void testNatural(const Spline &sp,
const double *x,
const double *y)
{
// test the common properties of splines
testCommon(sp, x, y);
static double eps = 1e-5;
size_t n = sp.numSamples();
// make sure the second derivatives at both end points are 0
double d0 = sp.evalDerivative(x[0]);
double d1 = sp.evalDerivative(x[0] + eps);
double d2 = sp.evalDerivative(x[n-1] - eps);
double d3 = sp.evalDerivative(x[n-1]);
if (std::abs(d1 - d0)/eps > 1000*eps)
OPM_THROW(std::runtime_error,
"Invalid second derivative at beginning of interval: is "
<< (d1 - d0)/eps << " ought to be 0");
if (std::abs(d3 - d2)/eps > 1000*eps)
OPM_THROW(std::runtime_error,
"Invalid second derivative at end of interval: is "
<< (d3 - d2)/eps << " ought to be 0");
}
void testMonotonic(const Spline &sp,
const double *x,
const double *y)
{
// test the common properties of splines
testCommon(sp, x, y);
size_t n = sp.numSamples();
for (size_t i = 0; i < n - 1; ++ i) {
// make sure that the spline is monotonic for each interval
// between sampling points
if (!sp.monotonic(x[i], x[i + 1]))
OPM_THROW(std::runtime_error,
"Spline says it is not monotonic in interval "
<< i << " where it should be");
// test the intersection methods
double d = (y[i] + y[i+1])/2;
double interX = sp.template intersectInterval<double>(x[i], x[i+1],
/*a=*/0, /*b=*/0, /*c=*/0, d);
double interY = sp.eval(interX);
if (std::abs(interY - d) > 1e-5)
OPM_THROW(std::runtime_error,
"Spline::intersectInterval() seems to be broken: "
<< sp.eval(interX) << " - " << d << " = " << sp.eval(interX) - d << "!");
}
// make sure the spline says to be monotonic on the (extrapolated)
// left and right sides
if (!sp.monotonic(x[0] - 1.0, (x[0] + x[1])/2, /*extrapolate=*/true))
OPM_THROW(std::runtime_error,
"Spline says it is not monotonic on left side where it should be");
if (!sp.monotonic((x[n - 2]+ x[n - 1])/2, x[n-1] + 1.0, /*extrapolate=*/true))
OPM_THROW(std::runtime_error,
"Spline says it is not monotonic on right side where it should be");
for (size_t i = 0; i < n - 2; ++ i) {
// make sure that the spline says that it is non-monotonic for
// if extrema are within the queried interval
if (sp.monotonic((x[i] + x[i + 1])/2, (x[i + 1] + x[i + 2])/2))
OPM_THROW(std::runtime_error,
"Spline says it is monotonic in interval "
<< i << " where it should not be");
}
}
void testFull(const Spline &sp,
const double *x,
const double *y,
double m0,
double m1)
{
// test the common properties of splines
testCommon(sp, x, y);
static double eps = 1e-5;
size_t n = sp.numSamples();
// make sure the derivative at both end points is correct
double d0 = sp.evalDerivative(x[0]);
double d1 = sp.evalDerivative(x[n-1]);
if (std::abs(d0 - m0) > eps)
OPM_THROW(std::runtime_error,
"Invalid derivative at beginning of interval: is "
<< d0 << " ought to be " << m0);
if (std::abs(d1 - m1) > eps)
OPM_THROW(std::runtime_error,
"Invalid derivative at end of interval: is "
<< d1 << " ought to be " << m1);
}
void testCommon(const Spline &sp,
const double *x,
const double *y)
{
static double eps = 1e-10;
static double epsFD = 1e-7;
size_t n = sp.numSamples();
for (size_t i = 0; i < n; ++i) {
// sure that we hit all sampling points
double y0 = (i>0)?sp.eval(x[i]-eps):y[0];
double y1 = sp.eval(x[i]);
double y2 = (i<n-1)?sp.eval(x[i]+eps):y[n-1];
if (std::abs(y0 - y[i]) > 100*eps || std::abs(y2 - y[i]) > 100*eps)
OPM_THROW(std::runtime_error,
"Spline seems to be discontinuous at sampling point " << i << "!");
if (std::abs(y1 - y[i]) > eps)
OPM_THROW(std::runtime_error,
"Spline does not capture sampling point " << i << "!");
// make sure the derivative is continuous (assuming that the
// second derivative is smaller than 1000)
double d1 = sp.evalDerivative(x[i]);
double d0 = (i>0)?sp.evalDerivative(x[i]-eps):d1;
double d2 = (i<n-1)?sp.evalDerivative(x[i]+eps):d1;
if (std::abs(d1 - d0) > 1000*eps || std::abs(d2 - d0) > 1000*eps)
OPM_THROW(std::runtime_error,
"Spline seems to exhibit a discontinuous derivative at sampling point " << i << "!");
}
// make sure the derivatives are consistent with the curve
size_t np = 3*n;
for (size_t i = 0; i < np; ++i) {
double xMin = sp.xAt(0);
double xMax = sp.xAt(sp.numSamples() - 1);
double xval = xMin + (xMax - xMin)*i/np;
// first derivative
double y1 = sp.eval(xval+epsFD);
double y0 = sp.eval(xval);
double mFD = (y1 - y0)/epsFD;
double m = sp.evalDerivative(xval);
if (std::abs( mFD - m ) > 1000*epsFD)
OPM_THROW(std::runtime_error,
"Derivative of spline seems to be inconsistent with cuve"
" (" << mFD << " - " << m << " = " << mFD - m << ")!");
// second derivative
y1 = sp.evalDerivative(xval+epsFD);
y0 = sp.evalDerivative(xval);
mFD = (y1 - y0)/epsFD;
m = sp.evalSecondDerivative(xval);
if (std::abs( mFD - m ) > 1000*epsFD)
OPM_THROW(std::runtime_error,
"Second derivative of spline seems to be inconsistent with cuve"
" (" << mFD << " - " << m << " = " << mFD - m << ")!");
// Third derivative
y1 = sp.evalSecondDerivative(xval+epsFD);
y0 = sp.evalSecondDerivative(xval);
mFD = (y1 - y0)/epsFD;
m = sp.evalThirdDerivative(xval);
if (std::abs( mFD - m ) > 1000*epsFD)
OPM_THROW(std::runtime_error,
"Third derivative of spline seems to be inconsistent with cuve"
" (" << mFD << " - " << m << " = " << mFD - m << ")!");
}
}
