public static IComplexFloatMatrix AU(IComplexFloatMatrix A, IROComplexFloatVector u, int r1, int r2, int c1, int c2)
{
if (r2 < r1)
{
return(A);
}
return(AU(A, u, r1, r2, c1, c2, new ComplexFloatVector(r2 - r1 + 1)));
}
public static IComplexFloatMatrix UA(IROComplexFloatVector u, IComplexFloatMatrix A, int r1, int r2, int c1, int c2)
{
if (c1 > c2)
{
return(A);
}
return(UA(u, A, r1, r2, c1, c2, new ComplexFloatVector(c2 - c1 + 1)));
}
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 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 IComplexFloatMatrix UA(IROComplexFloatVector u, IComplexFloatMatrix A, int r1, int r2, int c1, int c2, IComplexFloatVector v)
{
if (r2 < r1 || c2 < c1)
{
return(A);
}
if (r2 - r1 + 1 > u.Length)
{
throw new ArgumentException("Householder vector too short.", "u");
}
if (c2 - c1 + 1 > v.Length)
{
throw new ArgumentException("Work vector too short.", "v");
}
for (int j = c1; j <= c2; j++)
{
v[j - c1] = ComplexFloat.Zero;
}
for (int i = r1; i <= r2; i++)
{
for (int j = c1; j <= c2; j++)
{
v[j - c1] = new ComplexFloat(v[j - c1].Real + u[i - r1].Real * A[i, j].Real + u[i - r1].Imag * A[i, j].Imag,
v[j - c1].Imag + u[i - r1].Real * A[i, j].Imag - u[i - r1].Imag * A[i, j].Real);
}
}
for (int i = r1; i <= r2; i++)
{
for (int j = c1; j <= c2; j++)
{
A[i, j] = new ComplexFloat(A[i, j].Real - u[i - r1].Real * v[j - c1].Real + u[i - r1].Imag * v[j - c1].Imag,
A[i, j].Imag - u[i - r1].Real * v[j - c1].Imag - u[i - r1].Imag * v[j - c1].Real);
}
}
return(A);
}
public static IComplexFloatMatrix AU(IComplexFloatMatrix A, IROComplexFloatVector u, int r1, int r2, int c1, int c2)
{
if (r2 < r1)
{
return A;
}
return AU(A, u, r1, r2, c1, c2, new ComplexFloatVector(r2 - r1 + 1));
}
public static IComplexFloatMatrix AU(IComplexFloatMatrix A, IROComplexFloatVector u, int r1, int r2, int c1, int c2, IComplexFloatVector v)
{
if (r2 < r1 || c2 < c1)
{
return A;
}
if (c2 - c1 + 1 > u.Length)
{
throw new ArgumentException("Householder vector too short.", "u");
}
if (r2 - r1 + 1 > v.Length)
{
throw new ArgumentException("Work vector too short.", "v");
}
for (int i = r1; i <= r2; i++)
{
v[i - r1] = ComplexFloat.Zero;
for (int j = c1; j <= c2; j++)
{
v[i - r1] = new ComplexFloat(v[i - r1].Real + A[i, j].Real * u[j - c1].Real - A[i, j].Imag * u[j - c1].Imag,
v[i - r1].Imag + A[i, j].Real * u[j - c1].Imag + A[i, j].Imag * u[j - c1].Real);
}
}
for (int i = r1; i <= r2; i++)
{
for (int j = c1; j <= c2; j++)
{
A[i, j] = new ComplexFloat(A[i, j].Real - v[i - r1].Real * u[j - c1].Real - v[i - r1].Imag * u[j - c1].Imag,
A[i, j].Imag + v[i - r1].Real * u[j - c1].Imag - v[i - r1].Imag * u[j - c1].Real);
}
}
return A;
}
public static IComplexFloatMatrix UA(IROComplexFloatVector u, IComplexFloatMatrix A, int r1, int r2, int c1, int c2)
{
if (c1 > c2)
{
return A;
}
return UA(u, A, r1, r2, c1, c2, new ComplexFloatVector(c2 - c1 + 1));
}
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;
}
