2 / vac;
vac_g.W_g = uvw.v3 / vac;
aero_angles(&uvw, vac, &aero);
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
rdyn(&pqr, &LMN, &aircraft, &rates);
grad_U[0] = (rates.v1 - rates_ref.v1) / h;
grad_U[1] = (rates.v2 - rates_ref.v2) / h;
grad_U[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to U\n");
printf("Numerical %3.5E %3.5E %3.5E \n", grad_U[0], grad_U[1], grad_U[2]);
printf("Analytic %3.5E %3.5E %3.5E \n", sg[0].U_g, sg[1].U_g, sg[2].U_g);
printf("\n\n");
uvw.v1 -= h;
real grad_V[3];
uvw.v2 += h;
vac = sqrt(pow(uvw.v1, 2) + pow(uvw.v2, 2) + pow(uvw.v3, 2));
vac_g.U_g = uvw.v1 / vac;
vac_g.V_g = uvw.v2 / vac;
vac_g.W_g = uvw.v3 / vac;
aero_angles(&uvw, vac, &aero);
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
rdyn(&pqr, &LMN, &aircraft, &rates);
grad_V[0] = (rates.v1 - rates_ref.v1) / h;
grad_V[1] = (rates.v2 - rates_ref.v2) / h;
grad_V[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to V\n");
printf("Numerical %3.5E %3.5E %3.5E \n", grad_V[0], grad_V[1], grad_V[2]);
printf("Analytic %3.5E %3.5E %3.5E \n", sg[0].V_g, sg[1].V_g, sg[2].V_g);
printf("\n\n");
uvw.v2 -= h;
real grad_W[3];
uvw.v3 += h;
vac = sqrt(pow(uvw.v1, 2) + pow(uvw.v2, 2) + pow(uvw.v3, 2));
vac_g.U_g = uvw.v1 / vac;
vac_g.V_g = uvw.v2 / vac;
vac_g.W_g = uvw.v3 / vac;
aero_angles(&uvw, vac, &aero);
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
rdyn(&pqr, &LMN, &aircraft, &rates);
grad_W[0] = (rates.v1 - rates_ref.v1) / h;
grad_W[1] = (rates.v2 - rates_ref.v2) / h;
grad_W[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to W\n");
printf("Numerical %3.5E %3.5E %3.5E \n", grad_W[0], grad_W[1], grad_W[2]);
printf("Analytic %3.5E %3.5E %3.5E \n", sg[0].W_g, sg[1].W_g, sg[2].W_g);
printf("\n\n");
uvw.v3 -= h;
vac = sqrt(pow(uvw.v1, 2) + pow(uvw.v2, 2) + pow(uvw.v3, 2));
vac_g.U_g = uvw.v1 / vac;
vac_g.V_g = uvw.v2 / vac;
vac_g.W_g = uvw.v3 / vac;
aero_angles(&uvw, vac, &aero);
real grad_P[3];
pqr.v1 += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
rdyn(&pqr, &LMN, &aircraft, &rates);
grad_P[0] = (rates.v1 - rates_ref.v1) / h;
grad_P[1] = (rates.v2 - rates_ref.v2) / h;
grad_P[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to P\n");
printf("Numerical %3.5E %3.5E %3.5E \n", grad_P[0], grad_P[1], grad_P[2]);
printf("Analytic %3.5E %3.5E %3.5E \n", sg[0].P_g, sg[1].P_g, sg[2].P_g);
printf("\n\n");
pqr.v1 -= h;
real grad_Q[3];
pqr.v2 += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
rdyn(&pqr, &LMN, &aircraft, &rates);
grad_Q[0] = (rates.v1 - rates_ref.v1) / h;
grad_Q[1] = (rates.v2 - rates_ref.v2) / h;
grad_Q[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to Q\n");
printf("Numerical %3.5E %3.5E %3.5E \n", grad_Q[0], grad_Q[1], grad_Q[2]);
printf("Analytic %3.5E %3.5E %3.5E \n", sg[0].Q_g, sg[1].Q_g, sg[2].Q_g);
printf("\n\n");
pqr.v2 -= h;
real grad_R[3];
pqr.v3 += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
rdyn(&pqr, &LMN, &aircraft, &rates);
grad_R[0] = (rates.v1 - rates_ref.v1) / h;
grad_R[1] = (rates.v2 - rates_ref.v2) / h;
grad_R[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to R\n");
printf("Numerical %3.5E %3.5E %3.5E \n", grad_R[0], grad_R[1], grad_R[2]);
printf("Analytic %3.5E %3.5E %3.5E \n", sg[0].R_g, sg[1].R_g, sg[2].R_g);
printf("\n\n");
pqr.v3 -= h;
real grad_el[6];
aero_con.v1 += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
rdyn(&pqr, &LMN, &aircraft, &rates);
grad_el[0] = (rates.v1 - rates_ref.v1) / h;
grad_el[1] = (rates.v2 - rates_ref.v2) / h;
grad_el[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to Elevator\n");
printf("Numerical %3.5E %3.5E %3.5E \n", grad_el[0], grad_el[1], grad_el[2]);
printf("Analytic %3.5E %3.5E %3.5E \n", cg[0].elev_g, cg[1].elev_g, cg[2].elev_g);
printf("\n\n");
aero_con.v1 -= h;
real grad_ail[6];
aero_con.v2 += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
rdyn(&pqr, &LMN, &aircraft, &rates);
grad_ail[0] = (rates.v1 - rates_ref.v1) / h;
grad_ail[1] = (rates.v2 - rates_ref.v2) / h;
grad_ail[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to Aileron\n");
printf("Numerical %3.5E %3.5E %3.5E\n", grad_ail[0], grad_ail[1], grad_ail[2]);
printf("Analytic %3.5E %3.5E %3.5E\n", cg[0].aileron_g, cg[1].aileron_g, cg[2].aileron_g);
printf("\n\n");
aero_con.v2 -= h;
real grad_rud[6];
aero_con.v3 += h;
aero_forces(&aero, &pqr, &aero_con, &aircraft, rho, vac, &DEL, &LMN);
rdyn(&pqr, &LMN, &aircraft, &rates);
grad_rud[0] = (rates.v1 - rates_ref.v1) / h;
grad_rud[1] = (rates.v2 - rates_ref.v2) / h;
grad_rud[2] = (rates.v3 - rates_ref.v3) / h;
printf("Checking Gradient with respect to Rudder\n");
printf("Numerical %3.5E %3.5E %3.5E\n", grad_rud[0], grad_rud[1], grad_rud[2]);
printf("Analytic %3.5E %3.5E %3.5E\n", cg[0].rudder_g, cg[1].rudder_g, cg[2].rudder_g);
printf("\n\n");
aero_con.v3 -= h;
return 0;
}
int check_grad_rigid_body_dyn(real h, real tol)
{
real time = 0.0;
real state[12] = {1.0, 2.0, 3.0, 4.0, 5.0, 6.0,
7.0, 8.0, 9.0, 10.0, 11.0, 12.0};
// elevator aileron rudder thrust
real control[4] = {1.5, 2.5, 3.5, 4.5};
real out_ref[12];
real out[12];
real jac[144+48];
struct Aircraft aircraft;
pioneer_uav(&aircraft);
rigid_body_lin_forces(time, state, control, out_ref, NULL, &aircraft);
rigid_body_lin_forces_jac(time, state, control, out, jac, &aircraft);
printf("Checking value computation\n");
for (size_t ii = 0; ii < 12; ii++){
printf("%10.5E %10.5E %10.5E \n", out_ref[ii], out[ii],
out[ii] - out_ref[ii]);
}
printf("Checking gradient computation\n");
for (size_t ii = 0; ii < 12; ii++){
state[ii] += h;
rigid_body_lin_forces(time, state, control, out, NULL, &aircraft);
printf("\n\n\n");
printf("ii = %zu\n", ii);
for (size_t jj = 0; jj < 12; jj++){
real val = (out[jj] - out_ref[jj]) / h;
printf("\t %10.5E %10.5E %10.5E\n", val, jac[ii*12+jj], (val - jac[ii*12 + jj])/val);
}
state[ii] -= h;
}
printf("\n");
printf("--------------------------\n");
printf("Gradient wrt controls\n");
printf("--------------------------\n");
printf("\n");
for (size_t ii = 0; ii < 4; ii++){
control[ii] += h;
rigid_body_lin_forces(time, state, control, out, NULL, &aircraft);
printf("\n\n\n");
printf("ii = %zu\n", ii);
for (size_t jj = 0; jj < 12; jj++){
real val = (out[jj] - out_ref[jj]) / h;
printf("\t %10.5E %10.5E %10.5E\n", val, jac[144 + ii*12+jj],
(val - jac[144 + ii*12 + jj])/val);
}
control[ii] -= h;
}