/*------------------------------------------------------------------------------
 *	Copyright (c) 2023 by Bai Bing (seread@163.com)
 *	See COPYING file for copying and redistribution conditions.
 *
 *  Alians IT Studio.
 *----------------------------------------------------------------------------*/
#pragma once

#include "core/StaticAsserts.h"
#include "linalg/svd/ASSVD.h"
#include "ASMatrix.h"

namespace ais::linalg
{
    //============================================================================
    // Method Description:
    /// Solves the equation a x = b by computing a vector x
    /// that minimizes the Euclidean 2-norm || b - a x ||^2.
    /// The equation may be under-, well-, or over- determined
    /// (i.e., the number of linearly independent rows of a can
    /// be less than, equal to, or greater than its number of
    /// linearly independent columns). If a is square and of
    /// full rank, then x (but for round-off error) is the
    /// "exact" solution of the equation.
    ///
    /// SciPy Reference:
    /// https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.lstsq.html#scipy.linalg.lstsq
    ///
    /// @param inA: coefficient matrix
    /// @param inB: Ordinate or "dependent variable" values
    /// @param inTolerance (default 1e-12)
    ///
    /// @return Matrix
    ///
    template <typename dtype>
    Matrix<double> lstsq(const Matrix<dtype> &inA, const Matrix<dtype> &inB, double inTolerance = 1e-12)
    {
        STATIC_ASSERT_ARITHMETIC(dtype);

        SVD svdSolver(inA.template astype<double>());
        const double threshold = inTolerance * svdSolver.s().front();

        return svdSolver.solve(inB.template astype<double>(), threshold);
    }
} // namespace ais::linalg