/* ************************************************************************
 * Copyright (C) 2018-2025 Advanced Micro Devices, Inc. All rights reserved.
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell cop-
 * ies of the Software, and to permit persons to whom the Software is furnished
 * to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in all
 * copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IM-
 * PLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
 * FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
 * COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
 * IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNE-
 * CTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 *
 * ************************************************************************ */
/* ************************************************************************
 * Copyright (c) 1992-2022 The University of Tennessee and The University
                        of Tennessee Research Foundation.  All rights
                        reserved.
 * Copyright (c) 2000-2022 The University of California Berkeley. All
                        rights reserved.
 * Copyright (c) 2006-2022 The University of Colorado Denver.  All rights
                        reserved.

 * $COPYRIGHT$

 * Additional copyrights may follow

 * $HEADER$

 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are
 * met:

- Redistributions of source code must retain the above copyright
  notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above copyright
  notice, this list of conditions and the following disclaimer listed
  in this license in the documentation and/or other materials
  provided with the distribution.

- Neither the name of the copyright holders nor the names of its
  contributors may be used to endorse or promote products derived from
  this software without specific prior written permission.

 * The copyright holders provide no reassurances that the source code
 * provided does not infringe any patent, copyright, or any other
 * intellectual property rights of third parties.  The copyright holders
 * disclaim any liability to any recipient for claims brought against
 * recipient by any third party for infringement of that parties
 * intellectual property rights.

 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
 * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
 * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
 * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 * ************************************************************************ */
#pragma once

#include "hipblas.h"
#include "host_vector.hpp"

// These helpers are implemented as ILP64 API so single instantiation can be used for reference for both API

/* LAPACK library functionality */
template <typename T>
void lapack_xcombssq(T* ssq, T* colssq)
{
    if(ssq[0] >= colssq[0])
    {
        if(ssq[0] != T(0))
        {
            ssq[1] = ssq[1] + std::sqrt(colssq[0] / ssq[0]) * colssq[1];
        }
        else
        {
            ssq[1] = ssq[1] + colssq[1];
        }
    }
    else
    {
        ssq[1] = colssq[1] + std::sqrt(ssq[0] / colssq[0]) * ssq[1];
        ssq[0] = colssq[0];
    }
    return;
}

/*! \brief  lapack_xlassq computes the scale and sumsq*/
template <typename T>
void lapack_xlassq(int64_t n, T* X, int64_t incx, double& scale, double& sumsq)
{
    if(n > 0)
    {
        double abs_X = 0.0;
        for(int64_t i = 0; i < n; i++)
        {
            abs_X = hipblas_abs(is_complex<T> ? std::real(X[i * incx]) : X[i * incx]);
            if(abs_X > 0 || hipblas_isnan(abs_X))
            {
                if(scale < abs_X)
                {
                    sumsq = 1 + sumsq * std::sqrt(scale / abs_X);
                    scale = abs_X;
                }
                else
                {
                    sumsq = sumsq + std::sqrt(abs_X / scale);
                }
            }
            if(is_complex<T>)
            {
                abs_X = hipblas_abs(std::imag(X[i * incx]));
                if(abs_X > 0 || hipblas_isnan(abs_X))
                {
                    if(scale < abs_X || hipblas_isnan(abs_X))
                    {
                        sumsq = 1 + sumsq * std::sqrt(scale / abs_X);
                        scale = abs_X;
                    }
                    else
                    {
                        sumsq = sumsq + std::sqrt(abs_X / scale);
                    }
                }
            }
        }
    }
}

/*! \brief lapack_xlange-returns the value of the one norm,  or the Frobenius norm, or the  infinity norm of the matrix A.
    Implementation supports use on vectors with negative lda being negative increment */
template <typename T>
double lapack_xlange(char norm_type, int64_t m, int64_t n, T* A, int64_t lda, double* work)
{
    double value = 0.0;
    double sum   = 0.0;

    if(std::min(m, n) == 0)
        return value;

    int64_t a_offset = lda >= 0 ? 0 : lda * (1 - n); // e.g. vectors with negative inc
    if(norm_type == 'O' || norm_type == 'o' || norm_type == '1')
    {
        //Find the one norm of Matrix A.
        for(int64_t j = 0; j < n; j++)
        {
            sum = 0.0;
            for(int64_t i = 0; i < m; i++)
                sum = sum + hipblas_abs(A[a_offset + i + j * lda]);

            if(value < sum || hipblas_isnan(sum))
                value = sum;
        }
    }
    else if(norm_type == 'I' || norm_type == 'i')
    {
        //Find the infinity norm of Matrix A.
        for(int64_t j = 0; j < n; j++)
            for(int64_t i = 0; i < m; i++)
            {
                work[i] = work[i] + hipblas_abs(A[a_offset + i + j * lda]);
            }
        for(int64_t i = 0; i < m; i++)
            if(value < work[i] || hipblas_isnan(work[i]))
                value = work[i];
    }
    else if(norm_type == 'F' || norm_type == 'f')
    {
        //Find the Frobenius norm of Matrix A.
        //SSQ(1) is scale
        //SSQ(2) is sum-of-squares
        //For better accuracy, sum each column separately.
        host_vector<double> ssq(2);
        host_vector<double> colssq(2);
        ssq[0] = 0.0;
        ssq[1] = 1.0;
        for(int64_t j = 0; j < n; j++)
        {
            colssq[0] = 0.0;
            colssq[1] = 1.0;
            lapack_xlassq(m, A + a_offset + j * lda, 1, colssq[0], colssq[1]);
            lapack_xcombssq(ssq.data(), colssq.data());
        }
        value = ssq[0] * std::sqrt(ssq[1]);
    }
    return value;
}

/*! \brief lapack_xlansy-returns the value of the one norm,  or the Frobenius norm, or the  infinity norm of the matrix A.*/
template <bool HERM, typename T>
double lapack_xlansy(char norm_type, char uplo, int64_t n, T* A, int64_t lda, double* work)
{
    double value = 0.0;
    double sum   = 0.0;
    double abs_A = 0.0;
    if(n == 0)
        return value;

    else if(norm_type == 'O' || norm_type == 'o' || norm_type == 'I' || norm_type == 'i'
            || norm_type == '1')
    {
        //Since A is symmetric the infinity norm and the one norm is the same.
        if(uplo == 'U')
        {
            for(int64_t j = 0; j < n; j++)
            {
                sum = 0.0;
                for(int64_t i = 0; i < j; i++)
                {
                    abs_A   = hipblas_abs(A[i + j * lda]);
                    sum     = sum + abs_A;
                    work[i] = work[i] + abs_A;
                }
                work[j] = sum + hipblas_abs(HERM ? std::real(A[j + j * lda]) : A[j + j * lda]);
            }
            for(int64_t i = 0; i < n; i++)
            {
                sum = work[i];
                if(value < sum || hipblas_isnan(sum))
                    value = sum;
            }
        }
        else
        {
            for(int64_t i = 0; i < n; i++)
                work[i] = 0.0;
            for(int64_t j = 0; j < n; j++)
            {
                sum = work[j] + hipblas_abs(HERM ? std::real(A[j + j * lda]) : A[j + j * lda]);
                for(int64_t i = j + 1; j < n; j++)
                {
                    abs_A   = hipblas_abs(A[i + j * lda]);
                    sum     = sum + abs_A;
                    work[i] = work[i] + abs_A;
                }
                if(value < sum || hipblas_isnan(sum))
                    value = sum;
            }
        }
    }
    else if(norm_type == 'F' || norm_type == 'f')
    {
        //Find the Frobenius norm of Matrix A.
        //ssq[1] is scale
        //ssq[2] is sum-of-squares
        //For better accuracy, sum each column separately.
        host_vector<double> ssq(2);
        host_vector<double> colssq(2);
        ssq[0] = 0.0;
        ssq[1] = 1.0;

        if(uplo == 'U')
        {
            for(int64_t j = 1; j < n; j++)
            {
                colssq[0] = 0.0;
                colssq[1] = 1.0;
                lapack_xlassq(j - 1, A + j * lda, 1, colssq[0], colssq[1]);
                lapack_xcombssq(ssq.data(), colssq.data());
            }
        }
        else
        {
            for(int64_t j = 0; j < n - 1; j++)
            {
                colssq[0] = 0.0;
                colssq[1] = 1.0;
                lapack_xlassq(n - j, A + ((j + 1) + j * lda), 1, colssq[0], colssq[1]);
                lapack_xcombssq(ssq.data(), colssq.data());
            }
        }
        ssq[1] = 2 * ssq[1];

        //sum of diagonal
        if(HERM)
        {
            for(int64_t i = 0; i < n; i++)
            {
                if(std::real(A[i + i * lda]) != 0)
                {
                    abs_A = hipblas_abs(std::real(A[i + i * lda]));
                    if(ssq[0] < abs_A)
                    {
                        ssq[1] = 1.0 + ssq[1] * std::sqrt(ssq[0] / abs_A);
                        ssq[0] = abs_A;
                    }
                    else
                    {
                        ssq[1] = ssq[1] + std::sqrt(abs_A / ssq[0]);
                    }
                }
            }
        }
        else
        {
            colssq[0] = 0.0;
            colssq[1] = 1.0;
            lapack_xlassq(n, A, lda + 1, colssq[0], colssq[1]);
            lapack_xcombssq(ssq.data(), colssq.data());
        }
        value = ssq[0] * std::sqrt(ssq[1]);
    }
    return value;
}

template <typename T, typename U, typename V>
void lapack_xrot(
    const int64_t n, T* cx, const int64_t incx, T* cy, const int64_t incy, const U c, const V s)
{
    T stemp = T(0.0);
    if(n <= 0)
        return;
    if(incx == 1 && incy == 1)
    {
        for(int64_t i = 0; i < n; i++)
        {
            stemp = c * cx[i] + s * cy[i];
            cy[i] = c * cy[i] - (is_complex<V> ? hipblas_conjugate(s) : s) * cx[i];
            cx[i] = stemp;
        }
    }
    else
    {
        if(incx < 0)
            cx -= (n - 1) * incx;
        if(incy < 0)
            cy -= (n - 1) * incy;
        for(int64_t i = 0; i < n; i++)
        {
            stemp = c * cx[i * incx] + s * cy[i * incy];
            cy[i * incy]
                = c * cy[i * incy] - (is_complex<V> ? hipblas_conjugate(s) : s) * cx[i * incx];
            cx[i * incx] = stemp;
        }
    }
}

template <typename T, typename U>
void lapack_xrotg(T& ca, T& cb, U& c, T& s)
{
    if(hipblas_abs(ca) != 0)
    {
        const U scale = hipblas_abs(ca) + hipblas_abs(cb);
        const U norm  = scale
                       * std::sqrt((hipblas_abs(ca / scale)) * (hipblas_abs(ca / scale))
                                   + (hipblas_abs(cb / scale)) * (hipblas_abs(cb / scale)));
        T alpha = ca / T(hipblas_abs(ca));
        c       = hipblas_abs(ca) / norm;
        s       = alpha * hipblas_conjugate(cb) / norm;
        ca      = alpha * norm;
    }
    else
    {
        c  = 0.0;
        s  = T(1.0);
        ca = cb;
    }
}

// cblas_xsyr doesn't have complex support so implementation below for float/double complex
template <typename T>
void lapack_xsyr(hipblasFillMode_t uplo, int64_t n, T alpha, T* xa, int64_t incx, T* A, int64_t lda)
{
    if(n <= 0 || alpha == T(0))
        return;

    T* x = (incx < 0) ? xa - ptrdiff_t(incx) * (n - 1) : xa;

    if(uplo == HIPBLAS_FILL_MODE_UPPER)
    {
        for(int64_t j = 0; j < n; ++j)
        {
            T tmp = alpha * x[j * incx];
            for(int64_t i = 0; i <= j; ++i)
            {
                A[i + j * lda] = A[i + j * lda] + x[i * incx] * tmp;
            }
        }
    }
    else
    {
        for(int64_t j = 0; j < n; ++j)
        {
            T tmp = alpha * x[j * incx];
            for(int64_t i = j; i < n; ++i)
            {
                A[i + j * lda] = A[i + j * lda] + x[i * incx] * tmp;
            }
        }
    }
}

// cblas_xsymv doesn't have complex support so implementation below for float/double complex
template <typename T>
void lapack_xsymv(hipblasFillMode_t uplo,
                  int64_t           n,
                  T                 alpha,
                  T*                A,
                  int64_t           lda,
                  T*                xa,
                  int64_t           incx,
                  T                 beta,
                  T*                ya,
                  int64_t           incy)
{
    if(n <= 0)
        return;

    T* x = (incx < 0) ? xa - incx * (n - 1) : xa;
    T* y = (incy < 0) ? ya - incy * (n - 1) : ya;

    if(beta != T(1))
    {
        for(int64_t j = 0; j < n; j++)
        {
            y[j * incy] = beta == T(0) ? T(0) : y[j * incy] * beta;
        }
    }

    if(alpha == T(0))
        return;

    T temp1 = T(0);
    T temp2 = T(0);
    if(uplo == HIPBLAS_FILL_MODE_UPPER)
    {
        for(int64_t j = 0; j < n; j++)
        {
            temp1 = alpha * x[j * incx];
            temp2 = T(0);
            for(int64_t i = 0; i <= j - 1; i++)
            {
                y[i * incy] = y[i * incy] + temp1 * A[i + j * lda];
                temp2       = temp2 + A[i + j * lda] * x[i * incx];
            }
            y[j * incy] = y[j * incy] + temp1 * A[j + j * lda] + alpha * temp2;
        }
    }
    else
    {
        for(int64_t j = 0; j < n; j++)
        {
            temp1       = alpha * x[j * incx];
            temp2       = T(0);
            y[j * incy] = y[j * incy] + temp1 * A[j + j * lda];
            for(int64_t i = j + 1; i < n; i++)
            {
                y[i * incy] = y[i * incy] + temp1 * A[i + j * lda];
                temp2       = temp2 + A[i + j * lda] * x[i * incx];
            }
            y[j * incy] = y[j * incy] + alpha * temp2;
        }
    }
}

// cblas_xspr doesn't have complex support so implementation below for float/double complex
template <typename T>
void lapack_xspr(hipblasFillMode_t uplo, int64_t n, T alpha, T* xa, int64_t incx, T* A)
{
    if(n <= 0 || alpha == T(0))
        return;

    T*      x  = (incx < 0) ? xa - incx * (n - 1) : xa;
    int64_t kk = 0, k = 0;
    T       tmpx = T(0);
    if(uplo == HIPBLAS_FILL_MODE_UPPER)
    {
        for(int64_t j = 0; j < n; ++j)
        {
            if(x[j * incx] != T(0))
            {
                tmpx = alpha * x[j * incx];
                k    = kk;
                for(int64_t i = 0; i < j; ++i)
                {
                    A[k] = A[k] + x[i * incx] * tmpx;
                    k    = k + 1;
                }
                A[kk + j] += x[j * incx] * tmpx;
            }
            kk += j + 1;
        }
    }
    else
    {
        for(int64_t j = 0; j < n; ++j)
        {
            if(x[j * incx] != T(0))
            {
                tmpx = alpha * x[j * incx];
                A[kk] += x[j * incx] * tmpx;
                k = kk + 1;
                for(int64_t i = j + 1; i < n; ++i)
                {
                    A[k] = A[k] + x[i * incx] * tmpx;
                    k    = k + 1;
                }
            }
            kk += (n - 1) - j + 1;
        }
    }
}

// cblas_xsyr2 doesn't have complex support so implementation below for float/double complex
template <typename T>
inline void lapack_xsyr2(hipblasFillMode_t uplo,
                         int64_t           n,
                         T                 alpha,
                         T*                xa,
                         int64_t           incx,
                         T*                ya,
                         int64_t           incy,
                         T*                A,
                         int64_t           lda)
{
    if(n <= 0 || alpha == T(0))
        return;

    T* x = (incx < 0) ? xa - incx * (n - 1) : xa;
    T* y = (incy < 0) ? ya - incy * (n - 1) : ya;

    if(uplo == HIPBLAS_FILL_MODE_UPPER)
    {
        for(int64_t j = 0; j < n; ++j)
        {
            T tmpx = alpha * x[j * incx];
            T tmpy = alpha * y[j * incy];
            for(int64_t i = 0; i <= j; ++i)
            {
                A[i + j * lda] = A[i + j * lda] + x[i * incx] * tmpy + y[i * incy] * tmpx;
            }
        }
    }
    else
    {
        for(int64_t j = 0; j < n; ++j)
        {
            T tmpx = alpha * x[j * incx];
            T tmpy = alpha * y[j * incy];
            for(int64_t i = j; i < n; ++i)
            {
                A[i + j * lda] = A[i + j * lda] + x[i * incx] * tmpy + y[i * incy] * tmpx;
            }
        }
    }
}

// cblas doesn't have trti2 implementation for now so using the lapack trti2 implementation below
template <typename T>
void lapack_xtrti2(char uplo, char diag, int64_t n, T* A, int64_t lda)
{
    if(n < 0)
        return;

    T AJJ = T(0);

    if(uplo == 'U')
    {
        for(int64_t j = 0; j < n; j++)
        {
            if(diag == 'N')
            {
                A[j + j * lda] = T(1.0) / A[j + j * lda];
                AJJ            = -A[j + j * lda];
            }
            else
            {
                AJJ = T(-1.0);
            }
            //Compute elements 0:j-1 of j-th column.
            ref_trmv(HIPBLAS_FILL_MODE_UPPER,
                     HIPBLAS_OP_N,
                     char2hipblas_diagonal(diag),
                     j,
                     A,
                     lda,
                     A + (j * lda),
                     1);
            ref_scal(j, AJJ, A + (j * lda), 1);
        }
    }
    else
    {
        for(int64_t j = n - 1; j >= 0; j--)
        {
            if(diag == 'N')
            {
                A[j + j * lda] = T(1.0) / A[j + j * lda];
                AJJ            = -A[j + j * lda];
            }
            else
            {
                AJJ = T(-1.0);
            }
            if(j < n - 1)
            {
                //Compute elements 0:j-1 of j-th column.
                ref_trmv(HIPBLAS_FILL_MODE_LOWER,
                         HIPBLAS_OP_N,
                         char2hipblas_diagonal(diag),
                         n - j - 1,
                         A + ((j + 1) + (j + 1) * lda),
                         lda,
                         A + ((j + 1) + j * lda),
                         1);
                ref_scal(n - j - 1, AJJ, A + ((j + 1) + j * lda), 1);
            }
        }
    }
}

// cblas doesn't have trtri implementation for now so using the lapack trtri implementation below
template <typename T>
void lapack_xtrtri(char uplo, char diag, int64_t n, T* A, int64_t lda)
{
    if(n <= 0)
        return;

    int64_t NB = 64;
    int64_t JB = 0;
    if(NB <= 1 || NB >= n)
    {
        lapack_xtrti2(uplo, diag, n, A, lda);
    }
    else
    {
        if(uplo == 'U')
        {
            // Compute inverse of upper triangular matrix
            for(int64_t j = 0; j < n; j += NB)
            {
                JB = std::min(NB, n - j);

                // Compute rows 0:j-1 of current block column
                ref_trmm(HIPBLAS_SIDE_LEFT,
                         HIPBLAS_FILL_MODE_UPPER,
                         HIPBLAS_OP_N,
                         char2hipblas_diagonal(diag),
                         j,
                         JB,
                         T(1.0),
                         A,
                         lda,
                         A + (j * lda),
                         lda);
                ref_trsm(HIPBLAS_SIDE_RIGHT,
                         HIPBLAS_FILL_MODE_UPPER,
                         HIPBLAS_OP_N,
                         char2hipblas_diagonal(diag),
                         j,
                         JB,
                         T(-1.0),
                         A + (j + j * lda),
                         lda,
                         A + j * lda,
                         lda);
                lapack_xtrti2(uplo, diag, JB, A + (j + j * lda), lda);
            }
        }
        else
        {
            int64_t NN = ((n - 1) / NB) * NB;
            for(int64_t j = NN; j >= 0; j -= NB)
            {
                JB = std::min(NB, n - j);
                if(j + JB <= n)
                {
                    ref_trmm(HIPBLAS_SIDE_LEFT,
                             HIPBLAS_FILL_MODE_LOWER,
                             HIPBLAS_OP_N,
                             char2hipblas_diagonal(diag),
                             n - j - JB,
                             JB,
                             T(1.0),
                             A + ((j + JB) + (j + JB) * lda),
                             lda,
                             A + ((j + JB) + j * lda),
                             lda);
                    ref_trsm(HIPBLAS_SIDE_RIGHT,
                             HIPBLAS_FILL_MODE_LOWER,
                             HIPBLAS_OP_N,
                             char2hipblas_diagonal(diag),
                             n - j - JB,
                             JB,
                             T(-1.0),
                             A + (j + j * lda),
                             lda,
                             A + ((j + JB) + j * lda),
                             lda);
                }
                lapack_xtrti2(uplo, diag, JB, A + (j + j * lda), lda);
            }
        }
    }
}