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