三次样条插值(Cubic Spline Interpolation)及代码实现(C语言)

用C语言写了一个三次样条插值(自然边界)的S-Function，代码如下：

#define S_FUNCTION_NAME  cubic#define S_FUNCTION_LEVEL 2#include "simstruc.h"#include "malloc.h"  //方便使用变量定义数组大小static void mdlInitializeSizes(SimStruct *S){    /*参数只有一个，是n乘2的定点数组[xi, yi]:     * [ x1，y1;     *   x2, y2;     *   ..., ...;     *   xn, yn;    */    ssSetNumSFcnParams(S, 1);     if (ssGetNumSFcnParams(S) != ssGetSFcnParamsCount(S)) return;    ssSetNumContStates(S, 0);    ssSetNumDiscStates(S, 0);    if (!ssSetNumInputPorts(S, 1)) return;  //输入是x    ssSetInputPortWidth(S, 0, 1);    ssSetInputPortRequiredContiguous(S, 0, true);    ssSetInputPortDirectFeedThrough(S, 0, 1);    if (!ssSetNumOutputPorts(S, 1)) return;  //输出是S(x)    ssSetOutputPortWidth(S, 0, 1);    ssSetNumSampleTimes(S, 1);    ssSetNumRWork(S, 0);    ssSetNumIWork(S, 0);    ssSetNumPWork(S, 0);    ssSetNumModes(S, 0);    ssSetNumNonsampledZCs(S, 0);    ssSetSimStateCompliance(S, USE_DEFAULT_SIM_STATE);    ssSetOptions(S, 0);}static void mdlInitializeSampleTimes(SimStruct *S){    ssSetSampleTime(S, 0, CONTINUOUS_SAMPLE_TIME);    ssSetOffsetTime(S, 0, 0.0);}#define MDL_INITIALIZE_CONDITIONS#if defined(MDL_INITIALIZE_CONDITIONS)  static void mdlInitializeConditions(SimStruct *S)  {  }#endif#define MDL_START#if defined(MDL_START)   static void mdlStart(SimStruct *S)  {  }#endif /*  MDL_START */static void mdlOutputs(SimStruct *S, int_T tid){    const real_T *map = mxGetPr(ssGetSFcnParam(S,0));  //获取定点数据    const int_T *mapSize = mxGetDimensions(ssGetSFcnParam(S,0));  //定点数组维数    const real_T *x = (const real_T*) ssGetInputPortSignal(S,0);  //输入x    real_T       *y = ssGetOutputPortSignal(S,0); //输出y    int_T step = 0;  //输入x在定点数中的位置    int_T i;    real_T yval;    for (i = 0; i < mapSize[0]; i++)    {        if (x[0] >= map[i] && x[0] < map[i + 1])        {            step = i;            break;        }    }        cubic_getval(&yval, mapSize, map, x[0], step);    y[0] = yval;    }//自然边界的三次样条曲线函数void cubic_getval(real_T* y, const int_T* size, const real_T* map, const real_T x, const int_T step){    int_T n = size[0];        //曲线系数    real_T* ai = (real_T*)malloc(sizeof(real_T) * (n-1));    real_T* bi = (real_T*)malloc(sizeof(real_T) * (n-1));    real_T* ci = (real_T*)malloc(sizeof(real_T) * (n-1));    real_T* di = (real_T*)malloc(sizeof(real_T) * (n-1));        real_T* h = (real_T*)malloc(sizeof(real_T) * (n-1));  //x的??        /* M矩阵的系数     *[B0, C0, ...     *[A1, B1, C1, ...     *[0,  A2, B2, C2, ...     *[0, ...             An-1, Bn-1]     */    real_T* A = (real_T*)malloc(sizeof(real_T) * (n-2));    real_T* B = (real_T*)malloc(sizeof(real_T) * (n-2));    real_T* C = (real_T*)malloc(sizeof(real_T) * (n-2));    real_T* D = (real_T*)malloc(sizeof(real_T) * (n-2)); //等号右边的常数矩阵    real_T* E = (real_T*)malloc(sizeof(real_T) * (n-2)); //M矩阵        real_T* M = (real_T*)malloc(sizeof(real_T) * (n));  //包含端点的M矩阵        int_T i;        //计算x的步长    for ( i = 0; i < n -1; i++)    {        h[i] = map[i + 1] - map[i];    }        //指定系数    for( i = 0; i< n - 3; i++)    {        A[i] = h[i]; //忽略A[0]        B[i] = 2 * (h[i] + h[i+1]);        C[i] = h[i+1]; //忽略C(n-1)    }        //指定常数D    for (i = 0; i<n - 3; i++)    {        D[i] = 6 * ((map[n + i + 2] - map[n + i + 1]) / h[i + 1] - (map[n + i + 1] - map[n + i]) / h[i]);    }            //求解三对角矩阵，结果赋值给E    TDMA(E, n-3, A, B, C, D);        M[0] = 0; //自然边界的首端M为0    M[n-1] = 0;  //自然边界的末端M为0    for(i=1; i<n-1; i++)    {        M[i] = E[i-1]; //其它的M值    }        //?算三次?条曲?的系数    for( i = 0; i < n-1; i++)    {        ai[i] = map[n + i];        bi[i] = (map[n + i + 1] - map[n + i]) / h[i] - (2 * h[i] * M[i] + h[i] * M[i + 1]) / 6;        ci[i] = M[i] / 2;        di[i] = (M[i + 1] - M[i]) / (6 * h[i]);    }        *y = ai[step] + bi[step]*(x - map[step]) + ci[step] * (x - map[step]) * (x - map[step]) + di[step] * (x - map[step]) * (x - map[step]) * (x - map[step]);        free(h);    free(A);    free(B);    free(C);    free(D);    free(E);    free(M);    free(ai);    free(bi);    free(ci);    free(di);}void TDMA(real_T* X, const int_T n, real_T* A, real_T* B, real_T* C, real_T* D){    int_T i;    real_T tmp;    //上三角矩阵    C[0] = C[0] / B[0];    D[0] = D[0] / B[0];    for(i = 1; i<n; i++)    {        tmp = (B[i] - A[i] * C[i-1]);        C[i] = C[i] / tmp;        D[i] = (D[i] - A[i] * D[i-1]) / tmp;    }    //直接求出X的最后一个值    X[n-1] = D[n-1];    //逆向迭代， 求出X    for(i = n-2; i>=0; i--)    {        X[i] = D[i] - C[i] * X[i+1];    }}#define MDL_UPDATE #if defined(MDL_UPDATE)  static void mdlUpdate(SimStruct *S, int_T tid)  {  }#endif#define MDL_DERIVATIVES#if defined(MDL_DERIVATIVES)  static void mdlDerivatives(SimStruct *S)  {  }#endifstatic void mdlTerminate(SimStruct *S){}#ifdef  MATLAB_MEX_FILE  #include "simulink.c"#else#include "cg_sfun.h"#endif

Reference:

http://www.cnblogs.com/xpvincent/archive/2013/01/26/2878092.html