TEUCHOS_UNIT_TEST( Stokhos_NormalizedHermiteBasis, EvaluateBasesAndDerivatives ) {
double x = 0.1234;
Teuchos::Array<double> val1(setup.p+1), deriv1(setup.p+1),
val2(setup.p+1), deriv2(setup.p+1);
setup.basis.evaluateBasesAndDerivatives(x, val1, deriv1);
// evaluate bases and derivatives using formula:
// He_0(x) = 1
// He_1(x) = x
// He_i(x) = (x*He_{i-1}(x) - sqrt(i-1)*He_{i-2}(x))/sqrt(i), i=2,3,...
val2[0] = 1.0;
if (setup.p >= 1)
val2[1] = x;
for (int i=2; i<=setup.p; i++)
val2[i] = (x*val2[i-1] - std::sqrt(i-1.0)*val2[i-2])/std::sqrt(1.0*i);
deriv2[0] = 0.0;
if (setup.p >= 1)
deriv2[1] = 1.0;
for (int i=2; i<=setup.p; i++)
deriv2[i] = (val2[i-1] + x*deriv2[i-1] - std::sqrt(i-1.0)*deriv2[i-2]) /
std::sqrt(1.0*i);
success = Stokhos::compareArrays(val1, "val1", val2, "val2",
setup.rtol, setup.atol, out);
success = success &&
Stokhos::compareArrays(deriv1, "deriv1", deriv2, "deriv2",
setup.rtol, setup.atol, out);
}
TEUCHOS_UNIT_TEST( Stokhos_LegendreBasis, EvaluateBasesAndDerivatives ) {
double x = 0.1234;
Teuchos::Array<double> val1(setup.p+1), deriv1(setup.p+1),
val2(setup.p+1), deriv2(setup.p+1);
setup.basis.evaluateBasesAndDerivatives(x, val1, deriv1);
// evaluate bases and derivatives using formula:
// P_0(x) = 1
// P_1(x) = x
// P_i(x) = (2*i-1)/i*x*P_{i-1}(x) - (i-1)/i*P_{i-2}(x), i=2,3,...
// P_0'(x) = 0
// P_1'(x) = 1
// P_i'(x) = i*P_{i-1}(x) + x*P_{i-1}'(x), i=2,3,...
val2[0] = 1.0;
if (setup.p >= 1)
val2[1] = x;
for (int i=2; i<=setup.p; i++)
val2[i] = (2.0*i-1.0)/i*x*val2[i-1] - (i-1.0)/i*val2[i-2];
deriv2[0] = 0.0;
if (setup.p >= 1)
deriv2[1] = 1.0;
for (int i=2; i<=setup.p; i++)
deriv2[i] = i*val2[i-1] + x*deriv2[i-1];
success = Stokhos::compareArrays(val1, "val1", val2, "val2",
setup.rtol, setup.atol, out);
success = success &&
Stokhos::compareArrays(deriv1, "deriv1", deriv2, "deriv2",
setup.rtol, setup.atol, out);
}
int main(void)
{
int i = 0, j = 0;
int maxdeg;
while (maxdeg >= 0)
{
printf("Please enter the maximum degree of the polynomial: ");
scanf("%d",&maxdeg);
if (maxdeg < 0) {
break;
}
printf("Please enter the coefficients: ");
int *k;
k = malloc( sizeof(int)*(maxdeg+1));
free(k);
int *coeff = (int*) coeff[*k, sizeof(int)];
if (coeff != NULL) {
for (j = 0; j <= *k; j++) {
scanf("%d",&coeff[j]);
}
PofX1(i, *k, coeff, maxdeg);
deriv1(i, *k, coeff, maxdeg);
printf("\n\n");
}
}
}
inline double newton (double extr_a, double extr_b, double (*function) (double x), double (*deriv1) (double x), double (*deriv2) (double x), double precision) { // Require absolute
double zero; // Zero
double funz_a; // function(extr_a)
double X[MAX_INTER]; // X vector
double funz[MAX_INTER]; // Y vector
double der[MAX_INTER]; // Deriv1 vector
int inter = 0; // Iteration Number
funz_a = function (extr_a); // function(extr_a)
if ( funz_a*deriv2(extr_a) < 0 ) { // f(a)*DDf(x) < 0 seed = b
X[0] = extr_b;
}
if ( funz_a*deriv2(extr_b) > 0 ) { // f(a)*DDf(x) > 0 seed = a
X[0] = extr_a;
}
funz[0] = function (X[0]); // f(seed)
der[0] = deriv1 (X[0]); // deriv1(seed)
do {
inter ++; // Increase Interaction
X[inter] = X[inter-1] - (funz[inter-1] / der[inter-1] ); // New Point
funz[inter] = function (X[inter]); // function[X[i]
der[inter] = deriv1 (X[inter]); // deriv1(X[i]
} while (abs(X[inter - 1] - X[inter]) > precision || inter < MAX_INTER);
zero = X[inter];
return zero;
}
int main(int argc, char** argv)
{
if(argc<1) {
printf("usage: %s <>\n", argv[0]);
exit(EXIT_FAILURE);
}
std::vector<double> X(5), Y(5);
X[0]=0.1;
X[1]=0.4;
X[2]=1.2;
X[3]=1.8;
X[4]=2.0;
Y[0]=0.1;
Y[1]=0.7;
Y[2]=0.6;
Y[3]=1.1;
Y[4]=0.9;
tk::spline s;
// set_boundary() is optional and if omitted, natural boundary condition,
// f''(a)=f''(b)=0, will be used
// note, if natural boundary conditions are not used then extrapolation
// will be a quadratic function, unless the last argument is set to true,
// which forces linear extrapolation, but this will violate second order
// differentiability at the endpoint
s.set_boundary(tk::spline::second_deriv, 0.0,
tk::spline::first_deriv, -2.0, false);
s.set_points(X,Y);
for(size_t i=0; i<X.size(); i++) {
printf("%f %f\n", X[i], Y[i]);
}
printf("\n");
for(int i=-50; i<250; i++) {
double x=0.01*i;
printf("%f %f %f %f %f\n", x, s(x),
s.deriv(1,x), s.deriv(2,x), s.deriv(3,x));
// checking analytic derivatives and finite differences are close
assert(fabs(s.deriv(1,x)-deriv1(s,x)) < 1e-8);
assert(fabs(s.deriv(2,x)-deriv2(s,x)) < 1e-8);
}
printf("\n");
return EXIT_SUCCESS;
}
/******************************************************************************
* Syntax:
* int QRSFilter(int datum, int init) ;
* Description:
* QRSFilter() takes samples of an ECG signal as input and returns a sample of
* a signal that is an estimate of the local energy in the QRS bandwidth. In
* other words, the signal has a lump in it whenever a QRS complex, or QRS
* complex like artifact occurs. The filters were originally designed for data
* sampled at 200 samples per second, but they work nearly as well at sample
* frequencies from 150 to 250 samples per second.
*
* The filter buffers and static variables are reset if a value other than
* 0 is passed to QRSFilter through init.
*******************************************************************************/
int QRSFilter(int datum, int init)
{
if (init) {
hpfilt(0, 1); // Initialize filters.
lpfilt(0, 1);
mvwint(0, 1);
deriv1(0, 1);
deriv2(0, 1);
}
datum = lpfilt(datum, 0); // Low pass filter data.
datum = hpfilt(datum, 0); // High pass filter data.
datum = deriv2(datum, 0); // Take the derivative.
datum = abs(datum); // Take the absolute value.
datum = mvwint(datum, 0); // Average over an 80 ms window .
return datum;
}
TEUCHOS_UNIT_TEST( Stokhos_NormalizedLegendreBasis, EvaluateBasesAndDerivatives ) {
double x = 0.1234;
Teuchos::Array<double> val1(setup.p+1), deriv1(setup.p+1),
val2(setup.p+1), deriv2(setup.p+1);
setup.basis.evaluateBasesAndDerivatives(x, val1, deriv1);
// evaluate bases and derivatives using formula:
// P_0(x) = 1
// P_1(x) = sqrt(3)*x
// P_i(x) = (x*P_{i-1}(x) - b[i-1]*P_{i-2}(x))/b[i], i=2,3,...
// where b[i] = std::sqrt((i*i)/((2.0*i+1.0)*(2.0*i-1.0)))
// P_0'(x) = 0
// P_1'(x) = sqrt(3)
// P_i'(x) = (P_{i-1}(x) + x*P_{i-1}'(x) - b[i-1]*P_{i-2}')/b[i], i=2,3,...
double b1, b2;
b2 = std::sqrt(1.0/3.0);
b1 = b2;
val2[0] = 1.0;
if (setup.p >= 1)
val2[1] = x/b1;
for (int i=2; i<=setup.p; i++) {
b1 = std::sqrt((i*i)/((2.0*i+1.0)*(2.0*i-1.0)));
val2[i] = (x*val2[i-1] - b2*val2[i-2])/b1;
b2 = b1;
}
b2 = std::sqrt(1.0/3.0);
b1 = b2;
deriv2[0] = 0.0;
if (setup.p >= 1)
deriv2[1] = 1.0/b1;
for (int i=2; i<=setup.p; i++) {
b1 = std::sqrt((i*i)/((2.0*i+1.0)*(2.0*i-1.0)));
deriv2[i] = (val2[i-1] + x*deriv2[i-1] - b2*deriv2[i-2])/b1;
b2 = b1;
}
success = Stokhos::compareArrays(val1, "val1", val2, "val2",
setup.rtol, setup.atol, out);
success = success &&
Stokhos::compareArrays(deriv1, "deriv1", deriv2, "deriv2",
setup.rtol, setup.atol, out);
}
int qrsfilter( int datum, int init )
{
int fdatum ;
//初始化滤波器
if(init)
{
hpfilt( 0, 1 ) ;
lpfilt( 0, 1 ) ;
mvwint( 0, 1 ) ;
deriv1( 0, 1 ) ;
deriv2( 0, 1 ) ;
}
fdatum = lpfilt( datum, 0 ); //低通滤波
fdatum = hpfilt( fdatum, 0 ); //高通滤波
fdatum = deriv2( fdatum, 0 ); //差分滤波
fdatum = abs( fdatum ); //取绝对值
fdatum = mvwint( fdatum, 0 ); //积分窗求和
return(fdatum);
}
