/// <summary>
/// Adds a scaled vector to another: <c>result = y + alpha*x</c>.
/// </summary>
/// <param name="y">The vector to update.</param>
/// <param name="alpha">The value to scale <paramref name="x"/> by.</param>
/// <param name="x">The vector to add to <paramref name="y"/>.</param>
/// <param name="result">The result of the addition.</param>
/// <remarks>This is similar to the AXPY BLAS routine.</remarks>
public virtual void AddVectorToScaledVector(Complex32[] y, Complex32 alpha, Complex32[] x, Complex32[] result)
{
if (y == null)
{
throw new ArgumentNullException("y");
}
if (x == null)
{
throw new ArgumentNullException("x");
}
if (y.Length != x.Length)
{
throw new ArgumentException(Resources.ArgumentVectorsSameLength);
}
if (alpha.IsZero())
{
CommonParallel.For(0, y.Length, index => result[index] = y[index]);
}
else if (alpha.IsOne())
{
CommonParallel.For(0, y.Length, index => result[index] = y[index] + x[index]);
}
else
{
CommonParallel.For(0, y.Length, index => result[index] = y[index] + (alpha * x[index]));
}
}
/// <summary>
/// Multiplies each element of the matrix by a scalar and places results into the result matrix.
/// </summary>
/// <param name="scalar">The scalar to multiply the matrix with.</param>
/// <param name="result">The matrix to store the result of the multiplication.</param>
protected override void DoMultiply(Complex32 scalar, Matrix <Complex32> result)
{
if (scalar.IsZero())
{
result.Clear();
return;
}
if (scalar.IsOne())
{
CopyTo(result);
return;
}
var diagResult = result as DiagonalMatrix;
if (diagResult == null)
{
base.DoMultiply(scalar, result);
}
else
{
Control.LinearAlgebraProvider.ScaleArray(scalar, _data, diagResult._data);
}
}
/// <summary>
/// Adds a scaled vector to another: <c>result = y + alpha*x</c>.
/// </summary>
/// <param name="y">The vector to update.</param>
/// <param name="alpha">The value to scale <paramref name="x"/> by.</param>
/// <param name="x">The vector to add to <paramref name="y"/>.</param>
/// <param name="result">The result of the addition.</param>
/// <remarks>This is similar to the AXPY BLAS routine.</remarks>
public virtual void AddVectorToScaledVector(Complex32[] y, Complex32 alpha, Complex32[] x, Complex32[] result)
{
if (y == null)
{
throw new ArgumentNullException("y");
}
if (x == null)
{
throw new ArgumentNullException("x");
}
if (y.Length != x.Length)
{
throw new ArgumentException(Resources.ArgumentVectorsSameLength);
}
if (alpha.IsZero())
{
y.Copy(result);
}
else if (alpha.IsOne())
{
if (Control.ParallelizeOperation(x.Length))
{
CommonParallel.For(0, y.Length, index => result[index] = y[index] + x[index]);
}
else
{
for (var index = 0; index < x.Length; index++)
{
result[index] = y[index] + x[index];
}
}
}
else
{
if (Control.ParallelizeOperation(x.Length))
{
CommonParallel.For(0, y.Length, index => result[index] = y[index] + (alpha * x[index]));
}
else
{
for (var index = 0; index < x.Length; index++)
{
result[index] = y[index] + (alpha * x[index]);
}
}
}
}
//public override Complex32 Impedance(double W = 0)
//{
// Complex32 Y = Complex32.Zero;
// Complex32 Z2 = Complex32.Zero;
// foreach (var item in Components)
// {
// Z2 = item.Impedance(W);
// if (Z2.IsZero())
// return Complex32.PositiveInfinity;
// Y += 1 / Z2;
// }
// return 1 / Y;
//}
public override Complex32 Impedance(Complex32?W = null)
{
Complex32 Y = Complex32.Zero;
Complex32 Z2 = Complex32.Zero;
foreach (var item in Components)
{
Z2 = item.Impedance(W);
if (Z2.IsZero())
{
return(Complex32.PositiveInfinity);
}
Y += 1 / Z2;
}
return(1 / Y);
}
/// <summary>
/// Adds a scaled vector to another: <c>result = y + alpha*x</c>.
/// </summary>
/// <param name="y">The vector to update.</param>
/// <param name="alpha">The value to scale <paramref name="x"/> by.</param>
/// <param name="x">The vector to add to <paramref name="y"/>.</param>
/// <param name="result">The result of the addition.</param>
/// <remarks>This is similar to the AXPY BLAS routine.</remarks>
public virtual void AddVectorToScaledVector(Complex32[] y, Complex32 alpha, Complex32[] x, Complex32[] result)
{
if (y == null)
{
throw new ArgumentNullException("y");
}
if (x == null)
{
throw new ArgumentNullException("x");
}
if (y.Length != x.Length)
{
throw new ArgumentException(Resources.ArgumentVectorsSameLength);
}
if (alpha.IsZero())
{
y.Copy(result);
}
else if (alpha.IsOne())
{
CommonParallel.For(0, y.Length, 4096, (a, b) =>
{
for (int i = a; i < b; i++)
{
result[i] = y[i] + x[i];
}
});
}
else
{
CommonParallel.For(0, y.Length, 4096, (a, b) =>
{
for (int i = a; i < b; i++)
{
result[i] = y[i] + (alpha * x[i]);
}
});
}
}
/// <summary>
/// Adds a scaled vector to another: <c>y += alpha*x</c>.
/// </summary>
/// <param name="y">The vector to update.</param>
/// <param name="alpha">The value to scale <paramref name="x"/> by.</param>
/// <param name="x">The vector to add to <paramref name="y"/>.</param>
/// <remarks>This equivalent to the AXPY BLAS routine.</remarks>
public void AddVectorToScaledVector(Complex32[] y, Complex32 alpha, Complex32[] x)
{
if (y == null)
{
throw new ArgumentNullException("y");
}
if (x == null)
{
throw new ArgumentNullException("x");
}
if (y.Length != x.Length)
{
throw new ArgumentException(Resources.ArgumentVectorsSameLength);
}
if (alpha.IsZero())
{
return;
}
SafeNativeMethods.c_axpy(y.Length, ref alpha, x, y);
}
/// <summary>
/// Multiplies each element of the matrix by a scalar and places results into the result matrix.
/// </summary>
/// <param name="scalar">The scalar to multiply the matrix with.</param>
/// <param name="result">The matrix to store the result of the multiplication.</param>
/// <exception cref="ArgumentNullException">If the result matrix is <see langword="null" />.</exception>
/// <exception cref="ArgumentException">If the result matrix's dimensions are not the same as this matrix.</exception>
protected override void DoMultiply(Complex32 scalar, Matrix<Complex32> result)
{
if (scalar.IsZero())
{
result.Clear();
return;
}
if (scalar.IsOne())
{
CopyTo(result);
return;
}
var diagResult = result as DiagonalMatrix;
if (diagResult == null)
{
base.Multiply(scalar, result);
}
else
{
if (!ReferenceEquals(this, result))
{
CopyTo(diagResult);
}
Control.LinearAlgebraProvider.ScaleArray(scalar, Data, diagResult.Data);
}
}
public void CanDetermineIfZeroValueComplexNumber()
{
var complex = new Complex32(0, 0);
Assert.IsTrue(complex.IsZero(), "Zero complex number.");
}
public void CanDetermineIfZeroValueComplexNumber()
{
var complex = new Complex32(0, 0);
Assert.IsTrue(complex.IsZero(), "Zero complex number.");
}
/// <summary>
/// Multiplies two matrices and updates another with the result. <c>c = alpha*op(a)*op(b) + beta*c</c>
/// </summary>
/// <param name="transposeA">How to transpose the <paramref name="a"/> matrix.</param>
/// <param name="transposeB">How to transpose the <paramref name="b"/> matrix.</param>
/// <param name="alpha">The value to scale <paramref name="a"/> matrix.</param>
/// <param name="a">The a matrix.</param>
/// <param name="rowsA">The number of rows in the <paramref name="a"/> matrix.</param>
/// <param name="columnsA">The number of columns in the <paramref name="a"/> matrix.</param>
/// <param name="b">The b matrix</param>
/// <param name="rowsB">The number of rows in the <paramref name="b"/> matrix.</param>
/// <param name="columnsB">The number of columns in the <paramref name="b"/> matrix.</param>
/// <param name="beta">The value to scale the <paramref name="c"/> matrix.</param>
/// <param name="c">The c matrix.</param>
public void MatrixMultiplyWithUpdate(Transpose transposeA, Transpose transposeB, Complex32 alpha, Complex32[] a, int rowsA, int columnsA, Complex32[] b, int rowsB, int columnsB, Complex32 beta, Complex32[] c)
{
// Choose nonsensical values for the number of rows in c; fill them in depending
// on the operations on a and b.
int rowsC;
// First check some basic requirement on the parameters of the matrix multiplication.
if (a == null)
{
throw new ArgumentNullException("a");
}
if (b == null)
{
throw new ArgumentNullException("b");
}
if ((int)transposeA > 111 && (int)transposeB > 111)
{
if (rowsA != columnsB)
{
throw new ArgumentOutOfRangeException();
}
if (columnsA * rowsB != c.Length)
{
throw new ArgumentOutOfRangeException();
}
rowsC = columnsA;
}
else if ((int)transposeA > 111)
{
if (rowsA != rowsB)
{
throw new ArgumentOutOfRangeException();
}
if (columnsA * columnsB != c.Length)
{
throw new ArgumentOutOfRangeException();
}
rowsC = columnsA;
}
else if ((int)transposeB > 111)
{
if (columnsA != columnsB)
{
throw new ArgumentOutOfRangeException();
}
if (rowsA * rowsB != c.Length)
{
throw new ArgumentOutOfRangeException();
}
rowsC = rowsA;
}
else
{
if (columnsA != rowsB)
{
throw new ArgumentOutOfRangeException();
}
if (rowsA * columnsB != c.Length)
{
throw new ArgumentOutOfRangeException();
}
rowsC = rowsA;
}
if (alpha.IsZero() && beta.IsZero())
{
Array.Clear(c, 0, c.Length);
return;
}
// Check whether we will be overwriting any of our inputs and make copies if necessary.
// TODO - we can don't have to allocate a completely new matrix when x or y point to the same memory
// as result, we can do it on a row wise basis. We should investigate this.
Complex32[] adata;
if (ReferenceEquals(a, c))
{
adata = (Complex32[])a.Clone();
}
else
{
adata = a;
}
Complex32[] bdata;
if (ReferenceEquals(b, c))
{
bdata = (Complex32[])b.Clone();
}
else
{
bdata = b;
}
if (alpha.IsOne())
{
if (beta.IsZero())
{
if ((int)transposeA > 111 && (int)transposeB > 111)
{
CommonParallel.For(
0,
columnsA,
j =>
{
var jIndex = j * rowsC;
for (var i = 0; i != rowsB; i++)
{
var iIndex = i * rowsA;
Complex32 s = 0;
for (var l = 0; l != columnsB; l++)
{
s += adata[iIndex + l] * bdata[(l * rowsB) + j];
}
c[jIndex + i] = s;
}
});
}
else if ((int)transposeA > 111)
{
CommonParallel.For(
0,
columnsB,
j =>
{
var jcIndex = j * rowsC;
var jbIndex = j * rowsB;
for (var i = 0; i != columnsA; i++)
{
var iIndex = i * rowsA;
Complex32 s = 0;
for (var l = 0; l != rowsA; l++)
{
s += adata[iIndex + l] * bdata[jbIndex + l];
}
c[jcIndex + i] = s;
}
});
}
else if ((int)transposeB > 111)
{
CommonParallel.For(
0,
rowsB,
j =>
{
var jIndex = j * rowsC;
for (var i = 0; i != rowsA; i++)
{
Complex32 s = 0;
for (var l = 0; l != columnsA; l++)
{
s += adata[(l * rowsA) + i] * bdata[(l * rowsB) + j];
}
c[jIndex + i] = s;
}
});
}
else
{
CommonParallel.For(
0,
columnsB,
j =>
{
var jcIndex = j * rowsC;
var jbIndex = j * rowsB;
for (var i = 0; i != rowsA; i++)
{
Complex32 s = 0;
for (var l = 0; l != columnsA; l++)
{
s += adata[(l * rowsA) + i] * bdata[jbIndex + l];
}
c[jcIndex + i] = s;
}
});
}
}
else
{
if ((int)transposeA > 111 && (int)transposeB > 111)
{
CommonParallel.For(
0,
columnsA,
j =>
{
var jIndex = j * rowsC;
for (var i = 0; i != rowsB; i++)
{
var iIndex = i * rowsA;
Complex32 s = 0;
for (var l = 0; l != columnsB; l++)
{
s += adata[iIndex + l] * bdata[(l * rowsB) + j];
}
c[jIndex + i] = (c[jIndex + i] * beta) + s;
}
});
}
else if ((int)transposeA > 111)
{
CommonParallel.For(
0,
columnsB,
j =>
{
var jcIndex = j * rowsC;
var jbIndex = j * rowsB;
for (var i = 0; i != columnsA; i++)
{
var iIndex = i * rowsA;
Complex32 s = 0;
for (var l = 0; l != rowsA; l++)
{
s += adata[iIndex + l] * bdata[jbIndex + l];
}
c[jcIndex + i] = s + (c[jcIndex + i] * beta);
}
});
}
else if ((int)transposeB > 111)
{
CommonParallel.For(
0,
rowsB,
j =>
{
var jIndex = j * rowsC;
for (var i = 0; i != rowsA; i++)
{
Complex32 s = 0;
for (var l = 0; l != columnsA; l++)
{
s += adata[(l * rowsA) + i] * bdata[(l * rowsB) + j];
}
c[jIndex + i] = s + (c[jIndex + i] * beta);
}
});
}
else
{
CommonParallel.For(
0,
columnsB,
j =>
{
var jcIndex = j * rowsC;
var jbIndex = j * rowsB;
for (var i = 0; i != rowsA; i++)
{
Complex32 s = 0;
for (var l = 0; l != columnsA; l++)
{
s += adata[(l * rowsA) + i] * bdata[jbIndex + l];
}
c[jcIndex + i] = s + (c[jcIndex + i] * beta);
}
});
}
}
}
else
{
if ((int)transposeA > 111 && (int)transposeB > 111)
{
CommonParallel.For(
0,
columnsA,
j =>
{
var jIndex = j * rowsC;
for (var i = 0; i != rowsB; i++)
{
var iIndex = i * rowsA;
Complex32 s = 0;
for (var l = 0; l != columnsB; l++)
{
s += adata[iIndex + l] * bdata[(l * rowsB) + j];
}
c[jIndex + i] = (c[jIndex + i] * beta) + (alpha * s);
}
});
}
else if ((int)transposeA > 111)
{
CommonParallel.For(
0,
columnsB,
j =>
{
var jcIndex = j * rowsC;
var jbIndex = j * rowsB;
for (var i = 0; i != columnsA; i++)
{
var iIndex = i * rowsA;
Complex32 s = 0;
for (var l = 0; l != rowsA; l++)
{
s += adata[iIndex + l] * bdata[jbIndex + l];
}
c[jcIndex + i] = (alpha * s) + (c[jcIndex + i] * beta);
}
});
}
else if ((int)transposeB > 111)
{
CommonParallel.For(
0,
rowsB,
j =>
{
var jIndex = j * rowsC;
for (var i = 0; i != rowsA; i++)
{
Complex32 s = 0;
for (var l = 0; l != columnsA; l++)
{
s += adata[(l * rowsA) + i] * bdata[(l * rowsB) + j];
}
c[jIndex + i] = (alpha * s) + (c[jIndex + i] * beta);
}
});
}
else
{
CommonParallel.For(
0,
columnsB,
j =>
{
var jcIndex = j * rowsC;
var jbIndex = j * rowsB;
for (var i = 0; i != rowsA; i++)
{
Complex32 s = 0;
for (var l = 0; l != columnsA; l++)
{
s += adata[(l * rowsA) + i] * bdata[jbIndex + l];
}
c[jcIndex + i] = (alpha * s) + (c[jcIndex + i] * beta);
}
});
}
}
}
/// <summary>
/// Multiplies two matrices and updates another with the result. <c>c = alpha*op(a)*op(b) + beta*c</c>
/// </summary>
/// <param name="transposeA">How to transpose the <paramref name="a"/> matrix.</param>
/// <param name="transposeB">How to transpose the <paramref name="b"/> matrix.</param>
/// <param name="alpha">The value to scale <paramref name="a"/> matrix.</param>
/// <param name="a">The a matrix.</param>
/// <param name="rowsA">The number of rows in the <paramref name="a"/> matrix.</param>
/// <param name="columnsA">The number of columns in the <paramref name="a"/> matrix.</param>
/// <param name="b">The b matrix</param>
/// <param name="rowsB">The number of rows in the <paramref name="b"/> matrix.</param>
/// <param name="columnsB">The number of columns in the <paramref name="b"/> matrix.</param>
/// <param name="beta">The value to scale the <paramref name="c"/> matrix.</param>
/// <param name="c">The c matrix.</param>
public virtual void MatrixMultiplyWithUpdate(Transpose transposeA, Transpose transposeB, Complex32 alpha, Complex32[] a, int rowsA, int columnsA, Complex32[] b, int rowsB, int columnsB, Complex32 beta, Complex32[] c)
{
int m; // The number of rows of matrix op(A) and of the matrix C.
int n; // The number of columns of matrix op(B) and of the matrix C.
int k; // The number of columns of matrix op(A) and the rows of the matrix op(B).
// First check some basic requirement on the parameters of the matrix multiplication.
if (a == null)
{
throw new ArgumentNullException("a");
}
if (b == null)
{
throw new ArgumentNullException("b");
}
if ((int)transposeA > 111 && (int)transposeB > 111)
{
if (rowsA != columnsB)
{
throw new ArgumentOutOfRangeException();
}
if (columnsA * rowsB != c.Length)
{
throw new ArgumentOutOfRangeException();
}
m = columnsA;
n = rowsB;
k = rowsA;
}
else if ((int)transposeA > 111)
{
if (rowsA != rowsB)
{
throw new ArgumentOutOfRangeException();
}
if (columnsA * columnsB != c.Length)
{
throw new ArgumentOutOfRangeException();
}
m = columnsA;
n = columnsB;
k = rowsA;
}
else if ((int)transposeB > 111)
{
if (columnsA != columnsB)
{
throw new ArgumentOutOfRangeException();
}
if (rowsA * rowsB != c.Length)
{
throw new ArgumentOutOfRangeException();
}
m = rowsA;
n = rowsB;
k = columnsA;
}
else
{
if (columnsA != rowsB)
{
throw new ArgumentOutOfRangeException();
}
if (rowsA * columnsB != c.Length)
{
throw new ArgumentOutOfRangeException();
}
m = rowsA;
n = columnsB;
k = columnsA;
}
if (alpha.IsZero() && beta.IsZero())
{
Array.Clear(c, 0, c.Length);
return;
}
// Check whether we will be overwriting any of our inputs and make copies if necessary.
// TODO - we can don't have to allocate a completely new matrix when x or y point to the same memory
// as result, we can do it on a row wise basis. We should investigate this.
Complex32[] adata;
if (ReferenceEquals(a, c))
{
adata = (Complex32[])a.Clone();
}
else
{
adata = a;
}
Complex32[] bdata;
if (ReferenceEquals(b, c))
{
bdata = (Complex32[])b.Clone();
}
else
{
bdata = b;
}
if (beta.IsZero())
{
Array.Clear(c, 0, c.Length);
}
else if (!beta.IsOne())
{
Control.LinearAlgebraProvider.ScaleArray(beta, c, c);
}
if (alpha.IsZero())
{
return;
}
CacheObliviousMatrixMultiply(transposeA, transposeB, alpha, adata, 0, 0, bdata, 0, 0, c, 0, 0, m, n, k, m, n, k, true);
}
/// <summary>
/// Scales an array. Can be used to scale a vector and a matrix.
/// </summary>
/// <param name="alpha">The scalar.</param>
/// <param name="x">The values to scale.</param>
/// <param name="result">This result of the scaling.</param>
/// <remarks>This is similar to the SCAL BLAS routine.</remarks>
public virtual void ScaleArray(Complex32 alpha, Complex32[] x, Complex32[] result)
{
if (x == null)
{
throw new ArgumentNullException("x");
}
if (alpha.IsZero())
{
CommonParallel.For(0, x.Length, index => result[index] = Complex32.Zero);
}
else if (alpha.IsOne())
{
CommonParallel.For(0, x.Length, index => result[index] = x[index]);
}
else
{
CommonParallel.For(0, x.Length, index => { result[index] = alpha * x[index]; });
}
}
/// <summary>
/// Scales an array. Can be used to scale a vector and a matrix.
/// </summary>
/// <param name="alpha">The scalar.</param>
/// <param name="x">The values to scale.</param>
/// <param name="result">This result of the scaling.</param>
/// <remarks>This is similar to the SCAL BLAS routine.</remarks>
public virtual void ScaleArray(Complex32 alpha, Complex32[] x, Complex32[] result)
{
if (x == null)
{
throw new ArgumentNullException("x");
}
if (alpha.IsZero())
{
Array.Clear(result, 0, result.Length);
}
else if (alpha.IsOne())
{
x.Copy(result);
}
else
{
if (Control.ParallelizeOperation(x.Length))
{
CommonParallel.For(0, x.Length, 4096, (a, b) =>
{
for (int i = a; i < b; i++)
{
result[i] = alpha*x[i];
}
});
}
else
{
for (var index = 0; index < x.Length; index++)
{
result[index] = alpha*x[index];
}
}
}
}
/// <summary>
/// Initializes a new instance of the <see cref="SparseMatrix"/> class with all entries set to a particular value.
/// </summary>
/// <param name="rows">
/// The number of rows.
/// </param>
/// <param name="columns">
/// The number of columns.
/// </param>
/// <param name="value">The value which we assign to each element of the matrix.</param>
public SparseMatrix(int rows, int columns, Complex32 value)
: this(rows, columns)
{
if (value.IsZero())
{
return;
}
var rowPointers = _storage.RowPointers;
var valueCount = _storage.ValueCount = rows * columns;
var columnIndices = _storage.ColumnIndices = new int[valueCount];
var values = _storage.Values = new Complex32[valueCount];
for (int i = 0, j = 0; i < values.Length; i++, j++)
{
// Reset column position to "0"
if (j == columns)
{
j = 0;
}
values[i] = value;
columnIndices[i] = j;
}
// Set proper row pointers
for (var i = 0; i < rowPointers.Length; i++)
{
rowPointers[i] = ((i + 1) * columns) - columns;
}
}
