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WIP #1034 code formatting org.matheclipse.core.numerics
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@axkr
axkr committed Aug 1, 2024
1 parent be09c63 commit 206c0c2
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1,107 changes: 552 additions & 555 deletions ...matheclipse-core/src/main/java/org/matheclipse/core/numerics/integral/ClenshawCurtis.java
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2,299 changes: 1,152 additions & 1,147 deletions ...y/matheclipse-core/src/main/java/org/matheclipse/core/numerics/integral/GaussKronrod.java
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368 changes: 184 additions & 184 deletions .../matheclipse-core/src/main/java/org/matheclipse/core/numerics/integral/GaussLegendre.java
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import org.matheclipse.core.numerics.utils.SimpleMath;

/**
* Integrate a real function of one variable over a finite interval using an
* adaptive 8-point Legendre-Gauss algorithm. This algorithm is a translation of
* the corresponding subroutine dgaus8 from the SLATEC library.
* Integrate a real function of one variable over a finite interval using an adaptive 8-point
* Legendre-Gauss algorithm. This algorithm is a translation of the corresponding subroutine dgaus8
* from the SLATEC library.
*/
public final class GaussLegendre extends Quadrature {

private static final double X1 = 1.83434642495649805e-1;
private static final double X2 = 5.25532409916328986e-1;
private static final double X3 = 7.96666477413626740e-1;
private static final double X4 = 9.60289856497536232e-1;
private static final double W1 = 3.62683783378361983e-1;
private static final double W2 = 3.13706645877887287e-1;
private static final double W3 = 2.22381034453374471e-1;
private static final double W4 = 1.01228536290376259e-1;
private static final double SQ2 = Constants.SQRT2;

public GaussLegendre(final double tolerance, final int maxEvaluations) {
super(tolerance, maxEvaluations);
private static final double X1 = 1.83434642495649805e-1;
private static final double X2 = 5.25532409916328986e-1;
private static final double X3 = 7.96666477413626740e-1;
private static final double X4 = 9.60289856497536232e-1;
private static final double W1 = 3.62683783378361983e-1;
private static final double W2 = 3.13706645877887287e-1;
private static final double W3 = 2.22381034453374471e-1;
private static final double W4 = 1.01228536290376259e-1;
private static final double SQ2 = Constants.SQRT2;

public GaussLegendre(final double tolerance, final int maxEvaluations) {
super(tolerance, maxEvaluations);
}

@Override
final QuadratureResult properIntegral(final DoubleUnaryOperator f, final double a,
final double b) {

// prepare variables
final double[] err = {myTol};
final double[] ans = new double[1];
final int[] ierr = new int[1];
final int[] fev = new int[1];

// call main subroutine
dgaus8(f, a, b, err, ans, ierr, fev);
return new QuadratureResult(ans[0], err[0], fev[0], ierr[0] == 1 || ierr[0] == -1);
}

@Override
public final String getName() {
return "Gauss-Legendre";
}

private void dgaus8(final DoubleUnaryOperator fun, final double a, final double b,
final double[] err, final double[] ans, final int[] ierr, final int[] fev) {
int k, kml = 6, kmx = 5000, l, lmx, mxl, nbits, nib, nlmx;
double ae, anib, area, c, ce, ee, ef, eps, est, gl, glr, tol, vr;
final int[] lr = new int[61];
final double[] aa = new double[61], hh = new double[61], vl = new double[61],
gr = new double[61];

// Initialize
fev[0] = 0;
k = 53;
anib = SimpleMath.D1MACH[5 - 1] * k / 0.30102000;
nbits = (int) anib;
nlmx = Math.min(60, (nbits * 5) / 8);
ans[0] = 0.0;
ierr[0] = 1;
ce = 0.0;
if (a == b) {
if (err[0] < 0.0) {
err[0] = ce;
}
return;
}

@Override
final QuadratureResult properIntegral(final DoubleUnaryOperator f, final double a,
final double b) {

// prepare variables
final double[] err = { myTol };
final double[] ans = new double[1];
final int[] ierr = new int[1];
final int[] fev = new int[1];

// call main subroutine
dgaus8(f, a, b, err, ans, ierr, fev);
return new QuadratureResult(ans[0], err[0], fev[0], ierr[0] == 1 || ierr[0] == -1);
lmx = nlmx;
if (b != 0.0 && SimpleMath.sign(1.0, b) * a > 0.0) {
c = Math.abs(1.0 - a / b);
if (c <= 0.1) {
if (c <= 0.0) {
if (err[0] < 0.0) {
err[0] = ce;
}
return;
}
anib = 0.5 - Math.log(c) * Constants.LOG2_INV;
nib = (int) anib;
lmx = Math.min(nlmx, nbits - nib - 7);
if (lmx < 1) {
ierr[0] = -1;
if (err[0] < 0.0) {
err[0] = ce;
}
return;
}
}
}

@Override
public final String getName() {
return "Gauss-Legendre";
tol = Math.max(Math.abs(err[0]), SimpleMath.pow(2.0, 5 - nbits)) / 2.0;
if (err[0] == 0.0) {
tol = Math.sqrt(SimpleMath.D1MACH[4 - 1]);
}

private void dgaus8(final DoubleUnaryOperator fun, final double a, final double b,
final double[] err,
final double[] ans, final int[] ierr, final int[] fev) {
int k, kml = 6, kmx = 5000, l, lmx, mxl, nbits, nib, nlmx;
double ae, anib, area, c, ce, ee, ef, eps, est, gl, glr, tol, vr;
final int[] lr = new int[61];
final double[] aa = new double[61], hh = new double[61], vl = new double[61], gr = new double[61];

// Initialize
fev[0] = 0;
k = 53;
anib = SimpleMath.D1MACH[5 - 1] * k / 0.30102000;
nbits = (int) anib;
nlmx = Math.min(60, (nbits * 5) / 8);
ans[0] = 0.0;
ierr[0] = 1;
ce = 0.0;
if (a == b) {
if (err[0] < 0.0) {
err[0] = ce;
}
return;
}
lmx = nlmx;
if (b != 0.0 && SimpleMath.sign(1.0, b) * a > 0.0) {
c = Math.abs(1.0 - a / b);
if (c <= 0.1) {
if (c <= 0.0) {
if (err[0] < 0.0) {
err[0] = ce;
}
return;
}
anib = 0.5 - Math.log(c) * Constants.LOG2_INV;
nib = (int) anib;
lmx = Math.min(nlmx, nbits - nib - 7);
if (lmx < 1) {
ierr[0] = -1;
if (err[0] < 0.0) {
err[0] = ce;
}
return;
}
}
}

tol = Math.max(Math.abs(err[0]), SimpleMath.pow(2.0, 5 - nbits)) / 2.0;
if (err[0] == 0.0) {
tol = Math.sqrt(SimpleMath.D1MACH[4 - 1]);
}
eps = tol;
hh[1 - 1] = (b - a) / 4.0;
aa[1 - 1] = a;
lr[1 - 1] = 1;
l = 1;
est = g8(fun, aa[l - 1] + 2.0 * hh[l - 1], 2.0 * hh[l - 1]);
fev[0] += 8;
k = 8;
area = Math.abs(est);
ef = 0.5;
mxl = 0;

while (true) {

// Compute refined estimates, estimate the error, etc.
if (fev[0] - 8 >= myMaxEvals) {
// ans[0] = Double.NaN;
ierr[0] = 2;
return;
}
gl = g8(fun, aa[l - 1] + hh[l - 1], hh[l - 1]);
fev[0] += 8;
if (fev[0] - 8 >= myMaxEvals) {
// ans[0] = Double.NaN;
ierr[0] = 2;
return;
}
gr[l - 1] = g8(fun, aa[l - 1] + 3.0 * hh[l - 1], hh[l - 1]);
fev[0] += 8;

k += 16;
area += (Math.abs(gl) + Math.abs(gr[l - 1]) - Math.abs(est));
glr = gl + gr[l - 1];
ee = Math.abs(est - glr) * ef;
ae = Math.max(eps * area, tol * Math.abs(glr));
if (ee - ae > 0.0) {

// Consider the left half of this level
if (k > kmx) {
lmx = kml;
}
if (l >= lmx) {
mxl = 1;
} else {
++l;
eps *= 0.5;
ef /= SQ2;
hh[l - 1] = hh[l - 1 - 1] * 0.5;
lr[l - 1] = -1;
aa[l - 1] = aa[l - 1 - 1];
est = gl;
continue;
}
}

ce += (est - glr);
if (lr[l - 1] <= 0.0) {

// Proceed to right half at this level
vl[l - 1] = glr;
est = gr[l - 1 - 1];
lr[l - 1] = 1;
aa[l - 1] += 4.0 * hh[l - 1];
} else {

// Return one level
vr = glr;
while (true) {
if (l <= 1) {
ans[0] = vr;
if (mxl != 0 && Math.abs(ce) > 2.0 * tol * area) {
ierr[0] = 2;
}
if (err[0] < 0.0) {
err[0] = ce;
}
return;
}
--l;
eps *= 2.0;
ef *= SQ2;
if (lr[l - 1] <= 0.0) {
vl[l - 1] = vl[l + 1 - 1] + vr;
est = gr[l - 1 - 1];
lr[l - 1] = 1;
aa[l - 1] += 4.0 * hh[l - 1];
break;
} else {
vr += vl[l + 1 - 1];
}
}
}
}
}

private static double g8(final DoubleUnaryOperator fun, final double x, final double h) {
final double fx1 = fun.applyAsDouble(x - X1 * h) + fun.applyAsDouble(x + X1 * h);
final double fx2 = fun.applyAsDouble(x - X2 * h) + fun.applyAsDouble(x + X2 * h);
final double fx3 = fun.applyAsDouble(x - X3 * h) + fun.applyAsDouble(x + X3 * h);
final double fx4 = fun.applyAsDouble(x - X4 * h) + fun.applyAsDouble(x + X4 * h);
return h * (W1 * fx1 + W2 * fx2 + W3 * fx3 + W4 * fx4);
eps = tol;
hh[1 - 1] = (b - a) / 4.0;
aa[1 - 1] = a;
lr[1 - 1] = 1;
l = 1;
est = g8(fun, aa[l - 1] + 2.0 * hh[l - 1], 2.0 * hh[l - 1]);
fev[0] += 8;
k = 8;
area = Math.abs(est);
ef = 0.5;
mxl = 0;

while (true) {

// Compute refined estimates, estimate the error, etc.
if (fev[0] - 8 >= myMaxEvals) {
// ans[0] = Double.NaN;
ierr[0] = 2;
return;
}
gl = g8(fun, aa[l - 1] + hh[l - 1], hh[l - 1]);
fev[0] += 8;
if (fev[0] - 8 >= myMaxEvals) {
// ans[0] = Double.NaN;
ierr[0] = 2;
return;
}
gr[l - 1] = g8(fun, aa[l - 1] + 3.0 * hh[l - 1], hh[l - 1]);
fev[0] += 8;

k += 16;
area += (Math.abs(gl) + Math.abs(gr[l - 1]) - Math.abs(est));
glr = gl + gr[l - 1];
ee = Math.abs(est - glr) * ef;
ae = Math.max(eps * area, tol * Math.abs(glr));
if (ee - ae > 0.0) {

// Consider the left half of this level
if (k > kmx) {
lmx = kml;
}
if (l >= lmx) {
mxl = 1;
} else {
++l;
eps *= 0.5;
ef /= SQ2;
hh[l - 1] = hh[l - 1 - 1] * 0.5;
lr[l - 1] = -1;
aa[l - 1] = aa[l - 1 - 1];
est = gl;
continue;
}
}

ce += (est - glr);
if (lr[l - 1] <= 0.0) {

// Proceed to right half at this level
vl[l - 1] = glr;
est = gr[l - 1 - 1];
lr[l - 1] = 1;
aa[l - 1] += 4.0 * hh[l - 1];
} else {

// Return one level
vr = glr;
while (true) {
if (l <= 1) {
ans[0] = vr;
if (mxl != 0 && Math.abs(ce) > 2.0 * tol * area) {
ierr[0] = 2;
}
if (err[0] < 0.0) {
err[0] = ce;
}
return;
}
--l;
eps *= 2.0;
ef *= SQ2;
if (lr[l - 1] <= 0.0) {
vl[l - 1] = vl[l + 1 - 1] + vr;
est = gr[l - 1 - 1];
lr[l - 1] = 1;
aa[l - 1] += 4.0 * hh[l - 1];
break;
} else {
vr += vl[l + 1 - 1];
}
}
}
}
}

private static double g8(final DoubleUnaryOperator fun, final double x, final double h) {
final double fx1 = fun.applyAsDouble(x - X1 * h) + fun.applyAsDouble(x + X1 * h);
final double fx2 = fun.applyAsDouble(x - X2 * h) + fun.applyAsDouble(x + X2 * h);
final double fx3 = fun.applyAsDouble(x - X3 * h) + fun.applyAsDouble(x + X3 * h);
final double fx4 = fun.applyAsDouble(x - X4 * h) + fun.applyAsDouble(x + X4 * h);
return h * (W1 * fx1 + W2 * fx2 + W3 * fx3 + W4 * fx4);
}
}
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