public Complex acos() {
Complex result;
double tempRe, tempIm;
// acos(z) = -i * log( z + i * sqrt(1 - z*z) )
tempRe = 1.0 - ((re * re) - (im * im));
tempIm = 0.0 - ((re * im) + (im * re));
result = new Complex(tempRe, tempIm);
result = result.sqrt();
tempRe = -result.im;
tempIm = result.re;
result.re = re + tempRe;
result.im = im + tempIm;
tempRe = Math.log(result.abs());
tempIm = result.arg();
result.re = tempIm;
result.im = -tempRe;
return result;
}
public void testSqrtInf() {
TestUtils.assertSame(infNaN, oneInf.sqrt());
TestUtils.assertSame(infNaN, oneNegInf.sqrt());
TestUtils.assertSame(infZero, infOne.sqrt());
TestUtils.assertSame(zeroInf, negInfOne.sqrt());
TestUtils.assertSame(infNaN, infInf.sqrt());
TestUtils.assertSame(infNaN, infNegInf.sqrt());
TestUtils.assertSame(nanInf, negInfInf.sqrt());
TestUtils.assertSame(nanNegInf, negInfNegInf.sqrt());
}
public void testSqrtPolar() {
double r = 1;
for (int i = 0; i < 5; i++) {
r += i;
double theta = 0;
for (int j = 0; j < 11; j++) {
theta += pi / 12;
Complex z = ComplexUtils.polar2Complex(r, theta);
Complex sqrtz = ComplexUtils.polar2Complex(Math.sqrt(r), theta / 2);
TestUtils.assertEquals(sqrtz, z.sqrt(), 10e-12);
}
}
}
public Complex asinh() {
Complex result;
// asinh(z) = log(z + sqrt(z*z + 1))
result = new Complex(((re * re) - (im * im)) + 1, (re * im) + (im * re));
result = result.sqrt();
result.re += re;
result.im += im;
double temp = result.arg();
result.re = Math.log(result.abs());
result.im = temp;
return result;
}
public Complex asin() {
Complex result;
double tempRe, tempIm;
// asin(z) = -i * log(i*z + sqrt(1 - z*z))
tempRe = 1.0 - ((re * re) - (im * im));
tempIm = 0.0 - ((re * im) + (im * re));
result = new Complex(tempRe, tempIm);
result = result.sqrt();
result.re += -im;
result.im += re;
tempRe = Math.log(result.abs());
tempIm = result.arg();
result.re = tempIm;
result.im = -tempRe;
return result;
}
public void testSqrtImaginaryNegative() {
Complex z = new Complex(-3.0, -4.0);
Complex expected = new Complex(1.0, -2.0);
TestUtils.assertEquals(expected, z.sqrt(), 1.0e-5);
}
public void testSqrtImaginaryZero() {
Complex z = new Complex(-3.0, 0.0);
Complex expected = new Complex(0.0, 1.73205);
TestUtils.assertEquals(expected, z.sqrt(), 1.0e-5);
}
public void testSqrtRealNegative() {
Complex z = new Complex(-3.0, 4);
Complex expected = new Complex(1, 2);
TestUtils.assertEquals(expected, z.sqrt(), 1.0e-5);
}
public void testSqrtRealZero() {
Complex z = new Complex(0.0, 4);
Complex expected = new Complex(1.41421, 1.41421);
TestUtils.assertEquals(expected, z.sqrt(), 1.0e-5);
}
public void testSqrtRealPositive() {
Complex z = new Complex(3, 4);
Complex expected = new Complex(2, 1);
TestUtils.assertEquals(expected, z.sqrt(), 1.0e-5);
}
