void pendag(double a[], double b[], double c[], double d[], double e[], double r[], double u[], int n)
{
	int k;
    double w[100], beta[100], alpha[100], cg[100], h[100];
    w[1] = c[1];
    beta[1] = 0.0;
    beta[2] = d[1] / w[1];
    alpha[1] = 0.0;
    alpha[2] = e[1] / w[1];
    alpha[n] = 0.0;
    alpha[n + 1] = 0.0;
    for (k = 2; k<=n; k++)
	{
        cg[k] = b[k] - a[k] * beta[k - 1];
        w[k] = c[k] - a[k] * alpha[k - 1] - cg[k] * beta[k];
        if (w[k] == 0.0) 
		{
			cout<< "    w[k]=0.0 in pendag"<<endl;
		}
        beta[k + 1] = (d[k] - cg[k] * alpha[k]) / w[k];
        alpha[k + 1] = e[k] / w[k];
    }
        h[1] = 0.0;
        h[2] = r[1] / w[1];
    for (k = 2; k<=n; k++)
	{
        h[k+1] = (r[k]-a[k]*h[k-1]-cg[k]*h[k])/w[k];
    }
        u[n] = h[n + 1];
        u[n - 1] = h[n] - beta[n] * u[n];
    for (k = n - 2; k>=1; k--)
	{
        u[k] = h[k+1]-beta[k+1] * u[k+1] - alpha[k+1] * u[k+2];
    }
}