larf.hpp

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//
// Copyright (c) 2021-2023, University of Colorado Denver. All rights reserved.
//
// This file is part of <T>LAPACK.
// <T>LAPACK is free software: you can redistribute it and/or modify it under
// the terms of the BSD 3-Clause license. See the accompanying LICENSE file.
 
#ifndef TLAPACK_LARF_HH
#define TLAPACK_LARF_HH
 
#include "tlapack/base/utils.hpp"
#include "tlapack/blas/gemv.hpp"
#include "tlapack/blas/ger.hpp"
#include "tlapack/blas/geru.hpp"
 
namespace tlapack {
 
template <TLAPACK_SIDE side_t,
          TLAPACK_STOREV storage_t,
          TLAPACK_VECTOR vector_t,
          TLAPACK_WORKSPACE work_t,
          TLAPACK_SCALAR tau_t,
          TLAPACK_VECTOR vectorC0_t,
          TLAPACK_MATRIX matrixC1_t,
          enable_if_t<std::is_convertible_v<storage_t, StoreV>, int> = 0>
void larf_work(side_t side,
               storage_t storeMode,
               vector_t const& x,
               const tau_t& tau,
               vectorC0_t& C0,
               matrixC1_t& C1,
               work_t& work)
{
    // data traits
    using idx_t = size_type<vectorC0_t>;
    using T = type_t<work_t>;
    using real_t = real_type<T>;
 
    // constants
    const real_t one(1);
    const idx_t k = size(C0);
    const idx_t m = nrows(C1);
    const idx_t n = ncols(C1);
 
    // check arguments
    tlapack_check(side == Side::Left || side == Side::Right);
    tlapack_check(storeMode == StoreV::Columnwise ||
                  storeMode == StoreV::Rowwise);
    tlapack_check((idx_t)size(x) == (side == Side::Left) ? m : n);
 
    // Quick return if possible
    if (m == 0 || n == 0) {
        for (idx_t i = 0; i < k; ++i)
            C0[i] -= tau * C0[i];
        return;
    }
 
    // Vector w
    auto [w, work1] = reshape(work, k);
 
    if (side == Side::Left) {
        if (storeMode == StoreV::Columnwise) {
            // w := C0^H + C1^H*x
            for (idx_t i = 0; i < k; ++i)
                w[i] = conj(C0[i]);
            gemv(CONJ_TRANS, one, C1, x, one, w);
 
            // C1 := C1 - tau*x*w^H
            ger(-tau, x, w, C1);
 
            // C0 := C0 - tau*w^H
            for (idx_t i = 0; i < k; ++i)
                C0[i] -= tau * conj(w[i]);
        }
        else {
            // w := C0^t + C1^t*x
            for (idx_t i = 0; i < k; ++i)
                w[i] = C0[i];
            gemv(TRANSPOSE, one, C1, x, one, w);
 
            // C1 := C1 - tau*conj(x)*w^t
            for (idx_t j = 0; j < n; ++j)
                for (idx_t i = 0; i < m; ++i)
                    C1(i, j) -= tau * conj(x[i]) * w[j];
 
            // C0 := C0 - tau*w^t
            for (idx_t i = 0; i < k; ++i)
                C0[i] -= tau * w[i];
        }
    }
    else {  // side == Side::Right
        if (storeMode == StoreV::Columnwise) {
            // w := C0 + C1*x
            for (idx_t i = 0; i < k; ++i)
                w[i] = C0[i];
            gemv(NO_TRANS, one, C1, x, one, w);
 
            // C1 := C1 - tau*w*x^H
            ger(-tau, w, x, C1);
 
            // C0 := C0 - tau*w
            for (idx_t i = 0; i < k; ++i)
                C0[i] -= tau * w[i];
        }
        else {
            // w := C0 + C1*conj(x)
            for (idx_t i = 0; i < k; ++i)
                w[i] = C0[i];
            for (idx_t j = 0; j < n; ++j)
                for (idx_t i = 0; i < m; ++i)
                    w[i] += C1(i, j) * conj(x[j]);
 
            // C1 := C1 - tau*w*x^t
            geru(-tau, w, x, C1);
 
            // C0 := C0 - tau*w
            for (idx_t i = 0; i < k; ++i)
                C0[i] -= tau * w[i];
        }
    }
}
 
template <class T,
          TLAPACK_SIDE side_t,
          TLAPACK_STOREV storage_t,
          TLAPACK_VECTOR vector_t,
          TLAPACK_SCALAR tau_t,
          TLAPACK_VECTOR vectorC0_t,
          TLAPACK_MATRIX matrixC1_t,
          enable_if_t<std::is_convertible_v<storage_t, StoreV>, int> = 0>
constexpr WorkInfo larf_worksize(side_t side,
                                 storage_t storeMode,
                                 vector_t const& x,
                                 const tau_t& tau,
                                 const vectorC0_t& C0,
                                 const matrixC1_t& C1)
{
    using work_t = matrix_type<vectorC0_t, matrixC1_t, vector_t>;
    using idx_t = size_type<vectorC0_t>;
 
    // constants
    const idx_t m = nrows(C1);
    const idx_t n = ncols(C1);
 
    if constexpr (is_same_v<T, type_t<work_t>>)
        return (m > 0 && n > 0) ? WorkInfo((side == Side::Left) ? n : m)
                                : WorkInfo(0);
    else
        return WorkInfo(0);
}
 
template <TLAPACK_SIDE side_t,
          TLAPACK_STOREV storage_t,
          TLAPACK_VECTOR vector_t,
          TLAPACK_SCALAR tau_t,
          TLAPACK_VECTOR vectorC0_t,
          TLAPACK_MATRIX matrixC1_t,
          enable_if_t<std::is_convertible_v<storage_t, StoreV>, int> = 0>
void larf(side_t side,
          storage_t storeMode,
          vector_t const& x,
          const tau_t& tau,
          vectorC0_t& C0,
          matrixC1_t& C1)
{
    // data traits
    using work_t = matrix_type<vectorC0_t, matrixC1_t, vector_t>;
    using idx_t = size_type<vectorC0_t>;
    using T = type_t<work_t>;
 
    // Functor
    Create<work_t> new_matrix;
 
    // constants
    const idx_t k = size(C0);
    const idx_t m = nrows(C1);
    const idx_t n = ncols(C1);
 
    // check arguments
    tlapack_check(side == Side::Left || side == Side::Right);
    tlapack_check(storeMode == StoreV::Columnwise ||
                  storeMode == StoreV::Rowwise);
    tlapack_check((idx_t)size(x) == (side == Side::Left) ? m : n);
 
    // Quick return if possible
    if (m == 0 || n == 0) {
        for (idx_t i = 0; i < k; ++i)
            C0[i] -= tau * C0[i];
        return;
    }
 
    // Allocates workspace
    WorkInfo workinfo = larf_worksize<T>(side, storeMode, x, tau, C0, C1);
    std::vector<T> work_;
    auto work = new_matrix(work_, workinfo.m, workinfo.n);
 
    return larf_work(side, storeMode, x, tau, C0, C1, work);
}
 
template <TLAPACK_SIDE side_t,
          TLAPACK_DIRECTION direction_t,
          TLAPACK_STOREV storage_t,
          TLAPACK_SVECTOR vector_t,
          TLAPACK_WORKSPACE work_t,
          TLAPACK_SCALAR tau_t,
          TLAPACK_SMATRIX matrix_t,
          enable_if_t<std::is_convertible_v<direction_t, Direction>, int> = 0>
void larf_work(side_t side,
               direction_t direction,
               storage_t storeMode,
               vector_t const& v,
               const tau_t& tau,
               matrix_t& C,
               work_t& work)
{
    using idx_t = size_type<matrix_t>;
    using range = pair<idx_t, idx_t>;
 
    // constants
    const idx_t m = nrows(C);
    const idx_t n = ncols(C);
 
    // check arguments
    tlapack_check(side == Side::Left || side == Side::Right);
    tlapack_check(direction == Direction::Backward ||
                  direction == Direction::Forward);
    tlapack_check(storeMode == StoreV::Columnwise ||
                  storeMode == StoreV::Rowwise);
    tlapack_check((idx_t)size(v) == ((side == Side::Left) ? m : n));
 
    // quick return
    if (m == 0 || n == 0) return;
 
    // The following code was changed from:
    //
    // if( side == Side::Left ) {
    //     gemv(CONJ_TRANS, one, C, v, work);
    //     ger(-tau, v, work, C);
    // }
    // else{
    //     gemv(NO_TRANS, one, C, v, work);
    //     ger(-tau, work, v, C);
    // }
    //
    // This is so that v[0] doesn't need to be changed to 1,
    // which is better for thread safety.
 
    if (side == Side::Left) {
        auto C0 = (direction == Direction::Forward) ? row(C, 0) : row(C, m - 1);
        auto C1 = (direction == Direction::Forward) ? rows(C, range{1, m})
                                                    : rows(C, range{0, m - 1});
        auto x = (direction == Direction::Forward) ? slice(v, range{1, m})
                                                   : slice(v, range{0, m - 1});
        larf_work(LEFT_SIDE, storeMode, x, tau, C0, C1, work);
    }
    else {  // side == Side::Right
        auto C0 = (direction == Direction::Forward) ? col(C, 0) : col(C, n - 1);
        auto C1 = (direction == Direction::Forward) ? cols(C, range{1, n})
                                                    : cols(C, range{0, n - 1});
        auto x = (direction == Direction::Forward) ? slice(v, range{1, n})
                                                   : slice(v, range{0, n - 1});
        larf_work(RIGHT_SIDE, storeMode, x, tau, C0, C1, work);
    }
}
 
template <class T,
          TLAPACK_SIDE side_t,
          TLAPACK_DIRECTION direction_t,
          TLAPACK_STOREV storage_t,
          TLAPACK_SVECTOR vector_t,
          TLAPACK_SCALAR tau_t,
          TLAPACK_SMATRIX matrix_t,
          enable_if_t<std::is_convertible_v<direction_t, Direction>, int> = 0>
constexpr WorkInfo larf_worksize(side_t side,
                                 direction_t direction,
                                 storage_t storeMode,
                                 vector_t const& v,
                                 const tau_t& tau,
                                 const matrix_t& C)
{
    using idx_t = size_type<matrix_t>;
    using range = pair<idx_t, idx_t>;
 
    // constants
    const idx_t m = nrows(C);
    const idx_t n = ncols(C);
 
    if (side == Side::Left && m > 0) {
        auto&& C0 = row(C, 0);
        auto&& C1 = rows(C, range{1, m});
        auto&& x = slice(v, range{1, m});
        return larf_worksize<T>(LEFT_SIDE, storeMode, x, tau, C0, C1);
    }
    else if (side == Side::Right && n > 0) {
        auto&& C0 = col(C, 0);
        auto&& C1 = cols(C, range{1, n});
        auto&& x = slice(v, range{1, n});
        return larf_worksize<T>(RIGHT_SIDE, storeMode, x, tau, C0, C1);
    }
    else
        return WorkInfo(0);
}
 
template <TLAPACK_SIDE side_t,
          TLAPACK_DIRECTION direction_t,
          TLAPACK_STOREV storage_t,
          TLAPACK_SVECTOR vector_t,
          TLAPACK_SCALAR tau_t,
          TLAPACK_SMATRIX matrix_t,
          enable_if_t<std::is_convertible_v<direction_t, Direction>, int> = 0>
void larf(side_t side,
          direction_t direction,
          storage_t storeMode,
          vector_t const& v,
          const tau_t& tau,
          matrix_t& C)
{
    // data traits
    using work_t = matrix_type<matrix_t, vector_t>;
    using idx_t = size_type<matrix_t>;
    using T = type_t<work_t>;
 
    // Functor
    Create<work_t> new_matrix;
 
    // constants
    const idx_t m = nrows(C);
    const idx_t n = ncols(C);
 
    // check arguments
    tlapack_check(side == Side::Left || side == Side::Right);
    tlapack_check(direction == Direction::Backward ||
                  direction == Direction::Forward);
    tlapack_check(storeMode == StoreV::Columnwise ||
                  storeMode == StoreV::Rowwise);
    tlapack_check((idx_t)size(v) == ((side == Side::Left) ? m : n));
 
    // quick return
    if (m == 0 || n == 0) return;
 
    // Allocates workspace
    WorkInfo workinfo = larf_worksize<T>(side, direction, storeMode, v, tau, C);
    std::vector<T> work_;
    auto work = new_matrix(work_, workinfo.m, workinfo.n);
 
    return larf_work(side, direction, storeMode, v, tau, C, work);
}
 
}  // namespace tlapack
 
#endif  // TLAPACK_LARF_HH