blas/level1_cplx_impl.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
// SPDX-License-Identifier: MPL-2.0

#include "common.h"

struct scalar_norm1_op {
  typedef RealScalar result_type;
  inline RealScalar operator()(const Scalar &a) const { return Eigen::numext::norm1(a); }
};
namespace Eigen {
namespace internal {
template <>
struct functor_traits<scalar_norm1_op> {
  enum { Cost = 3 * NumTraits<Scalar>::AddCost, PacketAccess = 0 };
};
}  // namespace internal
}  // namespace Eigen

// computes |Re(z)| + |Im(z)| of a complex number z.
extern "C" EIGEN_BLAS_API RealScalar EIGEN_CAT(REAL_SCALAR_SUFFIX,
                                               EIGEN_CAT(cabs1, EIGEN_BLAS_FUNC_SUFFIX))(Complex *z) {
  return Eigen::numext::norm1(*z);
}

// computes the sum of magnitudes of all vector elements or, for a complex vector x, the sum
// res = |Rex1| + |Imx1| + |Rex2| + |Imx2| + ... + |Rexn| + |Imxn|, where x is a vector of order n
extern "C" RealScalar EIGEN_CAT(REAL_SCALAR_SUFFIX, EIGEN_BLAS_FUNC_NAME(asum))(EIGEN_BLAS_INT *n, RealScalar *px,
                                                                                EIGEN_BLAS_INT *incx) {
  if (*n <= 0 || *incx <= 0) return 0;

  // std::complex<T> is layout-compatible with T[2], so we can reinterpret
  // a complex vector of length n as a real vector of length 2*n and use
  // the fully vectorized cwiseAbs().sum() path.
  if (*incx == 1)
    return make_vector(px, 2 * *n).cwiseAbs().sum();
  else {
    // For non-unit stride, fall back to the scalar_norm1_op approach since
    // the real components are not contiguous across complex elements.
    Complex *x = reinterpret_cast<Complex *>(px);
    return make_vector(x, *n, std::abs(*incx)).unaryExpr<scalar_norm1_op>().sum();
  }
}

extern "C" EIGEN_BLAS_INT EIGEN_CAT(i, EIGEN_BLAS_FUNC_NAME(amax))(EIGEN_BLAS_INT *n, RealScalar *px,
                                                                   EIGEN_BLAS_INT *incx) {
  if (*n <= 0 || *incx <= 0) return 0;
  Scalar *x = reinterpret_cast<Scalar *>(px);

  Eigen::DenseIndex ret;
  if (*incx == 1)
    make_vector(x, *n).unaryExpr<scalar_norm1_op>().maxCoeff(&ret);
  else
    make_vector(x, *n, std::abs(*incx)).unaryExpr<scalar_norm1_op>().maxCoeff(&ret);
  return EIGEN_BLAS_INT(ret) + 1;
}

extern "C" EIGEN_BLAS_INT EIGEN_CAT(i, EIGEN_BLAS_FUNC_NAME(amin))(EIGEN_BLAS_INT *n, RealScalar *px,
                                                                   EIGEN_BLAS_INT *incx) {
  if (*n <= 0) return 0;
  Scalar *x = reinterpret_cast<Scalar *>(px);

  Eigen::DenseIndex ret;
  if (*incx == 1)
    make_vector(x, *n).unaryExpr<scalar_norm1_op>().minCoeff(&ret);
  else
    make_vector(x, *n, std::abs(*incx)).unaryExpr<scalar_norm1_op>().minCoeff(&ret);
  return EIGEN_BLAS_INT(ret) + 1;
}

// computes a dot product of a conjugated vector with another vector.
EIGEN_BLAS_FUNC(dotcw)
(EIGEN_BLAS_INT *n, RealScalar *px, EIGEN_BLAS_INT *incx, RealScalar *py, EIGEN_BLAS_INT *incy, RealScalar *pres) {
  //   std::cerr << "_dotc " << *n << " " << *incx << " " << *incy << "\n";
  Scalar *res = reinterpret_cast<Scalar *>(pres);

  if (*n <= 0) {
    *res = Scalar(0);
    return;
  }

  Scalar *x = reinterpret_cast<Scalar *>(px);
  Scalar *y = reinterpret_cast<Scalar *>(py);

  if (*incx == 1 && *incy == 1)
    *res = (make_vector(x, *n).dot(make_vector(y, *n)));
  else if (*incx >= 0 && *incy >= 0)
    *res = (make_vector(x, *n, *incx).dot(make_vector(y, *n, *incy)));
  else if (*incx < 0 && *incy >= 0)
    *res = (make_vector(x, *n, -*incx).reverse().dot(make_vector(y, *n, *incy)));
  else if (*incx >= 0 && *incy < 0)
    *res = (make_vector(x, *n, *incx).dot(make_vector(y, *n, -*incy).reverse()));
  else if (*incx < 0 && *incy < 0)
    *res = (make_vector(x, *n, -*incx).reverse().dot(make_vector(y, *n, -*incy).reverse()));
}

// computes a vector-vector dot product without complex conjugation.
EIGEN_BLAS_FUNC(dotuw)
(EIGEN_BLAS_INT *n, RealScalar *px, EIGEN_BLAS_INT *incx, RealScalar *py, EIGEN_BLAS_INT *incy, RealScalar *pres) {
  Scalar *res = reinterpret_cast<Scalar *>(pres);

  if (*n <= 0) {
    *res = Scalar(0);
    return;
  }

  Scalar *x = reinterpret_cast<Scalar *>(px);
  Scalar *y = reinterpret_cast<Scalar *>(py);

  if (*incx == 1 && *incy == 1)
    *res = (make_vector(x, *n).cwiseProduct(make_vector(y, *n))).sum();
  else if (*incx >= 0 && *incy >= 0)
    *res = (make_vector(x, *n, *incx).cwiseProduct(make_vector(y, *n, *incy))).sum();
  else if (*incx < 0 && *incy >= 0)
    *res = (make_vector(x, *n, -*incx).reverse().cwiseProduct(make_vector(y, *n, *incy))).sum();
  else if (*incx >= 0 && *incy < 0)
    *res = (make_vector(x, *n, *incx).cwiseProduct(make_vector(y, *n, -*incy).reverse())).sum();
  else if (*incx < 0 && *incy < 0)
    *res = (make_vector(x, *n, -*incx).reverse().cwiseProduct(make_vector(y, *n, -*incy).reverse())).sum();
}

extern "C" RealScalar EIGEN_CAT(REAL_SCALAR_SUFFIX, EIGEN_BLAS_FUNC_NAME(nrm2))(EIGEN_BLAS_INT *n, RealScalar *px,
                                                                                EIGEN_BLAS_INT *incx) {
  //   std::cerr << "__nrm2 " << *n << " " << *incx << "\n";
  if (*n <= 0) return 0;

  Scalar *x = reinterpret_cast<Scalar *>(px);

  if (*incx == 1) return make_vector(x, *n).stableNorm();

  return make_vector(x, *n, std::abs(*incx)).stableNorm();
}

EIGEN_BLAS_FUNC(EIGEN_CAT(REAL_SCALAR_SUFFIX, rot))
(EIGEN_BLAS_INT *n, RealScalar *px, EIGEN_BLAS_INT *incx, RealScalar *py, EIGEN_BLAS_INT *incy, RealScalar *pc,
 RealScalar *ps) {
  if (*n <= 0) return;

  Scalar *x = reinterpret_cast<Scalar *>(px);
  Scalar *y = reinterpret_cast<Scalar *>(py);
  RealScalar c = *pc;
  RealScalar s = *ps;

  StridedVectorType vx(make_vector(x, *n, std::abs(*incx)));
  StridedVectorType vy(make_vector(y, *n, std::abs(*incy)));

  Eigen::Reverse<StridedVectorType> rvx(vx);
  Eigen::Reverse<StridedVectorType> rvy(vy);

  // TODO implement mixed real-scalar rotations
  if (*incx < 0 && *incy > 0)
    Eigen::internal::apply_rotation_in_the_plane(rvx, vy, Eigen::JacobiRotation<Scalar>(c, s));
  else if (*incx > 0 && *incy < 0)
    Eigen::internal::apply_rotation_in_the_plane(vx, rvy, Eigen::JacobiRotation<Scalar>(c, s));
  else
    Eigen::internal::apply_rotation_in_the_plane(vx, vy, Eigen::JacobiRotation<Scalar>(c, s));
}

EIGEN_BLAS_FUNC(EIGEN_CAT(REAL_SCALAR_SUFFIX, scal))
(EIGEN_BLAS_INT *n, RealScalar *palpha, RealScalar *px, EIGEN_BLAS_INT *incx) {
  if (*n <= 0 || *incx <= 0) return;

  Scalar *x = reinterpret_cast<Scalar *>(px);
  RealScalar alpha = *palpha;

  //   std::cerr << "__scal " << *n << " " << alpha << " " << *incx << "\n";

  if (*incx == 1)
    make_vector(x, *n) *= alpha;
  else
    make_vector(x, *n, std::abs(*incx)) *= alpha;
}