Bliza++ 求函数的二阶导数

    //整理 by RobinKin

    下面在[0,1) 的范围中，以delta为步长 ，用[ 1 -2  1 ] 的方法计算二阶导数

    看看和精确值的误差
    */

    //整理 by RobinKin

    #include

    using namespace blitz;

    int main()
    {
        // In this example, the function cos(x)^2 and its second derivative
        // 2 (sin(x)^2 - cos(x)^2) are sampled over the range [0,1).
        // The second derivative is approximated numerically using a
        // [ 1 -2  1 ] mask, and the approximation error is computed.

    /* cos(x)^2  的二阶导数 是2 (sin(x)^2 - cos(x)^2)

    下面在[0,1) 的范围中，以delta为步长 ，用[ 1 -2  1 ] 的方法计算二阶导数

    看看和精确值的误差
    */

        const int numSamples = 100;              // Number of samples
        double delta = 1. / numSamples;          // Spacing of samples
        Range R(0, numSamples - 1);              // Index set of the vector

        // Sample the function y = cos(x)^2 over [0,1)
        //
        // An object of type Range can be treated as a vector, and used
        // as a term in vector expressions.
        //
        // The initialization for y (below) will be translated via expression
        // templates into something of the flavour
        //
        // for (unsigned i=0; i < 99; ++i)
        // {
        //     double _t1 = cos(i * delta);
        //     y[i] = _t1 * _t1;
        // }

        Vector y = sqr(cos(R * delta));

        // Sample the exact second derivative
        Vector y2exact = 2.0 * (sqr(sin(R * delta)) - sqr(cos(R * delta)));

        // Approximate the 2nd derivative using a [ 1 -2  1 ] mask
        // We can only apply this mask to the elements 1 .. 98, since
        // we need one element on either side to apply the mask.
        Range I(1,numSamples-2);
        Vector y2(numSamples);