private static void SolveTriangleMatrixRL <T>(bool isUnit, T alpha, INdArray <T> a, MutableNdArray <T> b)
{
var(m, n) = (b.Shape[0], b.Shape[1]);
/* reference Fortran
* DO 260, J = N, 1, -1
* IF( ALPHA.NE.ONE )THEN
* DO 220, I = 1, M
* B( I, J ) = ALPHA*B( I, J )
* 220 CONTINUE
* END IF
* DO 240, K = J + 1, N
* IF( A( K, J ).NE.ZERO )THEN
* DO 230, I = 1, M
* B( I, J ) = B( I, J ) - A( K, J )*B( I, K )
* 230 CONTINUE
* END IF
* 240 CONTINUE
* IF( NOUNIT )THEN
* TEMP = ONE/A( J, J )
* DO 250, I = 1, M
* B( I, J ) = TEMP*B( I, J )
* 250 CONTINUE
* END IF
* 260 CONTINUE
*/
for (var j = n - 1; j >= 0; --j)
{
if (ValueTrait.Equals(alpha, One <T>()))
{
for (var i = 0; i < m; ++i)
{
b[i, j] = Multiply(alpha, b[i, j]);
}
}
for (var k = j + 1; k < n; ++k)
{
if (!ValueTrait.Equals(a[k, j], Zero <T>()))
{
for (var i = 0; i < m; ++i)
{
b[i, j] = Subtract(b[i, j], Multiply(a[k, j], b[i, k]));
}
}
}
if (!isUnit)
{
var temp = Divide(One <T>(), a[j, j]);
for (var i = 0; i < m; ++i)
{
b[i, j] = Multiply(temp, b[i, j]);
}
}
}
}
private static void SolveTriangleMatrixRU <T>(bool isUnit, T alpha, INdArray <T> a, MutableNdArray <T> b)
{
var(m, n) = (b.Shape[0], b.Shape[1]);
/* reference Fortran
* DO 210, J = 1, N
* IF( ALPHA.NE.ONE )THEN
* DO 170, I = 1, M
* B( I, J ) = ALPHA*B( I, J )
* 170 CONTINUE
* END IF
* DO 190, K = 1, J - 1
* IF( A( K, J ).NE.ZERO )THEN
* DO 180, I = 1, M
* B( I, J ) = B( I, J ) - A( K, J )*B( I, K )
* 180 CONTINUE
* END IF
* 190 CONTINUE
* IF( NOUNIT )THEN
* TEMP = ONE/A( J, J )
* DO 200, I = 1, M
* B( I, J ) = TEMP*B( I, J )
* 200 CONTINUE
* END IF
* 210 CONTINUE
*/
for (var j = 0; j < n; ++j)
{
if (ValueTrait.Equals(alpha, One <T>()))
{
for (var i = 0; i < m; ++i)
{
b[i, j] = Multiply(alpha, b[i, j]);
}
}
for (var k = 0; k < j - 1; ++k)
{
if (!ValueTrait.Equals(a[k, j], Zero <T>()))
{
for (var i = 0; i < m; ++i)
{
b[i, j] = Subtract(b[i, j], Multiply(a[k, j], b[i, k]));
}
}
}
if (!isUnit)
{
var temp = Divide(One <T>(), a[j, j]);
for (var i = 0; i < m; ++i)
{
b[i, j] = Multiply(temp, b[i, j]);
}
}
}
}
/// <summary>
/// Gets the identity matrix which has the specified dimension.
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="n"></param>
/// <returns></returns>
public static NdArray <T> Identity <T>(int n)
{
var array = NdArray.CreateMutable(new T[n, n]);
for (var i = 0; i < n; ++i)
{
array[i, i] = ValueTrait.One <T>();
}
return(array.MoveToImmutable());
}
/// <summary>
/// Computes sum from all elements of the <paramref name="ndArray"/>.
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="ndArray"></param>
/// <returns></returns>
public static T Sum <T>(this INdArray <T> ndArray)
{
var value = ValueTrait.Zero <T>();
var len = ndArray.Shape.TotalLength;
for (var i = 0; i < len; ++i)
{
value = ValueTrait.Add(value, ndArray.GetItem(i));
}
return(value);
}
/// <summary>
/// Computes unbiased variance from all elements of the <paramref name="ndArray"/>.
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="ndArray"></param>
/// <returns></returns>
public static T UnbiasedVar <T>(this INdArray <T> ndArray)
{
var value = ValueTrait.Zero <T>();
var mean = ndArray.Mean();
var len = ndArray.Shape.TotalLength;
for (var i = 0; i < len; ++i)
{
var temp = ValueTrait.Subtract(ndArray.GetItem(i), mean);
value = ValueTrait.Multiply(temp, temp);
}
return(ValueTrait.Divide(value, ValueTrait.FromLong <T>(len - 1)));
}
public static Vector <T> GetVector <T>()
where T : unmanaged
{
Span <T> span = stackalloc T[Vector <T> .Count];
var x = ValueTrait.UnaryNegate(ValueTrait.One <T>());
for (var i = 0; i < Vector <T> .Count; ++i)
{
span[i] = x;
x = ValueTrait.Increment(x);
}
return(new Vector <T>(span));
}
/// <summary>
/// [Pure] Returns the 2-D norm of all elements of <paramref name="ndArray"/>.
/// </summary>
/// <param name="ndArray"></param>
/// <returns></returns>
public static T Norm2 <T>(this INdArray <T> ndArray)
{
var len = ndArray.Shape.TotalLength;
Guard.AssertOperation(len > 0, "ndArray has no elements.");
var norm = ValueTrait.Zero <T>();
for (var i = 0; i < len; ++i)
{
var element = ndArray.GetItem(i);
norm = ValueTrait.Add(norm, ValueTrait.Multiply(element, element));
}
return(NdMath.Sqrt(norm));
}
private static void SolveTriangleMatrixLU <T>(bool isUnit, T alpha, INdArray <T> a, MutableNdArray <T> b)
{
var(m, n) = (b.Shape[0], b.Shape[1]);
/* reference Fortran
* DO 60, J = 1, N
* IF( ALPHA.NE.ONE )THEN
* DO 30, I = 1, M
* B( I, J ) = ALPHA*B( I, J )
* 30 CONTINUE
* END IF
* DO 50, K = M, 1, -1
* IF( B( K, J ).NE.ZERO )THEN
* IF( NOUNIT )
* $ B( K, J ) = B( K, J )/A( K, K )
* DO 40, I = 1, K - 1
* B( I, J ) = B( I, J ) - B( K, J )*A( I, K )
* 40 CONTINUE
* END IF
* 50 CONTINUE
* 60 CONTINUE
*/
for (var j = 0; j < n; ++j)
{
if (!ValueTrait.Equals(alpha, One <T>()))
{
for (var i = 0; i < m; ++i)
{
b[i, j] = Multiply(alpha, b[i, j]);
}
}
for (var k = m - 1; k >= 0; --k)
{
if (!ValueTrait.Equals(b[k, j], Zero <T>()))
{
if (!isUnit)
{
b[k, j] = Divide(b[k, j], a[k, k]);
}
for (var i = 0; i < k - 1; ++i)
{
b[i, j] = Subtract(b[i, j], Multiply(b[k, j], a[i, k]));
}
}
}
}
}
private static void SolveTriangleMatrixLL <T>(bool isUnit, T alpha, INdArray <T> a, MutableNdArray <T> b)
{
var(m, n) = (b.Shape[0], b.Shape[1]);
/* reference Fortran
* DO 100, J = 1, N
* IF( ALPHA.NE.ONE )THEN
* DO 70, I = 1, M
* B( I, J ) = ALPHA*B( I, J )
* 70 CONTINUE
* END IF
* DO 90 K = 1, M
* IF( B( K, J ).NE.ZERO )THEN
* IF( NOUNIT )
* $ B( K, J ) = B( K, J )/A( K, K )
* DO 80, I = K + 1, M
* B( I, J ) = B( I, J ) - B( K, J )*A( I, K )
* 80 CONTINUE
* END IF
* 90 CONTINUE
* 100 CONTINUE
*/
for (var j = 0; j < n; ++j)
{
if (!ValueTrait.Equals(alpha, One <T>()))
{
for (var i = 0; i < m; ++i)
{
b[i, j] = Multiply(alpha, b[i, j]);
}
}
for (var k = 0; k < m; ++k)
{
if (!ValueTrait.Equals(b[k, j], Zero <T>()))
{
if (!isUnit)
{
b[k, j] = Divide(b[k, j], b[k, k]);
}
for (var i = k; i < m; ++i)
{
b[i, j] = Subtract(b[i, j], Divide(b[k, j], a[i, k]));
}
}
}
}
}
/// <summary>
/// Returns the largest value of the <paramref name="ndArray"/>.
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="ndArray"></param>
/// <returns></returns>
public static T Max <T>(this INdArray <T> ndArray)
{
var len = ndArray.Shape.TotalLength;
Guard.AssertOperation(len > 0, "ndArray has no elements.");
var max = ndArray.GetItem(0);
for (var i = 1; i < len; ++i)
{
var current = ndArray.GetItem(i);
if (ValueTrait.GreaterThan(current, max))
{
max = current;
}
}
return(max);
}
/// <summary>
/// Returns the index of the smallest value of the <paramref name="ndArray"/>.
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="ndArray"></param>
/// <returns></returns>
public static IndexArray ArgMin <T>(this INdArray <T> ndArray)
{
var len = ndArray.Shape.TotalLength;
Guard.AssertOperation(len > 0, "ndArray has no elements.");
var argmin = 0;
var min = ndArray.GetItem(0);
for (var i = 1; i < len; ++i)
{
var current = ndArray.GetItem(i);
if (ValueTrait.LessThan(current, min))
{
argmin = i;
min = current;
}
}
return(ndArray.ToShapedIndices(argmin));
}
// reference:
// https://github.com/xianyi/OpenBLAS/blob/develop/reference/dtrsmf.f
/// <summary>
/// [dtrsm] Solves one of the matrix equations:
/// <list type="bullet">
/// <item>
/// <term><c>(side, transa) = (Left, None)</c></term>
/// <description><c>A * X = alpha * B</c></description>
/// </item>
/// <item>
/// <term><c>(side, transa) = (Right, None)</c></term>
/// <description><c>X * A = alpha * B</c></description>
/// </item>
/// </list>
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="side"></param>
/// <param name="uplo"></param>
/// <param name="diag"> <c>true</c> if <paramref name="a"/> is a unit triangular; otherwise, <c>false</c>. </param>
/// <param name="alpha"></param>
/// <param name="a"></param>
/// <param name="b"></param>
public static void SolveTriangleMatrix <T>(OperandSide side, TriangleKind uplo, bool diag, T alpha, INdArray <T> a, MutableNdArray <T> b)
{
if (ValueTrait.Equals(alpha, Zero <T>()))
{
VectorOperation.Identity(NdArray.Zeros <T>(b.Shape), b);
return;
}
switch ((side, uplo))
{
case (OperandSide.Left, TriangleKind.Upper): SolveTriangleMatrixLU(diag, alpha, a, b); break;
case (OperandSide.Left, TriangleKind.Lower): SolveTriangleMatrixLL(diag, alpha, a, b); break;
case (OperandSide.Right, TriangleKind.Upper): SolveTriangleMatrixRU(diag, alpha, a, b); break;
case (OperandSide.Right, TriangleKind.Lower): SolveTriangleMatrixRL(diag, alpha, a, b); break;
default:
Guard.ThrowArgumentError("Invalid configs.");
break;
}
}
/// <summary>
/// Calculates dot product of the two specified sequences.
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="lhs"></param>
/// <param name="rhs"></param>
/// <returns></returns>
public static T Dot <T>(ReadOnlyMemory <T> lhs, ReadOnlyMemory <T> rhs)
{
Guard.AssertArgument(lhs.Length == rhs.Length, "lhs.Length == rhs.Length");
if (typeof(T) == typeof(byte))
{
var result = DotOptimized(
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <byte> >(ref lhs),
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <byte> >(ref rhs)
);
return(Unsafe.As <byte, T>(ref result));
}
if (typeof(T) == typeof(ushort))
{
var result = DotOptimized(
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <ushort> >(ref lhs),
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <ushort> >(ref rhs)
);
return(Unsafe.As <ushort, T>(ref result));
}
if (typeof(T) == typeof(uint))
{
var result = DotOptimized(
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <uint> >(ref lhs),
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <uint> >(ref rhs)
);
return(Unsafe.As <uint, T>(ref result));
}
if (typeof(T) == typeof(ulong))
{
var result = DotOptimized(
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <ulong> >(ref lhs),
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <ulong> >(ref rhs)
);
return(Unsafe.As <ulong, T>(ref result));
}
if (typeof(T) == typeof(sbyte))
{
var result = DotOptimized(
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <sbyte> >(ref lhs),
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <sbyte> >(ref rhs)
);
return(Unsafe.As <sbyte, T>(ref result));
}
if (typeof(T) == typeof(short))
{
var result = DotOptimized(
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <short> >(ref lhs),
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <short> >(ref rhs)
);
return(Unsafe.As <short, T>(ref result));
}
if (typeof(T) == typeof(int))
{
var result = DotOptimized(
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <int> >(ref lhs),
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <int> >(ref rhs)
);
return(Unsafe.As <int, T>(ref result));
}
if (typeof(T) == typeof(long))
{
var result = DotOptimized(
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <long> >(ref lhs),
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <long> >(ref rhs)
);
return(Unsafe.As <long, T>(ref result));
}
if (typeof(T) == typeof(float))
{
var result = DotOptimized(
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <float> >(ref lhs),
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <float> >(ref rhs)
);
return(Unsafe.As <float, T>(ref result));
}
if (typeof(T) == typeof(double))
{
var result = DotOptimized(
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <double> >(ref lhs),
Unsafe.As <ReadOnlyMemory <T>, ReadOnlyMemory <double> >(ref rhs)
);
return(Unsafe.As <double, T>(ref result));
}
{
var result = ValueTrait.Zero <T>();
for (var i = 0; i < lhs.Length; ++i)
{
result = ValueTrait.Add(result, ValueTrait.Multiply(lhs.Span[i], rhs.Span[i]));
}
return(result);
}
}
/// <summary>
/// Calculates dot product of the two specified sequences.
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="lhs"></param>
/// <param name="rhs"></param>
/// <returns></returns>
private static T DotOptimized <T>(ReadOnlyMemory <T> lhs, ReadOnlyMemory <T> rhs)
where T : unmanaged
{
var lhsVSpan = MemoryMarshal.Cast <T, Vector <T> >(lhs.Span);
var rhsVSpan = MemoryMarshal.Cast <T, Vector <T> >(rhs.Span);
var retval = ValueTrait.Zero <T>();
var i = 0;
for (var len = lhsVSpan.Length & ~0b1111; i < len; i += 16)
{
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i], rhsVSpan[i]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x1], rhsVSpan[i + 0x1]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x2], rhsVSpan[i + 0x2]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x3], rhsVSpan[i + 0x3]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x4], rhsVSpan[i + 0x4]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x5], rhsVSpan[i + 0x5]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x6], rhsVSpan[i + 0x6]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x7], rhsVSpan[i + 0x7]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x8], rhsVSpan[i + 0x8]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x9], rhsVSpan[i + 0x9]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0xA], rhsVSpan[i + 0xA]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0xB], rhsVSpan[i + 0xB]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0xC], rhsVSpan[i + 0xC]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0xD], rhsVSpan[i + 0xD]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0xE], rhsVSpan[i + 0xE]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0xF], rhsVSpan[i + 0xF]));
}
if (i < (lhsVSpan.Length & ~0b111))
{
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i], rhsVSpan[i]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x1], rhsVSpan[i + 0x1]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x2], rhsVSpan[i + 0x2]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x3], rhsVSpan[i + 0x3]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x4], rhsVSpan[i + 0x4]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x5], rhsVSpan[i + 0x5]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x6], rhsVSpan[i + 0x6]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x7], rhsVSpan[i + 0x7]));
i += 8;
}
if (i < (lhsVSpan.Length & ~0b11))
{
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i], rhsVSpan[i]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x1], rhsVSpan[i + 0x1]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x2], rhsVSpan[i + 0x2]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x3], rhsVSpan[i + 0x3]));
i += 4;
}
if (i < (lhsVSpan.Length & ~0b1))
{
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i], rhsVSpan[i]));
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i + 0x1], rhsVSpan[i + 0x1]));
i += 2;
}
if (i < lhsVSpan.Length)
{
retval = ValueTrait.Add(retval, Vector.Dot(lhsVSpan[i], rhsVSpan[i]));
++i;
}
var lhsRemainSpan = lhs.Span.Slice(Vector <T> .Count * i);
var rhsRemainSpan = rhs.Span.Slice(Vector <T> .Count * i);
var resultRemainSpan = lhs.Span.Slice(Vector <T> .Count * i);
for (var j = 0; j < resultRemainSpan.Length; ++j)
{
retval = ValueTrait.Add(retval, ValueTrait.Multiply(lhsRemainSpan[j], rhsRemainSpan[j]));
}
return(retval);
}
/// <summary> /// Computes mean from all elements of the <paramref name="ndArray"/>. /// </summary> /// <typeparam name="T"></typeparam> /// <param name="ndArray"></param> /// <returns></returns> public static T Mean <T>(this INdArray <T> ndArray) => ValueTrait.Divide(ndArray.Sum(), ValueTrait.FromLong <T>(ndArray.Shape.TotalLength));