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// Copyright (c) 2017-2023, University of Tennessee. All rights reserved.
// SPDX-License-Identifier: BSD-3-Clause
// This program 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 BLAS_ROTMG_HH
#define BLAS_ROTMG_HH
#include "blas/util.hh"
#include <limits>
namespace blas {
// =============================================================================
/// Construct modified (fast) plane rotation, H, that eliminates b, such that
/// \[
/// \begin{bmatrix} z \\ 0 \end{bmatrix}
/// = H
/// \begin{bmatrix} \sqrt{d_1} & 0 \\ 0 & \sqrt{d_2} \end{bmatrix}
/// \begin{bmatrix} a \\ b \end{bmatrix}.
/// \]
///
/// @see rotm to apply the rotation.
///
/// With modified plane rotations, vectors u and v are held in factored form as
/// \[
/// \begin{bmatrix} u^T \\ v^T \end{bmatrix} =
/// \begin{bmatrix} \sqrt{d_1} & 0 \\ 0 & \sqrt{d_2} \end{bmatrix}
/// \begin{bmatrix} x^T \\ y^T \end{bmatrix}.
/// \]
///
/// Application of H to vectors x and y requires 4n flops (2n mul, 2n add)
/// instead of 6n flops (4n mul, 2n add) as in standard plane rotations.
///
/// Let param = [ flag, $h_{11}, h_{21}, h_{12}, h_{22}$ ].
/// Then H has one of the following forms:
///
/// - For flag = -1,
/// \[
/// H = \begin{bmatrix}
/// h_{11} & h_{12}
/// \\ h_{21} & h_{22}
/// \end{bmatrix}
/// \]
///
/// - For flag = 0,
/// \[
/// H = \begin{bmatrix}
/// 1 & h_{12}
/// \\ h_{21} & 1
/// \end{bmatrix}
/// \]
///
/// - For flag = 1,
/// \[
/// H = \begin{bmatrix}
/// h_{11} & 1
/// \\ -1 & h_{22}
/// \end{bmatrix}
/// \]
///
/// - For flag = -2,
/// \[
/// H = \begin{bmatrix}
/// 1 & 0
/// \\ 0 & 1
/// \end{bmatrix}
/// \]
///
/// Generic implementation for arbitrary data types.
///
/// @param[in, out] d1
/// sqrt(d1) is scaling factor for vector x.
///
/// @param[in, out] d2
/// sqrt(d2) is scaling factor for vector y.
///
/// @param[in, out] a
/// On entry, scalar a. On exit, set to z.
///
/// @param[in] b
/// On entry, scalar b.
///
/// @param[out] param
/// Array of length 5 giving parameters of modified plane rotation,
/// as described above.
///
/// __Further details__
///
/// Hammarling, Sven. A note on modifications to the Givens plane rotation.
/// IMA Journal of Applied Mathematics, 13:215-218, 1974.
/// http://dx.doi.org/10.1093/imamat/13.2.215
/// (Note the notation swaps u <=> x, v <=> y, d_i -> l_i.)
///
/// @ingroup rotmg
template <typename T>
void rotmg(
T *d1,
T *d2,
T *a,
T b,
T param[5] )
{
using std::abs;
// Constants
const T zero = 0;
const T one = 1;
const T gam = 4096;
const T gamsq = gam*gam;
const T rgamsq = one/gamsq;
T& x1 = *a;
T& y1 = b;
T h11 = zero;
T h12 = zero;
T h21 = zero;
T h22 = zero;
if (*d1 < zero) {
param[0] = -1;
*d1 = zero;
*d2 = zero;
x1 = zero;
}
else {
T p2 = (*d2)*y1;
if (p2 == zero) {
param[0] = -2;
return;
}
T p1 = (*d1)*x1;
T q2 = p2*y1;
T q1 = p1*x1;
if (abs(q1) > abs(q2)) {
param[0] = zero;
h21 = -y1/x1;
h12 = p2/p1;
T u = one - h12*h21;
if (u > zero) {
*d1 /= u;
*d2 /= u;
x1 *= u;
}
}
else if (q2 < zero) {
param[0] = -1;
*d1 = zero;
*d2 = zero;
x1 = zero;
}
else {
param[0] = 1;
h11 = p1/p2;
h22 = x1/y1;
T u = one + h11*h22;
T stemp = *d2/u;
*d2 = *d1/u;
*d1 = stemp;
x1 = y1*u;
}
if (*d1 != zero) {
while ((*d1 <= rgamsq) || (*d1 >= gamsq)) {
if (param[0] == 0) {
h11 = one;
h22 = one;
param[0] = -1;
}
else {
h21 = -one;
h12 = one;
param[0] = -1;
}
if (*d1 <= rgamsq) {
*d1 *= gam*gam;
x1 /= gam;
h11 /= gam;
h12 /= gam;
}
else {
*d1 /= gam*gam;
x1 *= gam;
h11 *= gam;
h12 *= gam;
}
}
}
if (*d2 != zero) {
while ((abs(*d2) <= rgamsq) || (abs(*d2) >= gamsq)) {
if (param[0] == 0) {
h11=one;
h22=one;
param[0]=-1;
}
else {
h21=-one;
h12=one;
param[0]=-1;
}
if (abs(*d2) <= rgamsq) {
*d2 *= gam*gam;
h21 /= gam;
h22 /= gam;
}
else {
*d2 /= gam*gam;
h21 *= gam;
h22 *= gam;
}
}
}
}
if (param[0] < 0) {
param[1] = h11;
param[2] = h21;
param[3] = h12;
param[4] = h22;
}
else if (param[0] == 0) {
param[2] = h21;
param[3] = h12;
}
else {
param[1] = h11;
param[4] = h22;
}
}
} // namespace blas
#endif // #ifndef BLAS_ROTMG_HH
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