/**
* Applies the shifts {@code u} to the trace {@code g}.
*
* @param sf the sampling that {@code g} is being warped to.
* @param u the shifts to apply to {@code g}.
* @param sg the sampling of {@code g}.
* @param g the trace to be warped.
* @return the warped image.
*/
public static float[][][] applyShifts(
Sampling sf, final float[][][] u, Sampling sg, final float[][][] g) {
final int n1 = u[0][0].length;
final int n2 = u[0].length;
final int n3 = u.length;
final int ng = g[0][0].length;
final double dg = sg.getDelta();
final double df = sf.getDelta();
final double fg = sg.getDelta();
final double ff = sf.getDelta();
final float[][][] hf = new float[n3][n2][n1];
final SincInterp si = new SincInterp();
int n23 = n3 * n2;
Parallel.loop(
n23,
new Parallel.LoopInt() {
public void compute(int i23) {
int i2 = i23 % n2;
int i3 = i23 / n2;
double v = ff;
for (int i1 = 0; i1 < n1; i1++, v = ff + i1 * df) {
hf[i3][i2][i1] = si.interpolate(ng, dg, fg, g[i3][i2], (float) v + u[i3][i2][i1]);
}
}
});
return hf;
}
/**
* Get the {@code grid} as sample indices.
*
* @param s Sampling that this {@code grid} subsamples.
* @param grid the subsample locations defined in terms of Sampling {@code s}.
* @return the {@code grid} as sample indices.
* @throws IllegalArgumentException if any of the grid locations are not valid with the given
* Sampling {@code s}.
*/
public static int[] gridCoordsToSamples(Sampling s, float[] grid) {
Almost a = new Almost();
float f = (float) s.getFirst();
float l = (float) s.getLast();
int ng = grid.length;
int[] t = new int[ng]; // temp sample indices
int count = 0;
int is = -1; // save last index
for (int ig = 0; ig < ng; ig++) {
float v = grid[ig];
if (a.ge(v, f) && a.le(v, l)) {
int i = s.indexOfNearest(v);
if (i != is) { // no duplicate entries
t[count] = i;
count++;
}
is = i;
} else {
print("Error: value " + v + " is out of bounds! First=" + f + ", Last=" + l);
}
}
if (count != ng) {
print("Grid values:");
dump(grid);
throw new IllegalArgumentException(
"Error: Only "
+ count
+ " of "
+ ng
+ " input grid coordinates are valid "
+ "with the specified sampling "
+ s.toString());
}
return copy(count, t);
}
private static float[] getValues(Sampling s) {
int n = s.getCount();
double f = s.getFirst();
double d = s.getDelta();
float[] x = new float[n];
for (int i = 0; i < n; i++) x[i] = (float) (f + i * d);
return x;
}
public static float[] ps1ToPpTime(Sampling sf, float[] u1, Sampling sg, float[] g) {
int n1 = u1.length;
int ng = g.length;
float[] xg = new float[ng];
for (int ig = 0; ig < ng; ig++) xg[ig] = (float) sg.getValue(ig);
CubicInterpolator ci = new CubicInterpolator(Method.LINEAR, xg, g);
float[] gp = new float[n1];
for (int i1 = 0; i1 < n1; i1++) gp[i1] = ci.interpolate((float) (sf.getValue(i1) + u1[i1]));
return gp;
}
/**
* Applies the shifts {@code u} to the trace {@code g}.
*
* @param sf the sampling that {@code g} is being warped to.
* @param u the shifts to apply to {@code g}.
* @param sg the sampling of {@code g}.
* @param g the trace to be warped.
* @return the warped trace.
*/
public static float[] applyShifts(Sampling sf, final float[] u, Sampling sg, final float[] g) {
final int n1 = u.length;
final int ng = g.length;
final double dg = sg.getDelta();
final double df = sf.getDelta();
final double fg = sg.getDelta();
final double ff = sf.getDelta();
final float[] hf = new float[n1];
final SincInterp si = new SincInterp();
double v = ff;
for (int i1 = 0; i1 < n1; i1++, v = ff + i1 * df)
hf[i1] = si.interpolate(ng, dg, fg, g, (float) v + u[i1]);
return hf;
}
/**
* Computes an array of VpVs ratios an array of shifts u using a backward difference
* approximation. The relationship is defined as vpvs(t) = 1+2*(du/dt)
*
* @param u
* @return computed vpvs values.
*/
public static float[] vpvsBd(Sampling su, float[] u) {
float dui = 1.0f / (float) su.getDelta();
int n = u.length;
float[] vpvs = new float[n];
vpvs[0] = 1.0f + 2.0f * (u[1] - u[0]) * dui; // at i1=0, forward difference
for (int i1 = 1; i1 < n; ++i1) vpvs[i1] = 1.0f + 2.0f * (u[i1] - u[i1 - 1]) * dui;
return vpvs;
}
/**
* Gets the flattening shifts s(u1,u2,u3) = u1 - x1(u1,u2,u3).
*
* @return the flattening shifts.
*/
public float[][][] getShiftsS() {
int n1 = s1.getCount();
int n2 = s2.getCount();
int n3 = s3.getCount();
float[][][] s = new float[n3][n2][n1];
float d1 = (float) s1.getDelta();
float f1 = (float) s1.getFirst();
for (int i3 = 0; i3 < n3; ++i3) {
for (int i2 = 0; i2 < n2; ++i2) {
for (int i1 = 0; i1 < n1; ++i1) {
float u1i = f1 + i1 * d1;
s[i3][i2][i1] = u1i - x1[i3][i2][i1];
}
}
}
return s;
}
/**
* Scale shifts by compression factor c.
*
* @param sf the trace sampling corresponding to shifts.
* @param u array of shifts to compress.
* @param c scale factor. To stretch, c, to compress, 1/c.
* @return scaled shifts.
*/
public static float[] getScaledShifts(Sampling sf, float[] u, float c) {
int n = u.length;
float[] uc = new float[n];
for (int i = 0; i < n; i++) {
float fv = (float) sf.getValue(i);
uc[i] = (fv + u[i]) * c - fv;
}
return uc;
}
private float[][][] apply(final float[][][] ux, final float[][][] f) {
final int n1 = s1.getCount();
final int n2 = s2.getCount();
final int n3 = s3.getCount();
final double d1 = s1.getDelta();
final double f1 = s1.getFirst();
final SincInterpolator si = new SincInterpolator();
final float[][][] g = new float[n3][n2][n1];
Parallel.loop(
n3,
new Parallel.LoopInt() {
public void compute(int i3) {
for (int i2 = 0; i2 < n2; ++i2)
si.interpolate(n1, d1, f1, f[i3][i2], n1, ux[i3][i2], g[i3][i2]);
}
});
return g;
}
public static double[] getSubStrainMax(Sampling su, float[] u, double[] rmax) {
float dui = 1.0f / (float) su.getDelta();
int n = u.length;
int nm1 = n - 1;
double[] rmaxNew = new double[n];
rmaxNew[0] = rmax[0] - (u[1] - u[0]) * dui; // forward diff
rmaxNew[nm1] = rmax[nm1] - (u[nm1] - u[nm1 - 1]) * dui; // backward diff
for (int i1 = 1; i1 < nm1; i1++) rmaxNew[i1] = rmax[i1] - (u[i1 + 1] - u[i1 - 1]) * 0.5 * dui;
return rmaxNew;
}
/**
* Computes gammaS, a measure of the time delay between two split shear waves, from shifts between
* PP-PS2 {@code u2} and PS1-PS2 {@code uS}.
*
* @param sf PP time Sampling.
* @param u2 shifts between PP-PS2 in PP time.
* @param uS shifts between PS1-PS2 in PP time.
* @return gammaS
*/
public static float[] gammaSu2S(Sampling sf, float[] u2, float[] uS) {
int n1 = u2.length;
Check.argument(n1 == sf.getCount(), "u2 consistent with sampling");
Check.argument(n1 == uS.length, "u2.length==uS.length");
float[] du2 = firstDerivative(sf, u2);
float[] duS = firstDerivative(sf, uS);
float[] gs = new float[n1];
for (int i1 = 0; i1 < n1; i1++) gs[i1] = (2.0f * duS[i1]) / (1.0f + 2.0f * (du2[i1] - duS[i1]));
return gs;
}
public float[][][][] flattenWithShifts(
final Sampling s1, final float[][][] r, final float[][][] f) {
cleanShifts(r);
final int n3 = r.length;
final int n2 = r[0].length;
final int n1 = r[0][0].length;
// Compute u1(x1,x2,x3).
final double f1 = s1.getFirst();
final double d1 = s1.getDelta();
final float[][][] u1 = r;
for (int i3 = 0; i3 < n3; ++i3) {
for (int i2 = 0; i2 < n2; ++i2) {
for (int i1 = 0; i1 < n1; ++i1) {
float x1i = (float) (f1 + i1 * d1);
u1[i3][i2][i1] = (float) (x1i + r[i3][i2][i1] * d1);
}
}
}
// Compute x1(u1,u2).
final float[][][] x1 = new float[n3][n2][n1];
final InverseInterpolator ii = new InverseInterpolator(s1, s1);
Parallel.loop(
n3,
new Parallel.LoopInt() {
public void compute(int i3) {
for (int i2 = 0; i2 < n2; ++i2) ii.invert(u1[i3][i2], x1[i3][i2]);
}
});
final SincInterpolator si = new SincInterpolator();
final float[][][] g = new float[n3][n2][n1];
Parallel.loop(
n3,
new Parallel.LoopInt() {
public void compute(int i3) {
for (int i2 = 0; i2 < n2; ++i2)
si.interpolate(n1, d1, f1, f[i3][i2], n1, x1[i3][i2], g[i3][i2]);
}
});
return new float[][][][] {g, u1};
}
private static float[] firstDerivative(Sampling s, float[] f) {
int n = f.length;
int nm1 = n - 1;
float[] g = new float[n];
float di = 1.0f / (float) s.getDelta();
float di2 = 0.5f * di;
g[0] = (f[1] - f[0]) * di; // forward diff
g[nm1] = (f[nm1] - f[nm1 - 1]) * di; // backward diff
for (int i1 = 1; i1 < nm1; i1++) g[i1] = (f[i1 + 1] - f[i1 - 1]) * di2;
return g;
}
/**
* Gets mappings computed from specified slopes and planarities.
*
* @param s1 sampling of 1st dimension.
* @param s2 sampling of 2nd dimension.
* @param p2 array of slopes of image features.
* @param ep array of planarities of image features.
*/
public Mappings getMappingsFromSlopes(
Sampling s1, Sampling s2, Sampling s3, float[][][] p2, float[][][] p3, float[][][] ep) {
// Sampling parameters.
final int n1 = s1.getCount();
final int n2 = s2.getCount();
final int n3 = s3.getCount();
float d1 = (float) s1.getDelta();
float d2 = (float) s2.getDelta();
float d3 = (float) s3.getDelta();
float f1 = (float) s1.getFirst();
// If necessary, convert units for slopes to samples per sample.
if (d1 != d2) p2 = mul(d2 / d1, p2);
if (d1 != d3) p3 = mul(d3 / d1, p3);
// Compute shifts r(x1,x2,x3), in samples.
float[][][] b = new float[n3][n2][n1]; // right-hand side
float[][][] r = new float[n3][n2][n1]; // shifts, in samples
VecArrayFloat3 vb = new VecArrayFloat3(b);
VecArrayFloat3 vr = new VecArrayFloat3(r);
Smoother3 smoother3 = new Smoother3(n1, n2, n3, _sigma1, _sigma2, _sigma3, ep);
A3 a3 = new A3(smoother3, _weight1, ep, p2, p3);
CgSolver cs = new CgSolver(_small, _niter);
makeRhs(ep, p2, p3, b);
smoother3.applyTranspose(b);
cs.solve(a3, vb, vr);
smoother3.apply(r);
cleanShifts(r);
// Compute u1(x1,x2,x3).
final float[][][] u1 = r;
for (int i3 = 0; i3 < n3; ++i3) {
for (int i2 = 0; i2 < n2; ++i2) {
for (int i1 = 0; i1 < n1; ++i1) {
float x1i = f1 + i1 * d1;
u1[i3][i2][i1] = x1i + r[i3][i2][i1] * d1;
}
}
}
// Compute x1(u1,u2).
final float[][][] x1 = b;
final InverseInterpolator ii = new InverseInterpolator(s1, s1);
Parallel.loop(
n3,
new Parallel.LoopInt() {
public void compute(int i3) {
for (int i2 = 0; i2 < n2; ++i2) ii.invert(u1[i3][i2], x1[i3][i2]);
}
});
return new Mappings(s1, s2, s3, u1, x1);
}