我正在尝试使用系列扩展来编写数值积分器，但它目前在第二步中失败了。如果我使用printf打印出任何变量，这会得到修复，但我找不到原因。我已经阅读过很多关于类似场景的帖子，但似乎都没有回答我的问题。如果我在函数Integrate_One_Step（...）中打印出* t0，* Theta0和* Theta1的值，它们都具有正确的值，并显示t0，Theta0和Theta1以及每一步更新。有人能告诉我我错过了什么吗？请参阅下面的代码。 谢谢。
void main()
{
void Integrate_One_Step(double *Theta0, double *Theta1, double *t0, double t_final, double a, double epsilon, double gamma);
int i;
double a,epsilon,gamma,t0,t_final,Theta0,Theta1, tOld;
clock_t tic = clock();
epsilon = 0.1; a = 0.5; gamma = 0.07; t0 = 1e0; tOld = t0; t_final = 10;
Theta0 = 1.753317649649940; Theta1 = 1.759074746790801;
do{
//printf("t = %18.15f Theta = %18.15f dot_Theta = %18.15f\n", t0, Theta0,Theta1);
//printf("tstart = %18.15f\n", t0);
Integrate_One_Step(&Theta0,&Theta1,&t0,t_final,a,epsilon,gamma);
//printf("tfinish = %18.15f\n", t0);
//printf("theta = %18.15f\n", Theta0);
//printf("tOld = %18.15f\n", tOld);
//printf("t = %18.15f Theta = %18.15f dot_Theta = %18.15f\n", t0, Theta0,Theta1);
if(t0 <= tOld){
printf("\nTime Step became zero\n");
printf("t = %18.15f Theta = %18.15f dot_Theta = %18.15f\n", t0, Theta0,Theta1);
break;
}
else { tOld = t0; }
if(Theta0 != Theta0){
printf("t = %18.15f Theta = %18.15f dot_Theta = %18.15f\n", t0, Theta0,Theta1);
break;
}
if(Theta1 != Theta1){
printf("t = %18.15f Theta = %18.15f dot_Theta = %18.15f\n", t0, Theta0,Theta1);
break;
}
} while(t0 < t_final);
clock_t toc = clock();
printf("Elapsed: %f seconds\n", (double)(toc - tic) / CLOCKS_PER_SEC);
}
编辑： 我已经发布了下面的完整代码，供希望尝试自己运行的人使用。 感谢。
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#define OrderArray 25
#define HornerOrder 30
void SeriesMult(double A[], double B[], double C[], int length);
void Array_Division_By_Constant(double A[],double B[], double constant, int length);
void Array_Multiply_By_Constant(double A[],double B[], double constant, int length);
void ArrayAssign(double A[], double B[], int length);
void Series_Add(double A[],double B[], double C[], int length);
int Time_Steps_Used[] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
double Fac[OrderArray],SinFac[HornerOrder],CosFac[HornerOrder],time_step[] = {0.005,0.01,0.03,0.06,0.1,0.2,0.4,0.6,0.8,0.9,1,1.1,1.2,1.3,1.4,1.5,1.6,1.7};
void main()
{
void Integrate_One_Step(double *Theta0, double *Theta1, double *t0, double t_final, double a, double epsilon, double gamma);
int i;
double a,epsilon,gamma,t0,t_final,Theta0,Theta1, tOld;
clock_t tic = clock();
epsilon = 0.1; a = 0.5; gamma = 0.07; t0 = 1e0; tOld = t0; t_final = 10;
//Defines Fac[], SinFac[] and CosFac[] which are arrays of factorials
Fac[0] = 1e0; SinFac[0] = 1;
for (i = 1;i<= OrderArray-1;i++) Fac[i] = i*Fac[i-1];
for(i=1;i<=HornerOrder-1;i++){ SinFac[i] = -(2*i)*((2*i)+1); }
for(i=0;i<=HornerOrder-1;i++){ CosFac[i] = -(2*(i+1))*((2*i)+1); }
Theta0 = 1.753317649649940; Theta1 = 1.759074746790801;
do{
//printf("t = %18.15f Theta = %18.15f dot_Theta = %18.15f\n", t0, Theta0,Theta1);
//printf("tstart = %18.15f\n", t0);
Integrate_One_Step(&Theta0,&Theta1,&t0,t_final,a,epsilon,gamma);
//printf("tfinish = %18.15f\n", t0);
//printf("theta = %18.15f\n", Theta0);
//printf("tOld = %18.15f\n", tOld);
//printf("t = %18.15f Theta = %18.15f dot_Theta = %18.15f\n", t0, Theta0,Theta1);
if(t0 <= tOld){
printf("\nTime Step became zero\n");
printf("t = %18.15f Theta = %18.15f dot_Theta = %18.15f\n", t0, Theta0,Theta1);
break;
}else{ tOld = t0; }
if(Theta0 != Theta0){
printf("t = %18.15f Theta = %18.15f dot_Theta = %18.15f\n", t0, Theta0,Theta1);
break;
}
if(Theta1 != Theta1){
printf("t = %18.15f Theta = %18.15f dot_Theta = %18.15f\n", t0, Theta0,Theta1);
break;
}
//printf("tOld = %18.15f\n", tOld);
} while(t0 < t_final);
printf("\n\nt = %18.15f Theta = %18.15f dot_Theta = %18.15f\n", t0, Theta0,Theta1);
printf("Time steps used: ");
for(i = 0;i<=17;i++) printf("%i ",Time_Steps_Used[i]);
printf("\n\n");
clock_t toc = clock();
printf("Elapsed: %f seconds\n", (double)(toc - tic) / CLOCKS_PER_SEC);
}
void Integrate_One_Step(double *Theta0, double *Theta1, double *t0, double t_final, double a, double epsilon, double gamma)
{
double FGH_Nth_Position_Calc(double a, double epsilon, double gamma, double t0, double theta0, double X[], int Position, double dotTheta[], double ddotTheta[]);
int i,k;
double Theta[OrderArray],X[OrderArray],dotTheta[OrderArray-1],ddotTheta[OrderArray-2],/*FGH[OrderArray-2],*/ Thet,dotThet,ddotThet,EqnValue,Tol = pow(10,-12), t_inc = 0;
//printf("At the start of step t = %18.15f \n",*t0);
Theta[0] = *Theta0; Theta[1] = *Theta1; dotTheta[0] = Theta[1]; ddotTheta[0] = 0;
X[0] = 0; //X is Theta without the constant term
for(i=1;i<=OrderArray-1;i++){ X[i] = Theta[i];}
for(i=0;i<=OrderArray-3;i++){
//Calculate Theta i+2
Theta[i+2] = FGH_Nth_Position_Calc(a,epsilon,gamma,(*t0),Theta[0],X,i,dotTheta,ddotTheta);
//update X
X[i+2] = Theta[i+2];
//Update Theta' and Theta''
dotTheta[i+1] = (i+2)*Theta[i+2];
//ddotTheta[i] = (i+1)*(i+2)*Theta[i+2]; Slightly more multiplication, unnecessary.
ddotTheta[i] = (i+1)*dotTheta[i+1];
}
//printf("Theta series: ");
//for(i = 0;i<=OrderArray-1;i++) printf("%18.15f ",Theta[i]);
//printf("\n\n");
//Calculate dotTheta and ddotTheta, then check if the step works
for(k=0;k<=17;k++){
ddotThet = 0.0; dotThet = 0.0; Thet = Theta[OrderArray-1];
if(time_step[k] < (t_final - *t0)){
for(i = OrderArray-2;i>=0;i--){
ddotThet = ddotThet*time_step[k] + dotThet; dotThet = dotThet*time_step[k] + Thet; Thet = Thet*time_step[k] + Theta[i];
}
ddotThet *= 2e0;
EqnValue = ddotThet + (((epsilon*sin(*t0+time_step[k]))/(1 + epsilon*cos(*t0+time_step[k])))+gamma)*dotThet + (a/(1 + epsilon*cos(*t0+time_step[k])))*sin(Thet);
if(fabs(EqnValue) > Tol){ break;
}else{ t_inc = time_step[k]; *Theta0 = Thet; *Theta1 = dotThet; if(k>0){Time_Steps_Used[k-1] -= 1;} Time_Steps_Used[k] += 1; }
}else{
for(i = OrderArray-2;i>=0;i--){
ddotThet = ddotThet*(t_final-*t0) + dotThet; dotThet = dotThet*(t_final-*t0) + Thet; Thet = Thet*(t_final-*t0) + Theta[i];
}
ddotThet *= 2e0;
EqnValue = ddotThet + (((epsilon*sin(t_final))/(1 + epsilon*cos(t_final)))+gamma)*dotThet + (a/(1 + epsilon*cos(t_final)))*sin(Thet);
if(fabs(EqnValue) > Tol){ break; }else{ t_inc = (t_final - *t0); *Theta0 = Thet; *Theta1 = dotThet; }
}
}
//printf("After equation satisfied t0 = %18.15f\n",*t0);
//printf("t_inc = %18.15f \n",t_inc);
printf("theta = %18.15f dot_theta = %18.15f\n\n",*Theta0,*Theta1);
//Add time step to t0
*t0 = *t0 + t_inc;
//printf("After incremented t = %18.15f\n",*t0);
}
double FGH_Nth_Position_Calc(double a, double epsilon, double gamma, double t0, double theta0, double X[], int Position, double dotTheta[], double ddotTheta[])
{
void CosT_Calc(double coss[], double t0, int length);
void FCalc(double epsilon, double Cost[], double ddotTheta[], double F[], int length);
void HCalc(double a, double X[], double H[], double theta0, int Position);
void GCalc(double epsilon, double gamma, double t0, double Cost[], double G[], double dotTheta[], int Position);
int i;
double F[Position+1],H[Position+1],G[Position+1],Cost[Position+1],FGH[Position+1],Divider;
//for(i = 0;i<=Position;i++) printf("%18.15f ",dotTheta[i]);
//printf("\n\n");
//for(i = 0;i<=Position;i++) printf("%18.15f ",ddotTheta[i]);
//printf("\n\n");
//for(i = 0;i<=Position;i++) printf("%18.15f ",ddotTheta2[i]);
//printf("\n\n");
//Calculates coefficicients of cos(t) where t is the total time after the step is taken.
CosT_Calc(Cost,t0,Position+1);
//for(i=0;i<=Position;i++) printf("%18.15f ",Cost[i]); printf("\n");
//Calculates F = epsilon*cos(t - t0)* \theta''
FCalc(epsilon,Cost, ddotTheta, F, Position);
//for(i = 0;i<=Position;i++) printf("%18.15f ",F[i]);
//printf("\n\n");
//Calculates G = [epsilon*sin(t) + gamma*(1+epsilon*cos(t)) ]*theta'
GCalc(epsilon,gamma,t0,Cost,G,dotTheta,Position);
//for(i = 0;i<=Position;i++) printf("%18.15f ",G[i]);
//printf("\n\n");
//Calculates H = a*sin(Theta)
HCalc(a,X, H,theta0,Position);
//for(i = 0;i<=Position;i++) printf("%18.15f ",H[i]);
//printf("\n\n");
Series_Add(F,G,FGH,Position+1);
Series_Add(FGH,H,FGH,Position+1);
Divider = (Position+1)*(Position+2)*(1+epsilon*cos(t0)); //printf("Divider = %18.15f\n",Divider);
Array_Division_By_Constant(FGH,FGH,Divider, Position+1);
return(-FGH[Position]);
}
void GCalc(double epsilon, double gamma, double t0, double Cost[], double G[], double dotTheta[], int Position)
{
void SinT_Calc(double Sinn[], double t0, int length);
int i;
double Sint[Position+1],epsilSint[Position+1],epsilCostPlusOne[Position+1],g[Position+1];
//Calculates sin(t)
SinT_Calc(Sint,t0,Position+1);
//printf("Sin(t) series");
//for(i=0;i<=Position;i++) printf("%18.15f ",Sint[i]); printf("\n");
//multiplies sin(t) and cos(t) by epsilon
Array_Multiply_By_Constant(epsilSint,Sint,epsilon,Position+1);
Array_Multiply_By_Constant(epsilCostPlusOne,Cost,epsilon,Position+1);
//Calculates gamma*(1 + epsilon*cos(t))
epsilCostPlusOne[0] = epsilCostPlusOne[0]+1;
Array_Multiply_By_Constant(epsilCostPlusOne,epsilCostPlusOne,gamma,Position+1);
//Calculates g = [epsilon*sin(t) + gamma*(1+epsilon*cos(t)) ]
Series_Add(epsilSint,epsilCostPlusOne,g,Position+1); //This appears to be correct when comparing with maple
//for(i = 0;i<=Position;i++) printf("%18.15f ",g[i]);
//printf("\n\n");
//Multiples g by theta'
SeriesMult(g,dotTheta,G,Position+1);
}
void HCalc(double a, double X[], double H[], double theta0, int Position)
{
void SinTheta_Calc(double CosX[], double SinX[], double SinTheta[], double theta0, int length);
void CosX_Calc(double Xsquared[], double CosTemp[], int length);
void SinX_Calc(double X[], double Xsquared[], double Sinn[], int length);
double NthTerm(double A[], double B[], int n, int sizeA, int sizeB);
int i;
double Xsquared[Position+1],CosX[Position+1],SinX[Position+1],SinTheta[Position+1];
//Calculates Xsquared
for(i=0;i<=Position;i++){
Xsquared[i] = NthTerm(X,X,i,Position,Position);
}
//Calulate Cos(X), Sin(X)
CosX_Calc(Xsquared,CosX,Position+1); SinX_Calc(X,Xsquared,SinX,Position+1);
//Calculate Sin(Theta) from Sin(X) and Cos(X)
SinTheta_Calc(CosX,SinX,SinTheta,theta0, Position+1);
//H = a*SinTheta
Array_Multiply_By_Constant(H,SinTheta, a, Position+1);
}
void SinTheta_Calc(double CosX[], double SinX[], double SinTheta[], double theta0, int length)
{
int i;
double CosXTemp[length],SinXTemp[length], S_Theta0, C_Theta0;
S_Theta0 = sin(theta0); C_Theta0 = cos(theta0);
Array_Multiply_By_Constant(SinXTemp,SinX,C_Theta0,length);
Array_Multiply_By_Constant(CosXTemp,CosX,S_Theta0,length);
Series_Add(CosXTemp,SinXTemp,SinTheta,length);
}
void CosX_Calc(double Xsquared[], double CosTemp[], int length)
{
//Calculates Cos(X) where X is the series for Theta, without the constant term, outputs the final series for Cos(X) as CosTemp
int i,j,SubHornerOrder;
double Xsquared_divided[length], Coss[length];
if(length == 0){SubHornerOrder = 1; }
else if(length%2 == 0) {SubHornerOrder = length/2; }
else {SubHornerOrder = (length+1)/2; }
Array_Division_By_Constant(CosTemp,Xsquared,CosFac[SubHornerOrder-1],length);
CosTemp[0] = 1;
for(i=(SubHornerOrder-1);i>=1;i--){
Array_Division_By_Constant(Xsquared_divided,Xsquared,CosFac[i-1],length);
SeriesMult(Xsquared_divided, CosTemp, Coss, length);
ArrayAssign(CosTemp, Coss, length);
CosTemp[0] = 1;
}
}
void SinX_Calc(double X[], double Xsquared[], double Sinn[], int length)
{
//Calculate Sin(X) where X is the series for Theta, without the constant term, outputs the final series for Sin(X) as Sinn
int i,j, SubHornerOrder;
double Xsquared_divided[length], SinTemp[length];
if(length == 0){SubHornerOrder = 1; }
else if(length%2 == 0) {SubHornerOrder = length/2; }
else {SubHornerOrder = (length+1)/2; }
Array_Division_By_Constant(SinTemp,Xsquared,SinFac[SubHornerOrder-1],length);
SinTemp[0] = 1;
for(i=(SubHornerOrder-1);i>=2;i--){
Array_Division_By_Constant(Xsquared_divided,Xsquared,SinFac[i-1],length);
SeriesMult(Xsquared_divided, SinTemp, Sinn, length);
ArrayAssign(SinTemp, Sinn, length);
SinTemp[0] = 1;
}
SeriesMult(X,SinTemp,Sinn,length);
}
void FCalc(double epsilon, double Cost[], double ddotTheta[], double F[], int Position)
{
double epsilCost[Position+1];
//multiplies Cos(t) by epsilon
Array_Multiply_By_Constant(epsilCost,Cost,epsilon,Position+1);
//Calculates F = epsilon*cos(t - t0)* \theta''
SeriesMult(epsilCost, ddotTheta, F, Position+1);
}
void SinT_Calc(double sinn[], double t0, int length)
{ // Sets up Taylor series coefficients for sin(t) = cos(t0)sin(t-t0) + sin(t0)cos(t-t0)
int i;
double st0, ct0;
int m1n(int i);
st0 = sin(t0); ct0 = cos(t0);
for (i = 0; i <= length; i++)
{
if (i%2 == 0)
sinn[i] = st0*m1n(i/2)/Fac[i];
else
sinn[i] = ct0*m1n((i-1)/2)/Fac[i];
}
}
void CosT_Calc(double coss[], double t0, int length)
{ // Sets up Taylor series coefficients for cos(t) = cos(t0)cos(t-t0) - sin(t0)sin(t-t0)
int i;
double st0, ct0;
int m1n(int i);
st0 = sin(t0); ct0 = cos(t0);
for (i = 0; i <= length; i++)
{
if (i%2 == 0)
coss[i] = ct0*m1n(i/2)/Fac[i];
else
coss[i] = -st0*m1n((i-1)/2)/Fac[i];
}
}
int m1n(int i)
{
if (i%2 == 0) return(1);
else return(-1);
}
double NthTerm(double A[], double B[], int n, int sizeA, int sizeB)
{
//Multiplies returns the n-th term when 2 arrays are multiplied
double nth_term = 0;
int j;
for(j=0; j <= n;j++){
if (j < sizeA){
if ( (n-j)< sizeB){
nth_term += A[j]*B[n-j];
}
}
}
return(nth_term);
}
void Series_Add(double A[],double B[], double C[], int length)
{
int i;
for(i=0;i<=length-1;i++){
C[i] = A[i] + B[i];
}
}
void SeriesMult(double A[], double B[], double C[], int length)
{
//Multiplies two arrays, returns nothing but stores the answer in the array C
int i, j;
double c;
for(i=0; i<=length-1; i++){
c = 0;
for(j=0; j<=i; j++){
c = c + A[j]*B[i-j];
}
C[i] = c;
}
}
void Array_Multiply_By_Constant(double A[],double B[], double constant, int length)
{
int i;
for(i=0;i<=length-1;i++){
A[i] = B[i]*constant;
}
}
void Array_Division_By_Constant(double A[],double B[], double constant, int length)
{
int i;
for(i=0;i<=length-1;i++){
A[i] = B[i]/constant;
}
}
void ArrayAssign(double A[], double B[], int length)
{
int i;
for(i=0;i<=length-1;i++){
A[i] = B[i];
}
}
答案 0 :(得分：2)
在以下位置存在缓冲区溢出错误：
void SinT_Calc(double sinn[], double t0, int length)
{ // Sets up Taylor series coefficients for sin(t) = cos(t0)sin(t-t0) + sin(t0)cos(t-t0)
int i;
double st0, ct0;
int m1n(int i);
st0 = sin(t0); ct0 = cos(t0);
for (i = 0; i <= length; i++) // <=== BUFFER OVERFLOW, should be strict <
{
if (i%2 == 0)
sinn[i] = st0*m1n(i/2)/Fac[i];
else
sinn[i] = ct0*m1n((i-1)/2)/Fac[i];
}
}
如果我有另外一条不相关的建议，那就是永远不要在堆栈上使用动态大小的数组（实际上，这甚至编译都令人惊讶）：
double Xsquared[Position+1];
改为使用
double* Xsquared = (double*)malloc((Position + 1) * sizeof(double));
//...
free(Xsquared);