public static final Cmplx div(Cmplx a, Cmplx b) {
Cmplx c = new Cmplx();
double r, den;
if (Math.abs(b.r) >= Math.abs(b.i)) {
r = b.i / b.r;
den = b.r + r * b.i;
c.r = (a.r + r * a.i) / den;
c.i = (a.i - r * a.r) / den;
} else {
r = b.r / b.i;
den = b.i + r * b.r;
c.r = (a.r * r + a.i) / den;
c.i = (a.i * r - a.r) / den;
}
return c;
}
/** creates a unit mag complex number. zero is assigned (1,0) */
public final Cmplx unitVector() {
double mag = mag();
if (mag != 0) {
return Cmplx.div(this, mag);
} else {
return new Cmplx(1, 0);
}
}
public final Cmplx sqrt() {
Cmplx c = new Cmplx();
double x, y, w, r;
if ((this.r == 0.0) && (this.i == 0.0)) {
c.r = (c.i = 0.0);
return (c);
} else {
x = Math.abs(this.r);
y = Math.abs(this.i);
if (x >= y) {
r = y / x;
w = Math.sqrt(x) * Math.sqrt(0.5 * (1.0 + Math.sqrt(1.0 + r * r)));
} else {
r = x / y;
w = Math.sqrt(y) * Math.sqrt(0.5 * (r + Math.sqrt(1.0 + r * r)));
}
if (this.r >= 0.0) {
c.r = w;
c.i = this.i / (2.0 * w);
} else {
c.i = (this.i >= 0.0) ? w : -w;
c.r = this.i / (2.0 * c.i);
}
return (c);
}
}
/**
* Computes the correlation of fdata with gdata. The value of the output at index i is the sum
* over j of fdata[i+j]*gdata[j], although using the FFT is much faster than direct sum.
*
* @see http://www.ulib.org/webRoot/Books/Numerical_Recipes/bookcpdf.html section 13-2
*/
public static final float[] correlate(float[] fdata, float[] gdata) {
if (fdata.length != gdata.length) {
throw new IllegalArgumentException(
"fdata and gdata must have same length. " + fdata.length + " " + gdata.length);
}
Cmplx[] fTrans = fft(fdata);
Cmplx[] gTrans = fft(gdata);
for (int i = 0; i < fTrans.length; i++) {
fTrans[i] = Cmplx.mul(fTrans[i], gTrans[i].conjg());
} // end of for (int i=0; i<gdata.length; i++)
return fftInverse(fTrans, fdata.length);
}
public static final Cmplx mul(Cmplx a, Cmplx b) {
Cmplx c = new Cmplx();
c.r = a.r * b.r - a.i * b.i;
c.i = a.i * b.r + a.r * b.i;
return c;
}
public static final Cmplx mul(Cmplx a, double b) {
return Cmplx.mul(a, new Cmplx(b, 0));
}
public static final Cmplx mul(double a, Cmplx b) {
return Cmplx.mul(new Cmplx(a, 0), b);
}
public static final Cmplx sub(Cmplx a, Cmplx b) {
Cmplx c = new Cmplx();
c.r = a.r - b.r;
c.i = a.i - b.i;
return c;
}
public static final Cmplx sub(Cmplx a, double b) {
return Cmplx.sub(a, new Cmplx(b, 0));
}
public static final Cmplx sub(double a, Cmplx b) {
return Cmplx.sub(new Cmplx(a, 0), b);
}
public static final Cmplx add(Cmplx a, Cmplx b) {
Cmplx c = new Cmplx();
c.r = a.r + b.r;
c.i = a.i + b.i;
return c;
}
public static final Cmplx exp(Cmplx arg) {
Cmplx c = new Cmplx();
c.r = Math.exp(arg.r) * Math.cos(arg.i);
c.i = Math.exp(arg.r) * Math.sin(arg.i);
return c;
}
public final Cmplx conjg() {
Cmplx c = new Cmplx();
c.r = this.r;
c.i = -this.i;
return c;
}
