/// <summary>
/// Applies identity operations for a n-d array.
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="value"></param>
/// <param name="result"> It can be same instance with <paramref name="value"/>, and in that case the instance will be overwritten. </param>
/// <exception cref="ShapeMismatchException" />
/// <exception cref="NotSupportedException" />
public static void Identity <T>(INdArray <T> value, MutableNdArray <T> result)
{
Guard.AssertShapeMatch(value.Shape == result.Shape, "There is shape mismatch.");
if (value.TryGetBufferImpl(out var xvalue) && result is RawNdArray <T> xresult)
{
Identity(xvalue.Buffer, xresult.Entity.Buffer);
}
// reference:
// https://github.com/xianyi/OpenBLAS/blob/develop/reference/dlaswpf.f
/// <summary>
/// [dlaswp] Swaps rows on the matrix A.
/// </summary>
/// <typeparam name="T"></typeparam>
/// <param name="a"></param>
/// <param name="colstart"></param>
/// <param name="collength"></param>
/// <param name="ipiv"></param>
/// <remarks> The columns between <c>[colstart, colstart + collength)</c> </remarks>
public static void SwapRows <T>(MutableNdArray <T> a, int colstart, int collength, ReadOnlySpan <int> ipiv)
{
Guard.AssertArgumentRange(0 <= colstart, "0 <= colstart");
Guard.AssertArgumentRange(colstart + collength < a.Shape[1], "colstart + collength < a.Shape[1]");
if (a is RawNdArray <T> xa)
{
using var alloc = new AllocationSlim <T>(collength);
var tmp = alloc.Memory.Slice(0, collength);
var c = a.Shape[1];
for (var i = 0; i < ipiv.Length; ++i)
{
if (i == ipiv[i])
{
continue;
}
var row1 = xa.Entity.Buffer.Slice(c * ipiv[i] + colstart, collength);
var row2 = xa.Entity.Buffer.Slice(c * i + colstart, collength);
VectorOperation.Identity(row1, tmp);
VectorOperation.Identity(row2, row1);
VectorOperation.Identity(tmp, row2);
}
}
else
{
for (var i = 0; i < ipiv.Length; ++i)
{
if (i == ipiv[i])
{
continue;
}
for (var j = colstart; j < colstart + collength; ++j)
{
var tmp = a[i, j];
a[i, j] = a[ipiv[i], j];
a[ipiv[i], j] = tmp;
}
}
}
}
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]));
}
}
}
}
}
// 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;
}
}
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]);
}
}
}
}
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]));
}
}
}
}
}
