Skip to content
GitLab
Commit be306136 authored by Martin Reinecke's avatar Martin Reinecke
Browse files

remove real-only methods

parent c32c14c7
Hide whitespace changes
Inline Side-by-side
gridder_cxx.h
View file @ be306136
......@@ -31,35 +31,32 @@
#include "pocketfft_hdronly.h"
#include <array>
template<typename T, size_t ndim, bool c_contiguous> class mav
namespace gridder {
using namespace std;
template<typename T, size_t ndim> class mav
{
static_assert((ndim>0) && (ndim<3), "only supports 1D and 2D arrays");
private:
T *d;
std::array<size_t, ndim> shp;
std::array<ptrdiff_t, ndim> str;
array<size_t, ndim> shp;
array<ptrdiff_t, ndim> str;
public:
mav(T *d_, const std::array<size_t,ndim> &shp_,
const std::array<ptrdiff_t,ndim> &str_)
: d(d_), shp(shp_), str(str_)
{ static_assert(!c_contiguous, "this type does not accept strides"); }
mav(T *d_, const std::array<size_t,ndim> &shp_)
mav(T *d_, const array<size_t,ndim> &shp_,
const array<ptrdiff_t,ndim> &str_)
: d(d_), shp(shp_), str(str_) {}
mav(T *d_, const array<size_t,ndim> &shp_)
: d(d_), shp(shp_)
{
static_assert(c_contiguous, "this type requires strides");
str[ndim-1]=1;
for (size_t d=2; d<=ndim; ++d)
str[ndim-d] = str[ndim-d+1]*shp[ndim-d+1];
}
operator mav<const T, ndim, true>() const
{
static_assert(c_contiguous);
return mav<const T, ndim, true>(d,shp);
}
operator mav<const T, ndim, false>() const
{ return mav<const T, ndim, false>(d,shp, str); }
operator mav<const T, ndim>() const
{ return mav<const T, ndim>(d,shp,str); }
T &operator[](size_t i)
{ return operator()(i); }
const T &operator[](size_t i) const
......@@ -67,25 +64,25 @@ template<typename T, size_t ndim, bool c_contiguous> class mav
T &operator()(size_t i)
{
static_assert(ndim==1, "ndim must be 1");
return c_contiguous ? d[i] : d[str[0]*i];
return d[str[0]*i];
}
const T &operator()(size_t i) const
{
static_assert(ndim==1, "ndim must be 1");
return c_contiguous ? d[i] : d[str[0]*i];
return d[str[0]*i];
}
T &operator()(size_t i, size_t j)
{
static_assert(ndim==2, "ndim must be 2");
return c_contiguous ? d[str[0]*i + j] : d[str[0]*i + str[1]*j];
return d[str[0]*i + str[1]*j];
}
const T &operator()(size_t i, size_t j) const
{
static_assert(ndim==2, "ndim must be 2");
return c_contiguous ? d[str[0]*i + j] : d[str[0]*i + str[1]*j];
return d[str[0]*i + str[1]*j];
}
size_t shape(size_t i) const { return shp[i]; }
const std::array<size_t,ndim> &shape() const { return shp; }
const array<size_t,ndim> &shape() const { return shp; }
size_t size() const
{
size_t res=1;
......@@ -94,20 +91,11 @@ template<typename T, size_t ndim, bool c_contiguous> class mav
}
size_t stride(size_t i) const { return str[i]; }
T *data()
{
// static_assert(c_contiguous, "type is not C contiguous");
return d;
}
{ return d; }
const T *data() const
{
// static_assert(c_contiguous, "type is not C contiguous");
return d;
}
{ return d; }
};
template<typename T, size_t ndim> using cmav = mav<T,ndim,true>;
template<typename T, size_t ndim> using smav = mav<T,ndim,false>;
//
// basic utilities
//
......@@ -115,11 +103,11 @@ template<typename T, size_t ndim> using smav = mav<T,ndim,false>;
void myassert(bool cond, const char *msg)
{
if (cond) return;
throw std::runtime_error(msg);
throw runtime_error(msg);
}
template<size_t ndim> void checkShape
(const std::array<size_t, ndim> &shp1, const std::array<size_t, ndim> &shp2)
(const array<size_t, ndim> &shp1, const array<size_t, ndim> &shp2)
{
for (size_t i=0; i<ndim; ++i)
myassert(shp1[i]==shp2[i], "shape mismatch");
......@@ -138,27 +126,12 @@ template<typename T> inline T fmodulo (T v1, T v2)
static size_t nthreads = 1;
constexpr auto set_nthreads_DS = R"""(
Specifies the number of threads to be used by the module
Parameters
==========
nthreads: int
the number of threads to be used. Must be >=1.
)""";
void set_nthreads(size_t nthreads_)
{
myassert(nthreads_>=1, "nthreads must be >= 1");
nthreads = nthreads_;
}
constexpr auto get_nthreads_DS = R"""(
Returns the number of threads used by the module
Returns
=======
int : the number of threads used by the module
)""";
size_t get_nthreads()
{ return nthreads; }
......@@ -169,7 +142,7 @@ size_t get_nthreads()
static inline double one_minus_x2 (double x)
{ return (fabs(x)>0.1) ? (1.+x)*(1.-x) : 1.-x*x; }
void legendre_prep(int n, std::vector<double> &x, std::vector<double> &w)
void legendre_prep(int n, vector<double> &x, vector<double> &w)
{
constexpr double pi = 3.141592653589793238462643383279502884197;
constexpr double eps = 3e-14;
......@@ -229,7 +202,7 @@ void legendre_prep(int n, std::vector<double> &x, std::vector<double> &w)
size_t get_supp(double epsilon)
{
static const std::vector<double> maxmaperr { 1e8, 0.32, 0.021, 6.2e-4,
static const vector<double> maxmaperr { 1e8, 0.32, 0.021, 6.2e-4,
1.08e-5, 1.25e-7, 8.25e-10, 5.70e-12, 1.22e-13, 2.48e-15, 4.82e-17,
6.74e-19, 5.41e-21, 4.41e-23, 7.88e-25, 3.9e-26 };
......@@ -237,70 +210,7 @@ size_t get_supp(double epsilon)
for (size_t i=1; i<maxmaperr.size(); ++i)
if (epssq>maxmaperr[i]) return i;
throw std::runtime_error("requested epsilon too small - minimum is 2e-13");
}
template<typename T> void complex2hartley
(const smav<const std::complex<T>, 2> &grid, smav<T,2> &grid2)
{
myassert(grid.shape()==grid2.shape(), "shape mismatch");
size_t nu=grid.shape(0), nv=grid.shape(1);
#pragma omp parallel for num_threads(nthreads)
for (size_t u=0; u<nu; ++u)
{
size_t xu = (u==0) ? 0 : nu-u;
for (size_t v=0; v<nv; ++v)
{
size_t xv = (v==0) ? 0 : nv-v;
grid2(u,v) += T(0.5)*(grid( u, v).real()+grid( u, v).imag()+
grid(xu,xv).real()-grid(xu,xv).imag());
}
}
}
template<typename T> void hartley2complex
(const smav<const T,2> &grid, smav<std::complex<T>,2> &grid2)
{
myassert(grid.shape()==grid2.shape(), "shape mismatch");
size_t nu=grid.shape(0), nv=grid.shape(1);
#pragma omp parallel for num_threads(nthreads)
for (size_t u=0; u<nu; ++u)
{
size_t xu = (u==0) ? 0 : nu-u;
for (size_t v=0; v<nv; ++v)
{
size_t xv = (v==0) ? 0 : nv-v;
T v1 = T(0.5)*grid( u, v);
T v2 = T(0.5)*grid(xu,xv);
grid2(u,v) = std::complex<T>(v1+v2, v1-v2);
}
}
}
template<typename T> void hartley2_2D(const smav<const T,2> &in, smav<T,2> &out)
{
myassert(in.shape()==out.shape(), "shape mismatch");
size_t nu=in.shape(0), nv=in.shape(1), sz=sizeof(T);
pocketfft::stride_t str{ptrdiff_t(sz*nv), ptrdiff_t(sz)};
auto d_i = in.data();
auto ptmp = out.data();
pocketfft::r2r_separable_hartley({nu, nv}, str, str, {0,1}, d_i, ptmp, T(1),
nthreads);
#pragma omp parallel for num_threads(nthreads)
for(size_t i=1; i<(nu+1)/2; ++i)
for(size_t j=1; j<(nv+1)/2; ++j)
{
T a = ptmp[i*nv+j];
T b = ptmp[(nu-i)*nv+j];
T c = ptmp[i*nv+nv-j];
T d = ptmp[(nu-i)*nv+nv-j];
ptmp[i*nv+j] = T(0.5)*(a+b+c-d);
ptmp[(nu-i)*nv+j] = T(0.5)*(a+b+d-c);
ptmp[i*nv+nv-j] = T(0.5)*(a+c+d-b);
ptmp[(nu-i)*nv+nv-j] = T(0.5)*(b+c+d-a);
}
throw runtime_error("requested epsilon too small - minimum is 2e-13");
}
template<typename T> class EC_Kernel
......@@ -322,7 +232,7 @@ template<typename T> class EC_Kernel_with_correction: public EC_Kernel<T>
protected:
static constexpr T pi = T(3.141592653589793238462643383279502884197L);
int p;
std::vector<T> x, wgt, psi;
vector<T> x, wgt, psi;
using EC_Kernel<T>::supp;
public:
......@@ -347,10 +257,10 @@ template<typename T> class EC_Kernel_with_correction: public EC_Kernel<T>
};
/* Compute correction factors for the ES gridding kernel
This implementation follows eqs. (3.8) to (3.10) of Barnett et al. 2018 */
std::vector<double> correction_factors (size_t n, size_t nval, size_t supp)
vector<double> correction_factors (size_t n, size_t nval, size_t supp)
{
EC_Kernel_with_correction<double> kernel(supp);
std::vector<double> res(nval);
vector<double> res(nval);
double xn = 1./n;
#pragma omp parallel for schedule(static) num_threads(nthreads)
for (size_t k=0; k<nval; ++k)
......@@ -370,12 +280,12 @@ template<typename T> struct UVW
template<typename T> class Baselines
{
protected:
std::vector<UVW<T>> coord;
std::vector<T> f_over_c;
vector<UVW<T>> coord;
vector<T> f_over_c;
size_t nrows, nchan;
public:
Baselines(const smav<const T,2> &coord_, const smav<const T,1> &freq)
Baselines(const mav<const T,2> &coord_, const mav<const T,1> &freq)
{
constexpr double speedOfLight = 299792458.;
myassert(coord_.shape(1)==3, "dimension mismatch");
......@@ -401,7 +311,7 @@ template<typename T> class Baselines
size_t Nrows() const { return nrows; }
size_t Nchannels() const { return nchan; }
void effectiveUVW(const smav<const uint32_t,1> &idx, smav<T,2> &res) const
void effectiveUVW(const mav<const uint32_t,1> &idx, mav<T,2> &res) const
{
size_t nvis = idx.shape(0);
myassert(res.shape(0)==nvis, "shape mismatch");
......@@ -415,8 +325,8 @@ template<typename T> class Baselines
}
}
template<typename T2> void ms2vis(const smav<const T2,2> &ms,
const smav<const uint32_t,1> &idx, smav<T2,1> &vis) const
template<typename T2> void ms2vis(const mav<const T2,2> &ms,
const mav<const uint32_t,1> &idx, mav<T2,1> &vis) const
{
myassert(ms.shape(0)==nrows, "shape mismatch");
myassert(ms.shape(1)==nchan, "shape mismatch");
......@@ -432,8 +342,8 @@ template<typename T> class Baselines
}
}
template<typename T2> void vis2ms(const smav<const T2,1> &vis,
const smav<const uint32_t,1> &idx, smav<T2,2> &ms) const
template<typename T2> void vis2ms(const mav<const T2,1> &vis,
const mav<const uint32_t,1> &idx, mav<T2,2> &ms) const
{
size_t nvis = vis.shape(0);
myassert(idx.shape(0)==nvis, "shape mismatch");
......@@ -457,11 +367,10 @@ template<typename T> class GridderConfig
double eps, psx, psy;
size_t supp, nsafe, nu, nv;
T beta;
std::vector<T> cfu, cfv;
vector<T> cfu, cfv;
std::complex<T> wscreen(double x, double y, double w, bool adjoint) const
complex<T> wscreen(double x, double y, double w, bool adjoint) const
{
using namespace std;
constexpr double pi = 3.141592653589793238462643383279502884197;
#if 1
double eps = sqrt(x+y);
......@@ -482,7 +391,7 @@ template<typename T> class GridderConfig
: nx_dirty(nxdirty), ny_dirty(nydirty), eps(epsilon),
psx(pixsize_x), psy(pixsize_y),
supp(get_supp(epsilon)), nsafe((supp+1)/2),
nu(std::max(2*nsafe,2*nx_dirty)), nv(std::max(2*nsafe,2*ny_dirty)),
nu(max(2*nsafe,2*nx_dirty)), nv(max(2*nsafe,2*ny_dirty)),
beta(2.3*supp),
cfu(nx_dirty), cfv(ny_dirty)
{
......@@ -514,78 +423,30 @@ template<typename T> class GridderConfig
size_t Nsafe() const { return nsafe; }
T Beta() const { return beta; }
void grid2dirty(const smav<const T,2> &grid, smav<T,2> &grid2) const
{
checkShape(grid.shape(), {nu,nv});
std::vector<T> tmpdat(nu*nv);
auto tmp=smav<T,2>(tmpdat.data(),{nu,nv},{nv,1});
hartley2_2D<T>(grid, tmp);
checkShape(grid2.shape(), {nx_dirty, ny_dirty});
for (size_t i=0; i<nx_dirty; ++i)
for (size_t j=0; j<ny_dirty; ++j)
{
size_t i2 = nu-nx_dirty/2+i;
if (i2>=nu) i2-=nu;
size_t j2 = nv-ny_dirty/2+j;
if (j2>=nv) j2-=nv;
grid2(i,j) = tmp(i2,j2)*cfu[i]*cfv[j];
}
}
#if 0
pyarr_c<T> apply_taper(const pyarr_c<T> &img, bool divide) const
{
checkArray(img, "img", {nx_dirty, ny_dirty});
auto pin = img.data();
auto res = makeArray<T>({nx_dirty, ny_dirty});
auto pout = res.mutable_data();
void apply_taper(const mav<const T,2> &img, mav<T,2> &img2, bool divide) const
{
py::gil_scoped_release release;
checkShape(img.shape(), {nx_dirty, ny_dirty});
checkShape(img2.shape(), {nx_dirty, ny_dirty});
if (divide)
for (size_t i=0; i<nx_dirty; ++i)
for (size_t j=0; j<ny_dirty; ++j)
pout[ny_dirty*i + j] = pin[ny_dirty*i + j]/(cfu[i]*cfv[j]);
img2(i,j) = img(i,j)/(cfu[i]*cfv[j]);
else
for (size_t i=0; i<nx_dirty; ++i)
for (size_t j=0; j<ny_dirty; ++j)
pout[ny_dirty*i + j] = pin[ny_dirty*i + j]*cfu[i]*cfv[j];
}
return res;
}
pyarr_c<complex<T>> grid2dirty_c(const pyarr_c<complex<T>> &grid) const
{
checkArray(grid, "grid", {nu, nv});
auto tmp = makeArray<complex<T>>({nu, nv});
auto ptmp = tmp.mutable_data();
pocketfft::c2c({nu,nv},{grid.strides(0),grid.strides(1)},
{tmp.strides(0), tmp.strides(1)}, {0,1}, pocketfft::BACKWARD,
grid.data(), tmp.mutable_data(), T(1), nthreads);
auto res = makeArray<complex<T>>({nx_dirty, ny_dirty});
auto pout = res.mutable_data();
{
py::gil_scoped_release release;
for (size_t i=0; i<nx_dirty; ++i)
for (size_t j=0; j<ny_dirty; ++j)
{
size_t i2 = nu-nx_dirty/2+i;
if (i2>=nu) i2-=nu;
size_t j2 = nv-ny_dirty/2+j;
if (j2>=nv) j2-=nv;
pout[ny_dirty*i + j] = ptmp[nv*i2+j2]*cfu[i]*cfv[j];
}
}
return res;
img2(i,j) = img(i,j)*cfu[i]*cfv[j];
}
pyarr_c<T> dirty2grid(const pyarr_c<T> &dirty) const
{
checkArray(dirty, "dirty", {nx_dirty, ny_dirty});
auto pdirty = dirty.data();
auto tmp = makeArray<T>({nu, nv});
auto ptmp = tmp.mutable_data();
void grid2dirty_c(const mav<const complex<T>,2> &grid, mav<complex<T>,2> &dirty) const
{
py::gil_scoped_release release;
for (size_t i=0; i<nu*nv; ++i)
ptmp[i] = 0.;
checkShape(grid.shape(), {nu,nv});
checkShape(dirty.shape(), {nx_dirty,ny_dirty});
vector<complex<T>> tmpdat(nu*nv);
auto tmp=mav<complex<T>,2>(tmpdat.data(),{nu,nv},{nv,1});
constexpr auto sc = sizeof(complex<T>);
pocketfft::c2c({nu,nv},{grid.stride(0)*sc,grid.stride(1)*sc},
{tmp.stride(0)*sc, tmp.stride(1)*sc}, {0,1}, pocketfft::BACKWARD,
grid.data(), tmp.data(), T(1), nthreads);
for (size_t i=0; i<nx_dirty; ++i)
for (size_t j=0; j<ny_dirty; ++j)
{
......@@ -593,12 +454,10 @@ template<typename T> class GridderConfig
if (i2>=nu) i2-=nu;
size_t j2 = nv-ny_dirty/2+j;
if (j2>=nv) j2-=nv;
ptmp[nv*i2+j2] = pdirty[ny_dirty*i + j]*cfu[i]*cfv[j];
dirty(i,j) = tmp(i2,j2)*cfu[i]*cfv[j];
}
}
hartley2_2D<T>(tmp, tmp);
return tmp;
}
#if 0
pyarr_c<complex<T>> dirty2grid_c(const pyarr_c<complex<T>> &dirty) const
{
checkArray(dirty, "dirty", {nx_dirty, ny_dirty});
......@@ -677,7 +536,7 @@ template<typename T> class GridderConfig
constexpr int logsquare=4;
template<typename T, typename T2=std::complex<T>> class Helper
template<typename T, typename T2=complex<T>> class Helper
{
private:
const GridderConfig<T> &gconf;
......@@ -689,7 +548,7 @@ template<typename T, typename T2=std::complex<T>> class Helper
int iu0, iv0; // start index of the current visibility
int bu0, bv0; // start index of the current buffer
std::vector<T2> rbuf, wbuf;
vector<T2> rbuf, wbuf;
void dump() const
{
......@@ -731,7 +590,7 @@ template<typename T, typename T2=std::complex<T>> class Helper
public:
const T2 *p0r;
T2 *p0w;
std::vector<T> kernel;
vector<T> kernel;
Helper(const GridderConfig<T> &gconf_, const T2 *grid_r_, T2 *grid_w_)
: gconf(gconf_), nu(gconf.Nu()), nv(gconf.Nv()), nsafe(gconf.Nsafe()),
......@@ -775,4 +634,6 @@ template<typename T, typename T2=std::complex<T>> class Helper
}
};
} // namespace gridder
#endif
nifty_gridder.cc
View file @ be306136
......@@ -25,6 +25,7 @@
#include "gridder_cxx.h"
using namespace std;
using namespace gridder;
namespace py = pybind11;
......@@ -39,15 +40,27 @@ auto None = py::none();
//
// Start of real gridder functionality
//
constexpr auto set_nthreads_DS = R"""(
Specifies the number of threads to be used by the module
Parameters
==========
nthreads: int
the number of threads to be used. Must be >=1.
)""";
constexpr auto get_nthreads_DS = R"""(
Returns the number of threads used by the module
Returns
=======
int : the number of threads used by the module
)""";
template<typename T>
using pyarr = py::array_t<T>;
// The "_c" suffix here stands for "C memory order, contiguous"
template<typename T>
using pyarr_c = py::array_t<T, py::array::c_style | py::array::forcecast>;
template<typename T> pyarr_c<T> makeArray(const vector<size_t> &shape)
{ return pyarr_c<T>(shape); }
template<typename T> pyarr<T> makeArray(const vector<size_t> &shape)
{ return pyarr<T>(shape); }
void checkArray(const py::array &arr, const char *aname,
const vector<size_t> &shape)
......@@ -94,7 +107,7 @@ template<typename T> pyarr<T> providePotentialArray(const py::object &in,
return tmp_;
}
template<typename T> pyarr_c<T> provideCArray(py::object &in,
template<typename T> pyarr<T> provideCArray(py::object &in,
const vector<size_t> &shape)
{
if (in.is_none())
......@@ -106,19 +119,12 @@ template<typename T> pyarr_c<T> provideCArray(py::object &in,
tmp[i] = T(0);
return tmp_;
}
auto tmp_ = in.cast<pyarr_c<T>>();
auto tmp_ = in.cast<pyarr<T>>();
checkArray(tmp_, "temporary", shape);
return tmp_;
}
template<size_t ndim, typename T> cmav<T,ndim> make_cmav(pyarr_c<T> &in)
{
myassert(ndim==in.ndim(), "dimension mismatch");
array<size_t,ndim> dims;
for (size_t i=0; i<ndim; ++i) dims[i]=in.shape(i);
return cmav<T, ndim>(in.mutable_data(),dims);
}
template<size_t ndim, typename T> smav<T,ndim> make_smav(pyarr<T> &in)
template<size_t ndim, typename T> mav<T,ndim> make_mav(pyarr<T> &in)
{
myassert(ndim==in.ndim(), "dimension mismatch");
array<size_t,ndim> dims;
......@@ -129,9 +135,9 @@ template<size_t ndim, typename T> smav<T,ndim> make_smav(pyarr<T> &in)
str[i]=in.strides(i)/sizeof(T);
myassert(str[i]*ptrdiff_t(sizeof(T))==in.strides(i), "weird strides");
}
return smav<T, ndim>(in.mutable_data(),dims,str);
return mav<T, ndim>(in.mutable_data(),dims,str);
}
template<size_t ndim, typename T> smav<T,ndim> make_smav(pyarr_c<T> &in)
template<size_t ndim, typename T> mav<const T,ndim> make_const_mav(const pyarr<T> &in)
{
myassert(ndim==in.ndim(), "dimension mismatch");
array<size_t,ndim> dims;
......@@ -142,77 +148,7 @@ template<size_t ndim, typename T> smav<T,ndim> make_smav(pyarr_c<T> &in)
str[i]=in.strides(i)/sizeof(T);
myassert(str[i]*ptrdiff_t(sizeof(T))==in.strides(i), "weird strides");
}
return smav<T, ndim>(in.mutable_data(),dims,str);
}
template<size_t ndim, typename T> cmav<const T,ndim> make_const_cmav(const pyarr_c<T> &in)
{
myassert(ndim==in.ndim(), "dimension mismatch");
array<size_t,ndim> dims;
for (size_t i=0; i<ndim; ++i) dims[i]=in.shape(i);
return cmav<const T, ndim>(in.data(),dims);
}
template<size_t ndim, typename T> smav<const T,ndim> make_const_smav(const pyarr<T> &in)
{
myassert(ndim==in.ndim(), "dimension mismatch");
array<size_t,ndim> dims;
array<ptrdiff_t,ndim> str;
for (size_t i=0; i<ndim; ++i)
{
dims[i]=in.shape(i);
str[i]=in.strides(i)/sizeof(T);
myassert(str[i]*ptrdiff_t(sizeof(T))==in.strides(i), "weird strides");
}
return smav<const T, ndim>(in.data(),dims,str);
}
template<size_t ndim, typename T> smav<const T,ndim> make_const_smav(const pyarr_c<T> &in)
{
myassert(ndim==in.ndim(), "dimension mismatch");
array<size_t,ndim> dims;
array<ptrdiff_t,ndim> str;
for (size_t i=0; i<ndim; ++i)
{
dims[i]=in.shape(i);
str[i]=in.strides(i)/sizeof(T);
myassert(str[i]*ptrdiff_t(sizeof(T))==in.strides(i), "weird strides");
}
return smav<const T, ndim>(in.data(),dims,str);
}
template<typename T> pyarr_c<T> complex2hartley
(const pyarr_c<complex<T>> &grid_, py::object &grid_in)
{
auto grid = make_const_smav<2>(grid_);
size_t nu=grid.shape(0), nv=grid.shape(1);
auto res = provideCArray<T>(grid_in, {nu, nv});
auto grid2 = make_smav<2>(res);
{
py::gil_scoped_release release;
complex2hartley(grid, grid2);
}
return res;
}
template<typename T> pyarr_c<complex<T>> hartley2complex
(const pyarr_c<T> &grid_)
{
auto grid = make_const_smav<2>(grid_);
size_t nu=grid.shape(0), nv=grid.shape(1);
auto res = makeArray<complex<T>>({nu, nv});
auto grid2 = make_smav<2>(res);
{