public static ComplexDoubleVector GenerateRow(IComplexDoubleMatrix A, int r, int c1, int c2)
{
int cu = c2 - c1 + 1;
ComplexDoubleVector u = new ComplexDoubleVector(cu);
for (int j = c1; j <= c2; j++)
{
u[j - c1] = A[r, j];
A[r, j] = Complex.Zero;
}
double norm = u.GetNorm();
if (c1 == c2 || norm == 0)
{
A[r, c1] = new Complex(-u[0].Real, -u[0].Imag);
u[0] = System.Math.Sqrt(2);
return(u);
}
Complex scale = new Complex(1 / norm);
Complex t = Complex.Zero;
Complex t1 = Complex.Zero;
if (u[0].Real != 0 || u[0].Imag != 0)
{
t = u[0];
t1 = ComplexMath.Conjugate(u[0]);
t = ComplexMath.Absolute(t);
t = t1 / t;
scale = scale * t;
}
A[r, c1] = -Complex.One / scale;
for (int j = 0; j < cu; j++)
{
u[j] *= scale;
}
u[0] = new Complex(u[0].Real + 1);
double s = System.Math.Sqrt(1 / u[0].Real);
for (int j = 0; j < cu; j++)
{
u[j] = new Complex(s * u[j].Real, -s * u[j].Imag);
}
return(u);
}
public static ComplexDoubleVector GenerateColumn(IComplexDoubleMatrix A, int r1, int r2, int c)
{
int ru = r2 - r1 + 1;
ComplexDoubleVector u = new ComplexDoubleVector(r2 - r1 + 1);
for (int i = r1; i <= r2; i++)
{
u[i - r1] = A[i, c];
A[i, c] = Complex.Zero;
}
double norm = u.GetNorm();
if (r1 == r2 || norm == 0)
{
A[r1, c] = new Complex(-u[0]);
u[0] = System.Math.Sqrt(2);
return(u);
}
Complex scale = new Complex(1 / norm, 0);
Complex t = Complex.Zero;
Complex t1 = Complex.Zero;
if (u[0].Real != 0 || u[0].Imag != 0)
{
t = u[0];
t1 = ComplexMath.Conjugate(u[0]);
t = ComplexMath.Absolute(t);
t = t1 / t;
scale = scale * t;
}
A[r1, c] = -Complex.One / scale;
for (int i = 0; i < ru; i++)
{
u[i] = u[i] * scale;
}
u[0] = new Complex(u[0].Real + 1, 0);
double s = System.Math.Sqrt(1 / u[0].Real);
for (int i = 0; i < ru; i++)
{
u[i] = new Complex(s * u[i].Real, s * u[i].Imag);
}
return(u);
}
public static ComplexDoubleVector GenerateColumn(IComplexDoubleMatrix A, int r1, int r2, int c)
{
int ru = r2 - r1 + 1;
ComplexDoubleVector u = new ComplexDoubleVector(r2 - r1 + 1);
for (int i = r1; i <= r2; i++)
{
u[i - r1] = A[i, c];
A[i, c] = Complex.Zero;
}
double norm = u.GetNorm();
if (r1 == r2 || norm == 0)
{
A[r1, c] = new Complex(-u[0]);
u[0] = System.Math.Sqrt(2);
return u;
}
Complex scale = new Complex(1 / norm, 0);
Complex t = Complex.Zero;
Complex t1 = Complex.Zero;
if (u[0].Real != 0 || u[0].Imag != 0)
{
t = u[0];
t1 = ComplexMath.Conjugate(u[0]);
t = ComplexMath.Absolute(t);
t = t1 / t;
scale = scale * t;
}
A[r1, c] = -Complex.One / scale;
for (int i = 0; i < ru; i++)
{
u[i] = u[i] * scale;
}
u[0] = new Complex(u[0].Real + 1, 0);
double s = System.Math.Sqrt(1 / u[0].Real);
for (int i = 0; i < ru; i++)
{
u[i] = new Complex(s * u[i].Real, s * u[i].Imag);
}
return u;
}
public void GetNorm()
{
ComplexDoubleVector a = new ComplexDoubleVector(new double[4]{0,1,2,3});
ComplexDoubleVector b = new ComplexDoubleVector(new double[4]{4,5,6,7});
Assert.AreEqual(a.GetNorm(),System.Math.Sqrt(14));
Assert.AreEqual(a.GetNorm(),a.GetNorm(2));
Assert.AreEqual(a.GetNorm(0),3);
Assert.AreEqual(b.GetNorm(),3*System.Math.Sqrt(14));
Assert.AreEqual(b.GetNorm(),b.GetNorm(2));
Assert.AreEqual(b.GetNorm(0),7);
}
public static ComplexDoubleVector GenerateRow(IComplexDoubleMatrix A, int r, int c1, int c2)
{
int cu = c2 - c1 + 1;
ComplexDoubleVector u = new ComplexDoubleVector(cu);
for (int j = c1; j <= c2; j++)
{
u[j - c1] = A[r, j];
A[r, j] = Complex.Zero;
}
double norm = u.GetNorm();
if (c1 == c2 || norm == 0)
{
A[r, c1] = new Complex(-u[0].Real, -u[0].Imag);
u[0] = System.Math.Sqrt(2);
return u;
}
Complex scale = new Complex(1 / norm);
Complex t = Complex.Zero;
Complex t1 = Complex.Zero;
if (u[0].Real != 0 || u[0].Imag != 0)
{
t = u[0];
t1 = ComplexMath.Conjugate(u[0]);
t = ComplexMath.Absolute(t);
t = t1 / t;
scale = scale * t;
}
A[r, c1] = -Complex.One / scale;
for (int j = 0; j < cu; j++)
{
u[j] *= scale;
}
u[0] = new Complex(u[0].Real + 1);
double s = System.Math.Sqrt(1 / u[0].Real);
for (int j = 0; j < cu; j++)
{
u[j] = new Complex(s * u[j].Real, -s * u[j].Imag);
}
return u;
}