/// <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(Complex[] y, Complex alpha, Complex[] x, Complex[] 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 (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]));
}
}
public void IsOneTest()
{
Assert.IsFalse(a.IsOne());
Complex one = new Complex(field, BigInt.ONE);
Assert.IsTrue(one.IsOne());
}
/// <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(Complex[] y, Complex alpha, Complex[] x, Complex[] 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 (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]);
}
}
}
}
/// <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>
/// <remarks>This is equivalent to the SCAL BLAS routine.</remarks>
public void ScaleArray(Complex alpha, Complex[] x)
{
if (x == null)
{
throw new ArgumentNullException("x");
}
if (alpha.IsOne())
{
return;
}
SafeNativeMethods.z_scale(x.Length, ref alpha, x);
}
public void CanDetermineIfOneValueComplexNumber()
{
var complex = new Complex(1, 0);
Assert.IsTrue(complex.IsOne(), "Complex number with a value of one.");
}
/// <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, Complex alpha, Complex[] a, int rowsA, int columnsA, Complex[] b, int rowsB, int columnsB, Complex beta, Complex[] 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.
Complex[] adata;
if (ReferenceEquals(a, c))
{
adata = (Complex[])a.Clone();
}
else
{
adata = a;
}
Complex[] bdata;
if (ReferenceEquals(b, c))
{
bdata = (Complex[])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(Complex alpha, Complex[] x, Complex[] 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, index => { result[index] = alpha * x[index]; });
}
else
{
for (var index = 0; index < 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(Complex alpha, Complex[] x, Complex[] result)
{
if (x == null)
{
throw new ArgumentNullException("x");
}
if (alpha.IsZero())
{
CommonParallel.For(0, x.Length, index => result[index] = Complex.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>
/// 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, Complex alpha, Complex[] a, int rowsA, int columnsA, Complex[] b, int rowsB, int columnsB, Complex beta, Complex[] 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.
Complex[] adata;
if (ReferenceEquals(a, c))
{
adata = (Complex[])a.Clone();
}
else
{
adata = a;
}
Complex[] bdata;
if (ReferenceEquals(b, c))
{
bdata = (Complex[])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;
Complex 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;
Complex 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++)
{
Complex 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++)
{
Complex 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;
Complex 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;
Complex 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++)
{
Complex 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++)
{
Complex 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;
Complex 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;
Complex 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++)
{
Complex 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++)
{
Complex 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);
}
});
}
}
}
public void CanDetermineIfOneValueComplexNumber()
{
var complex = new Complex(1, 0);
Assert.IsTrue(complex.IsOne(), "Complex number with a value of one.");
}
