TheRock/rocm-libraries/projects/hipblas/clients/include/hipblas_init.hpp

/* ************************************************************************
 * Copyright (C) 2018-2024 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
 * copies 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
 * IMPLIED, 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 CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 * SOFTWARE.
 *
 * ************************************************************************ */

#pragma once

#ifdef _OPENMP
#include <omp.h>
#endif
#include <assert.h>

#include "hipblas.h"
#include "host_batch_vector.hpp"
#include "host_strided_batch_vector.hpp"
#include "host_vector.hpp"
#include "type_utils.h"

//!
//! @brief enum to check for NaN initialization of the Input vector/matrix
//!
typedef enum hipblas_client_nan_init_
{
    // Alpha sets NaN
    hipblas_client_alpha_sets_nan,

    // Beta sets NaN
    hipblas_client_beta_sets_nan,

    //  Never set NaN
    hipblas_client_never_set_nan

} hipblas_client_nan_init;

/*************************************************************************************************************************
//! @brief enum for the type of matrix
 ************************************************************************************************************************/
typedef enum hipblas_matrix_type_
{
    // General matrix
    hipblas_general_matrix,

    // Hermitian matrix
    hipblas_hermitian_matrix,

    // Symmetric matrix
    hipblas_symmetric_matrix,

    // Triangular matrix
    hipblas_triangular_matrix,

    // Diagonally dominant triangular matrix
    hipblas_diagonally_dominant_triangular_matrix,

} hipblas_matrix_type;

template <typename T>
void hipblas_init(
    T* A, int64_t M, int64_t N, int64_t lda, hipblasStride stride = 0, int64_t batch_count = 1)
{
    for(int64_t b = 0; b < batch_count; b++)
        for(int64_t i = 0; i < M; ++i)
            for(int64_t j = 0; j < N; ++j)
                A[i + j * lda + b * stride] = random_generator<T>();
}

/* ============================================================================================ */
/*! \brief  Initialize an array with random data, with NaN where appropriate */

template <typename T>
inline void hipblas_init_nan(T* A, size_t N)
{
    for(size_t i = 0; i < N; ++i)
        A[i] = T(hipblas_nan_rng());
}

template <typename U, typename T>
void hipblas_init_matrix_alternating_sign(hipblas_matrix_type matrix_type,
                                          const char          uplo,
                                          T                   rand_gen(),
                                          U&                  hA)
{
    auto M   = hA.m();
    auto N   = hA.n();
    auto lda = hA.lda();

    for(int64_t batch_index = 0; batch_index < hA.batch_count(); ++batch_index)
    {
        auto* A = hA[batch_index];

        if(matrix_type == hipblas_general_matrix)
        {
#ifdef _OPENMP
#pragma omp parallel for
#endif
            for(size_t i = 0; i < M; ++i)
                for(size_t j = 0; j < N; ++j)
                {
                    auto value     = rand_gen();
                    A[i + j * lda] = (i ^ j) & 1 ? T(value) : T(hipblas_negate(value));
                }
        }
        else if(matrix_type == hipblas_triangular_matrix)
        {
#ifdef _OPENMP
#pragma omp parallel for
#endif
            for(size_t i = 0; i < M; ++i)
                for(size_t j = 0; j < N; ++j)
                {
                    auto value     = uplo == 'U' ? (j >= i ? rand_gen() : T(0.0f))
                                                 : (j <= i ? rand_gen() : T(0.0f));
                    A[i + j * lda] = (i ^ j) & 1 ? T(value) : T(hipblas_negate(value));
                }
        }
        else
        {
            throw std::invalid_argument(
                "Invalid matrix_type for hipblas_init_matrix_alternating_sign function!");
        }
    }
}

// Initialize vector so adjacent entries have alternating sign.
template <typename T>
void hipblas_init_vector_alternating_sign(T rand_gen(), T* x, int64_t N, int64_t incx)
{
    if(incx < 0)
        x -= (N - 1) * incx;

#ifdef _OPENMP
#pragma omp parallel for
#endif
    for(int64_t j = 0; j < N; ++j)
    {
        auto value  = rand_gen();
        x[j * incx] = j & 1 ? T(value) : T(hipblas_negate(value));
    }
}

template <typename U, typename T>
void hipblas_init_matrix(hipblas_matrix_type matrix_type, const char uplo, T rand_gen(), U& hA)
{
    using R = real_t<T>;

    for(int64_t batch_index = 0; batch_index < hA.batch_count(); ++batch_index)
    {
        auto*   A   = hA[batch_index];
        int64_t M   = hA.m();
        int64_t N   = hA.n();
        int64_t lda = hA.lda();
        if(matrix_type == hipblas_general_matrix)
        {
#ifdef _OPENMP
#pragma omp parallel for
#endif
            for(size_t j = 0; j < N; ++j)
                for(size_t i = 0; i < M; ++i)
                    A[i + j * lda] = rand_gen();
        }
        else if(matrix_type == hipblas_hermitian_matrix)
        {
#ifdef _OPENMP
#pragma omp parallel for
#endif
            for(size_t i = 0; i < N; ++i)
                for(size_t j = 0; j <= i; ++j)
                {
                    auto value = rand_gen();
                    if(i == j)
                        A[j + i * lda] = hipblas_real(value);
                    else if(uplo == 'U')
                    {
                        A[j + i * lda] = value;
                        A[i + j * lda] = T(0.0f);
                    }
                    else if(uplo == 'L')
                    {
                        A[j + i * lda] = T(0.0f);
                        A[i + j * lda] = value;
                    }
                    else
                    {
                        A[j + i * lda] = value;
                        A[i + j * lda] = hipblas_conjugate(value);
                    }
                }
        }
        else if(matrix_type == hipblas_symmetric_matrix)
        {
#ifdef _OPENMP
#pragma omp parallel for
#endif
            for(size_t i = 0; i < N; ++i)
                for(size_t j = 0; j <= i; ++j)
                {
                    auto value = rand_gen();
                    if(i == j)
                        A[j + i * lda] = value;
                    else if(uplo == 'U')
                    {
                        A[j + i * lda] = value;
                        A[i + j * lda] = T(0.0f);
                    }
                    else if(uplo == 'L')
                    {
                        A[j + i * lda] = T(0.0f);
                        A[i + j * lda] = value;
                    }
                    else
                    {
                        A[j + i * lda] = value;
                        A[i + j * lda] = value;
                    }
                }
        }
        else if(matrix_type == hipblas_triangular_matrix)
        {
#ifdef _OPENMP
#pragma omp parallel for
#endif
            for(size_t j = 0; j < N; ++j)
                for(size_t i = 0; i < M; ++i)
                {
                    auto value     = uplo == 'U' ? (j >= i ? rand_gen() : T(0.0f))
                                                 : (j <= i ? rand_gen() : T(0.0f));
                    A[i + j * lda] = value;
                }
        }
        else if(matrix_type == hipblas_diagonally_dominant_triangular_matrix)
        {
            //An n x n triangle matrix with random entries has a condition number that grows exponentially with n ("Condition numbers of random triangular matrices" D. Viswanath and L.N.Trefethen).
            //Here we use a triangle matrix with random values that is strictly row and column diagonal dominant.
            //This matrix should have a lower condition number. An alternative is to calculate the Cholesky factor of an SPD matrix with random values and make it diagonal dominant.
            //This approach is not used because it is slow.

#ifdef _OPENMP
#pragma omp parallel for
#endif
            for(size_t j = 0; j < N; ++j)
                for(size_t i = 0; i < M; ++i)
                {
                    auto value     = uplo == 'U' ? (j >= i ? rand_gen() : T(0.0f))
                                                 : (j <= i ? rand_gen() : T(0.0f));
                    A[i + j * lda] = value;
                }

            const R multiplier = R(
                1.01f); // Multiplying factor to slightly increase the base value of (abs_sum_off_diagonal_row + abs_sum_off_diagonal_col) dominant diagonal element. If tests fail and it seems that there are numerical stability problems, try increasing multiplier, it should decrease the condition number of the matrix and thereby avoid numerical stability issues.

            if(uplo == 'U') // hipblas_fill_upper
            {
#ifdef _OPENMP
#pragma omp parallel for
#endif
                for(size_t i = 0; i < N; i++)
                {
                    R abs_sum_off_diagonal_row = R(
                        0.0f); //store absolute sum of entire row of the particular diagonal element
                    R abs_sum_off_diagonal_col = R(
                        0.0f); //store absolute sum of entire column of the particular diagonal element

                    for(size_t j = i + 1; j < N; j++)
                        abs_sum_off_diagonal_row
                            = R(abs_sum_off_diagonal_row + hipblas_abs(A[i + j * lda]));
                    for(size_t j = 0; j < i; j++)
                        abs_sum_off_diagonal_col
                            = R(abs_sum_off_diagonal_col + hipblas_abs(A[j + i * lda]));

                    A[i + i * lda]
                        = (abs_sum_off_diagonal_row + abs_sum_off_diagonal_col) == R(0.0f)
                              ? R(1.0f)
                              : R((abs_sum_off_diagonal_row + abs_sum_off_diagonal_col)
                                  * multiplier);
                }
            }
            else // hipblas_fill_lower
            {
#ifdef _OPENMP
#pragma omp parallel for
#endif
                for(size_t j = 0; j < N; j++)
                {
                    R abs_sum_off_diagonal_row = R(
                        0.0f); //store absolute sum of entire row of the particular diagonal element
                    R abs_sum_off_diagonal_col = R(
                        0.0f); //store absolute sum of entire column of the particular diagonal element

                    for(size_t i = j + 1; i < N; i++)
                        abs_sum_off_diagonal_col
                            = R(abs_sum_off_diagonal_col + hipblas_abs(A[i + j * lda]));

                    for(size_t i = 0; i < j; i++)
                        abs_sum_off_diagonal_row
                            = R(abs_sum_off_diagonal_row + hipblas_abs(A[j + i * lda]));

                    A[j + j * lda]
                        = (abs_sum_off_diagonal_row + abs_sum_off_diagonal_col) == R(0.0f)
                              ? R(1.0f)
                              : R((abs_sum_off_diagonal_row + abs_sum_off_diagonal_col)
                                  * multiplier);
                }
            }
        }
        else
        {
            throw std::invalid_argument("Invalid matrix_type for hipblas_init_matrix function!");
        }
    }
}

/*! \brief  vector initialization: */
// Initialize vectors with rand_int/hpl/NaN values

template <typename T>
void hipblas_init_vector(T rand_gen(), T* x, int64_t N, int64_t incx)
{
    if(incx < 0)
        x -= (N - 1) * incx;

#ifdef _OPENMP
#pragma omp parallel for
#endif
    for(int64_t j = 0; j < N; ++j)
        x[j * incx] = rand_gen();
}

template <typename T, typename U>
void hipblas_init_matrix_trig(hipblas_matrix_type matrix_type,
                              const char          uplo,
                              U&                  hA,
                              bool                seedReset = false)
{
    for(int64_t batch_index = 0; batch_index < hA.batch_count(); ++batch_index)
    {
        auto* A   = hA[batch_index];
        auto  M   = hA.m();
        auto  N   = hA.n();
        auto  lda = hA.lda();

        if(matrix_type == hipblas_general_matrix)
        {
#ifdef _OPENMP
#pragma omp parallel for
#endif
            for(size_t i = 0; i < M; ++i)
                for(size_t j = 0; j < N; ++j)
                    A[i + j * lda] = T(seedReset ? cos(i + j * M) : sin(i + j * M));
        }
        else if(matrix_type == hipblas_hermitian_matrix)
        {
#ifdef _OPENMP
#pragma omp parallel for
#endif
            for(size_t i = 0; i < N; ++i)
                for(size_t j = 0; j <= i; ++j)
                {
                    auto value = T(seedReset ? cos(i + j * N) : sin(i + j * N));

                    if(i == j)
                        A[j + i * lda] = hipblas_real(value);
                    else if(uplo == 'U')
                    {
                        A[j + i * lda] = value;
                        A[i + j * lda] = T(0.0f);
                    }
                    else if(uplo == 'L')
                    {
                        A[j + i * lda] = T(0.0f);
                        A[i + j * lda] = value;
                    }
                    else
                    {
                        A[j + i * lda] = value;
                        A[i + j * lda] = hipblas_conjugate(value);
                    }
                }
        }
        else if(matrix_type == hipblas_symmetric_matrix)
        {
#ifdef _OPENMP
#pragma omp parallel for
#endif
            for(size_t i = 0; i < N; ++i)
                for(size_t j = 0; j <= i; ++j)
                {
                    auto value = T(seedReset ? cos(i + j * N) : sin(i + j * N));
                    if(i == j)
                        A[j + i * lda] = value;
                    else if(uplo == 'U')
                    {
                        A[j + i * lda] = value;
                        A[i + j * lda] = T(0.0f);
                    }
                    else if(uplo == 'L')
                    {
                        A[j + i * lda] = T(0.0f);
                        A[i + j * lda] = value;
                    }
                    else
                    {
                        A[j + i * lda] = value;
                        A[i + j * lda] = value;
                    }
                }
        }
        else if(matrix_type == hipblas_triangular_matrix)
        {
#ifdef _OPENMP
#pragma omp parallel for
#endif
            for(size_t i = 0; i < M; ++i)
                for(size_t j = 0; j < N; ++j)
                {
                    auto value
                        = uplo == 'U'
                              ? (j >= i ? T(seedReset ? cos(i + j * M) : sin(i + j * M)) : T(0.0f))
                              : (j <= i ? T(seedReset ? cos(i + j * M) : sin(i + j * M)) : T(0.0f));
                    A[i + j * lda] = value;
                }
        }
        else
        {
            throw std::invalid_argument(
                "Invalid matrix_type for hipblas_init_matrix_trig function!");
        }
    }
}

/*! \brief  Trigonometric vector initialization: */
// Initialize vector with rand_int/hpl/NaN values

template <typename T>
void hipblas_init_vector_trig(T* x, int64_t N, int64_t incx, bool seedReset = false)
{
    if(incx < 0)
        x -= (N - 1) * incx;

#ifdef _OPENMP
#pragma omp parallel for
#endif
    for(int64_t j = 0; j < N; ++j)
        x[j * incx] = T(seedReset ? cos(j) : sin(j));
}

/* ============================================================================================ */
/*! \brief  Initialize an array with zero */

template <typename T, typename U>
void hipblas_init_vector_zero(U& hx)
{
    int64_t N      = hx.n();
    int64_t incx   = hx.inc();
    int64_t stride = hx.stride();

#ifdef _OPENMP
#pragma omp parallel for
#endif
    for(size_t batch_index = 0; batch_index < hx.batch_count(); batch_index++)
    {
        auto* x = hx[batch_index];

        for(size_t j = 0; j < N; ++j)
            x[j * incx] = T(0.0f);
    }
}

/* ============================================================================ */
/* \brief For testing purposes, to convert a regular matrix to a banded matrix. */
template <typename T>
inline void regular_to_banded(
    bool upper, const T* A, int64_t lda, T* AB, int64_t ldab, int64_t n, int64_t k)
{
    // convert regular hA matrix to banded hAB matrix.
    for(int64_t j = 0; j < n; j++)
    {
        int64_t min1 = upper ? std::max(int64_t(0), j - k) : j;
        int64_t max1 = upper ? j : std::min(n - 1, j + k);
        int64_t m    = upper ? k - j : -j;

        // Move bands of hA into new banded hAB format.
        for(int64_t i = min1; i <= max1; i++)
            AB[j * ldab + (m + i)] = A[j * lda + i];

        min1 = upper ? k + 1 : std::min(k + 1, n - j);
        max1 = ldab - 1;

        // fill in bottom with random data to ensure we aren't using it.
        // for !upper, fill in bottom right triangle as well.
        for(int64_t i = min1; i <= max1; i++)
            hipblas_init<T>(AB + j * ldab + i, 1, 1, 1);

        // for upper, fill in top left triangle with random data to ensure
        // we aren't using it.
        if(upper)
        {
            for(int64_t i = 0; i < m; i++)
                hipblas_init<T>(AB + j * ldab + i, 1, 1, 1);
        }
    }
}

/* ============================================================================= */
/*! \brief For testing purposes, to convert a regular matrix to a banded matrix.
 *         This routine is for host batched and strided batched vectors */

template <typename T>
inline void regular_to_banded(bool upper, const T& h_A, T& h_AB, int64_t k)
{
    size_t  lda  = h_A.lda();
    size_t  ldab = h_AB.lda();
    int64_t n    = h_AB.n();

#ifdef _OPENMP
#pragma omp parallel for
#endif
    for(int64_t batch_index = 0; batch_index < h_A.batch_count(); ++batch_index)
    {
        auto* A  = h_A[batch_index];
        auto* AB = h_AB[batch_index];

        // convert regular A matrix to banded AB matrix
        for(int64_t j = 0; j < n; j++)
        {
            int64_t min1 = upper ? std::max(int64_t(0), j - k) : j;
            int64_t max1 = upper ? j : std::min(n - 1, j + k);
            int64_t m    = upper ? k - j : -j;

            // Move bands of A into new banded AB format.
            for(int i = min1; i <= max1; i++)
                AB[j * ldab + (m + i)] = A[j * lda + i];

            min1 = upper ? k + 1 : std::min(k + 1, n - j);
            max1 = ldab - 1;

            // fill in bottom with random data to ensure we aren't using it.
            // for !upper, fill in bottom right triangle as well.
            for(int i = min1; i <= max1; i++)
                hipblas_init(AB + j * ldab + i, 1, 1, 1);

            // for upper, fill in top left triangle with random data to ensure
            // we aren't using it.
            if(upper)
            {
                for(int i = 0; i < m; i++)
                    hipblas_init(AB + j * ldab + i, 1, 1, 1);
            }
        }
    }
}

/* ============================================================================== */
/* \brief For testing purposes, zeros out elements not needed in a banded matrix. */
template <typename T>
inline void banded_matrix_setup(bool upper, T* A, int64_t lda, int64_t n, int64_t k)
{
    // Make A a banded matrix with k sub/super diagonals.
    for(int64_t i = 0; i < n; i++)
    {
        for(int64_t j = 0; j < n; j++)
        {
            if(upper && (j > k + i || i > j))
                A[j * n + i] = T(0.0);
            else if(!upper && (i > k + j || j > i))
                A[j * n + i] = T(0.0);
        }
    }
}

/* =============================================================================== */
/*! \brief For testing purposes, zeros out elements not needed in a banded matrix.
 *         This routine is for host batched and strided batched vectors */

template <typename U, typename T>
inline void banded_matrix_setup(bool upper, T& h_A, int64_t k)
{
    int64_t n = h_A.n();

#ifdef _OPENMP
#pragma omp parallel for
#endif
    for(int64_t batch_index = 0; batch_index < h_A.batch_count(); ++batch_index)
    {
        auto* A = h_A[batch_index];
        // Made A a banded matrix with k sub/super-diagonals
        for(int i = 0; i < n; i++)
        {
            for(int j = 0; j < n; j++)
            {
                if(upper && (j > k + i || i > j))
                    A[j * size_t(n) + i] = U(0);
                else if(!upper && (i > k + j || j > i))
                    A[j * size_t(n) + i] = U(0);
            }
        }
    }
}

/* ============================================================================================= */
/*! \brief For testing purposes, makes a matrix hA into a unit_diagonal matrix and               *
 *         randomly initialize the diagonal.                                                     */
template <typename T>
void make_unit_diagonal(hipblasFillMode_t uplo, T* hA, int64_t lda, int64_t N)
{
    if(uplo == HIPBLAS_FILL_MODE_LOWER)
    {
        for(int64_t i = 0; i < N; i++)
        {
            T diag = hA[i + i * lda];
            for(int64_t j = 0; j <= i; j++)
                hA[i + j * lda] = hA[i + j * lda] / diag;
        }
    }
    else // HIPBLAS_FILL_MODE_UPPER
    {
        for(int64_t j = 0; j < N; j++)
        {
            T diag = hA[j + j * lda];
            for(int64_t i = 0; i <= j; i++)
                hA[i + j * lda] = hA[i + j * lda] / diag;
        }
    }

    // randomly initalize diagonal to ensure we aren't using it's values for tests.
    for(int64_t i = 0; i < N; i++)
    {
        hipblas_init<T>(hA + i * lda + i, 1, 1, 1);
    }
}

/* ============================================================================================= */
/*! \brief For testing purposes, makes the square matrix hA into a unit_diagonal matrix and               *
 *         randomly initialize the diagonal. This routine is for host batched and strided batched vectors */
template <typename T>
void make_unit_diagonal(hipblasFillMode_t uplo, T& h_A)
{
    int64_t N   = h_A.n();
    size_t  lda = h_A.lda();

#ifdef _OPENMP
#pragma omp parallel for
#endif
    for(int64_t batch_index = 0; batch_index < h_A.batch_count(); ++batch_index)
    {
        auto* A = h_A[batch_index];

        if(uplo == HIPBLAS_FILL_MODE_LOWER)
        {
            for(int i = 0; i < N; i++)
            {
                auto diag = A[i + i * lda];
                for(int j = 0; j <= i; j++)
                    A[i + j * lda] = A[i + j * lda] / diag;
            }
        }
        else // HIPBLAS_FILL_MODE_UPPER
        {
            for(int j = 0; j < N; j++)
            {
                auto diag = A[j + j * lda];
                for(int i = 0; i <= j; i++)
                    A[i + j * lda] = A[i + j * lda] / diag;
            }
        }
        // randomly initalize diagonal to ensure we aren't using it's values for tests.
        for(int i = 0; i < N; i++)
        {
            hipblas_init(A + i * lda + i, 1, 1, 1);
        }
    }
}

/* ============================================================================================= */
/*! \brief For testing purposes, to convert a regular matrix to a packed matrix.                  */
template <typename T>
inline void regular_to_packed(bool upper, const T* A, T* AP, int64_t n)
{
    int64_t index = 0;
    if(upper)
        for(int64_t i = 0; i < n; i++)
            for(int64_t j = 0; j <= i; j++)
                AP[index++] = A[j + i * n];
    else
        for(int64_t i = 0; i < n; i++)
            for(int64_t j = i; j < n; j++)
                AP[index++] = A[j + i * n];
}

/* ============================================================================================= */
/*! \brief For testing purposes, to convert a regular matrix to a packed matrix.
 *         This routine is for host batched and strided batched matrices */

template <typename U>
inline void regular_to_packed(bool upper, U& h_A, U& h_AP, int64_t n)
{
#ifdef _OPENMP
#pragma omp parallel for
#endif
    for(int64_t batch_index = 0; batch_index < h_A.batch_count(); ++batch_index)
    {
        auto*  AP    = h_AP[batch_index];
        auto*  A     = h_A[batch_index];
        size_t index = 0;
        if(upper)
        {
            for(int i = 0; i < n; i++)
            {
                for(int j = 0; j <= i; j++)
                {
                    AP[index++] = A[j + i * size_t(n)];
                }
            }
        }
        else
        {
            for(int i = 0; i < n; i++)
            {
                for(int j = i; j < n; j++)
                {
                    AP[index++] = A[j + i * size_t(n)];
                }
            }
        }
    }
}