diff --git a/README.md b/README.md index 2bdb864..2d67ffd 100644 --- a/README.md +++ b/README.md @@ -6,11 +6,16 @@ [![Playground](https://img.shields.io/badge/playground-try%20it%20in%20your%20browser-013243)](https://go-ndarray.github.io/playground/) [![License](https://img.shields.io/badge/license-BSD--3--Clause-blue)](LICENSE) [![Go](https://img.shields.io/badge/go-1.27.2%2B-00ADD8)](https://go.dev/dl/) -[![Status](https://img.shields.io/badge/status-numpy%20parity%20(float64)-9a6700)](docs/plan-ndarray.md) +[![Status](https://img.shields.io/badge/status-numpy%20parity%20(13%20dtypes)-9a6700)](docs/plan-ndarray.md) **A pure-Go (CGO=0) NumPy-style N-dimensional array library.** Row-major (C-order) strided arrays with: +- **Thirteen dtypes** — bool, int8…int64, uint8…uint64, float32/float64, + complex64/complex128, chosen at run time with **NumPy 2 promotion** (`AsType`, + `ZerosOf`, `FromSlice`, typed access with `Data[T]`/`Item[T]`, weak Go + scalars with `Scalar`). Float64 is the default and the SIMD-accelerated one + ([docs/design-dtypes.md](docs/design-dtypes.md)). - **Creation** — `New`/`Zeros`/`Ones`/`Full`/`FromData`/`Arange`/`Linspace`/ `Eye`/`Identity`. - **Shape & views** — `Reshape` (with `-1` inference), `Ravel`/`Flatten`, @@ -18,8 +23,9 @@ returning strided views that share data. - **Elementwise** — `Add`/`Sub`/`Mul`/`Div` (+ scalar) with full **NumPy broadcasting**, `Map`/`Neg`/`Abs`, math **ufuncs** (`Sqrt`/`Exp`/`Log`/`Sin`/ - `Cos`/…), and broadcasting **comparisons** (`Greater`/`Equal`/… as 0/1 masks) - plus `Maximum`/`Minimum`. + `Cos`/…), broadcasting **comparisons** (`Greater`/`Equal`/… returning Bool + masks), `Maximum`/`Minimum`, `Logical*`, and the complex parts + `Real`/`Imag`/`Conj`/`Angle`. - **Reductions** — whole-array (`Sum`/`Prod`/`Max`/`Min`/`Mean`), per-axis (`SumAxis`/… with `keepdims`), index reductions (`ArgMax`/`ArgMin` flat and per-axis), cumulative scans (`CumSum`/`CumProd`), `Clip`, and `Where`. @@ -27,6 +33,9 @@ `MaskSelect` (`a[mask]`), `Nonzero` (`flatnonzero`), and `Take`. - **Manipulation** — `Concatenate`/`Stack`/`VStack`/`HStack`. - **Linear algebra** — `MatMul`/`Dot`/`Inner`/`Outer`. +- **Fourier transforms** — package [`fft`](fft) is `numpy.fft` on arrays + (`FFT`/`RFFT`/`FFT2`/`FFTN`/… with `n`/`s`, `axes` and `norm`, single + precision kept), on [go-fft](https://github.com/go-fft/fft). - **Memory reuse** — `Workspace`, an arena for loops: bind the inputs with `ws.Use`, compute as usual, `ws.Reset()` at the end of each pass. Results stop costing the garbage collector anything (see below). @@ -108,7 +117,7 @@ and `Max` by 92–96% ([docs/perf.md](docs/perf.md), *SIMD coverage*). It is a **standalone, reusable** module and the cgo-free ndarray backend behind [go-embedded-ruby](https://github.com/go-embedded-ruby/ruby)'s `NDArray` class. -> ⚠️ **Status: float64 NumPy parity for the core surface.** Creation, +> ⚠️ **Status: NumPy parity for the core surface, in 13 dtypes.** Creation, > slicing/views, broadcasting elementwise + ufuncs, reductions (incl. > arg/cumulative/clip/where), manipulation, linear algebra and `Workspace` are > complete, **100%-covered**, and differentially checked against NumPy. CI runs @@ -117,7 +126,7 @@ and `Max` by 92–96% ([docs/perf.md](docs/perf.md), *SIMD coverage*). It is a > pair Go supports; v0.1.0 and v0.2.0 were also run on real amd64, arm64, > ppc64le, riscv64 and loong64 hardware, v0.3.0 on real amd64, arm64, ppc64le > and loong64. See **[docs/plan-ndarray.md](docs/plan-ndarray.md)** -> for the roadmap (more dtypes, more SIMD targets). +> for the roadmap (SIMD for float32, linear algebra decompositions). ## Why this module? @@ -186,8 +195,17 @@ row1, _ := m.Slice(ndarray.A(1)) // m[1]: unindexed axes are // ufuncs and masks roots := m.Sqrt() -two, _ := ndarray.Full(2, 1) -mask, _ := m.Greater(two) // broadcast 0/1 mask of m > 2 +mask, _ := m.Greater(ndarray.Scalar(2)) // Bool mask of m > 2 +big, _ := m.MaskSelect(mask) // m[m > 2] -> [3 4 5] + +// dtypes, with NumPy's promotion +i8, _ := ndarray.FromSlice([]int8{1, 2, 3}, 3) +x, _ := i8.Add(ndarray.Scalar(1)) // int8: a Go int is weak +y, _ := i8.Div(i8) // float64: true division +z := i8.AsType(ndarray.Complex128) // complex128 + +// numpy.fft +spec, _ := fft.RFFT(row) // complex128, 2 bins // linear algebra b, _ := ndarray.Arange(0, 6, 1) diff --git a/fft/fft.go b/fft/fft.go new file mode 100644 index 0000000..ed6cbb7 --- /dev/null +++ b/fft/fft.go @@ -0,0 +1,502 @@ +// Package fft is numpy.fft for ndarray arrays: the discrete Fourier +// transforms of go-fft (github.com/go-fft/fft), applied along any axes of an +// N-dimensional array, with numpy's n/s, axes and norm arguments and its +// dtypes. +// +// Every transform takes an array of any dtype. As in NumPy 2, float32 and +// complex64 inputs are transformed in single precision and give complex64 +// (or float32 for the real inverses); every other dtype is transformed in +// double precision. Problems NumPy reports with an exception — an axis out of +// range or repeated, a length below one — are errors here. +package fft + +import ( + "errors" + "fmt" + + gofft "github.com/go-fft/fft" + "github.com/go-ndarray/ndarray" +) + +// Norm selects how a forward/inverse pair is scaled, as numpy.fft's norm +// argument does. The zero value, Backward, is numpy's default: the forward +// transform is unscaled and the inverse divides by n. +type Norm = gofft.Norm + +// The three scalings. +const ( + Backward = gofft.NormBackward + Ortho = gofft.NormOrtho + Forward = gofft.NormForward +) + +// ErrArgs is returned for arguments numpy.fft rejects: an axis out of range, +// a length below one, S and Axes of different lengths, or a complex input to +// a transform of real signals. An axis listed twice is accepted, as NumPy +// accepts it: the transform runs along it twice. +var ErrArgs = errors.New("fft: invalid arguments") + +// Options carries numpy.fft's optional arguments. Its zero value is numpy's +// defaults, so FFTWith(a, Options{}) is FFT(a). +type Options struct { + // S is numpy's n (for the 1-D transforms, one entry) or s (for the + // others): the length of each transformed axis. The input is truncated or + // zero-padded to it along that axis. For the real inverses (IRFFT, + // IRFFTN, HFFT) it is the length of the real output along the last + // transformed axis. nil keeps the input's lengths (and, for the real + // inverses, 2*(m-1) along the last axis, m being its number of bins). + S []int + + // Axes are the axes to transform; negative values count from the end. + // nil means numpy's default: the last axis for the 1-D transforms, the + // last two for the 2-D ones, all of them for the N-D ones (or the last + // len(S) when S is set). + Axes []int + + // Norm scales the result. + Norm Norm +} + +// kind is the family of a transform. +type kind uint8 + +const ( + c2c kind = iota // complex to complex + r2c // real to half complex + c2r // half complex to real + herm // hfft: half Hermitian to real, scaled as a forward transform + iherm // ihfft: real to half Hermitian, scaled as an inverse transform +) + +// FFT is numpy.fft.fft: the 1-D discrete Fourier transform along the last +// axis. +func FFT(a *ndarray.Array) (*ndarray.Array, error) { return FFTWith(a, Options{}) } + +// FFTWith is numpy.fft.fft(a, n, axis, norm). +func FFTWith(a *ndarray.Array, o Options) (*ndarray.Array, error) { + return run(a, o, c2c, false, oneD) +} + +// IFFT is numpy.fft.ifft: the inverse of FFT. +func IFFT(a *ndarray.Array) (*ndarray.Array, error) { return IFFTWith(a, Options{}) } + +// IFFTWith is numpy.fft.ifft(a, n, axis, norm). +func IFFTWith(a *ndarray.Array, o Options) (*ndarray.Array, error) { + return run(a, o, c2c, true, oneD) +} + +// RFFT is numpy.fft.rfft: the transform of a real signal along the last +// axis, keeping the n/2+1 non-negative frequencies. A complex input is an +// error, as in NumPy 2. +func RFFT(a *ndarray.Array) (*ndarray.Array, error) { return RFFTWith(a, Options{}) } + +// RFFTWith is numpy.fft.rfft(a, n, axis, norm). +func RFFTWith(a *ndarray.Array, o Options) (*ndarray.Array, error) { + return run(a, o, r2c, false, oneD) +} + +// IRFFT is numpy.fft.irfft: the inverse of RFFT, a real signal of length +// 2*(m-1) for m bins unless Options.S says otherwise. +func IRFFT(a *ndarray.Array) (*ndarray.Array, error) { return IRFFTWith(a, Options{}) } + +// IRFFTWith is numpy.fft.irfft(a, n, axis, norm). +func IRFFTWith(a *ndarray.Array, o Options) (*ndarray.Array, error) { + return run(a, o, c2r, true, oneD) +} + +// HFFT is numpy.fft.hfft: the transform of a signal with Hermitian symmetry, +// given by its first half, which is real. +func HFFT(a *ndarray.Array) (*ndarray.Array, error) { return HFFTWith(a, Options{}) } + +// HFFTWith is numpy.fft.hfft(a, n, axis, norm). +func HFFTWith(a *ndarray.Array, o Options) (*ndarray.Array, error) { + return run(a, o, herm, false, oneD) +} + +// IHFFT is numpy.fft.ihfft: the inverse of HFFT. +func IHFFT(a *ndarray.Array) (*ndarray.Array, error) { return IHFFTWith(a, Options{}) } + +// IHFFTWith is numpy.fft.ihfft(a, n, axis, norm). +func IHFFTWith(a *ndarray.Array, o Options) (*ndarray.Array, error) { + return run(a, o, iherm, true, oneD) +} + +// FFT2 is numpy.fft.fft2: the transform over the last two axes. +func FFT2(a *ndarray.Array) (*ndarray.Array, error) { return FFT2With(a, Options{}) } + +// FFT2With is numpy.fft.fft2(a, s, axes, norm). +func FFT2With(a *ndarray.Array, o Options) (*ndarray.Array, error) { + return run(a, o, c2c, false, twoD) +} + +// IFFT2 is numpy.fft.ifft2. +func IFFT2(a *ndarray.Array) (*ndarray.Array, error) { return IFFT2With(a, Options{}) } + +// IFFT2With is numpy.fft.ifft2(a, s, axes, norm). +func IFFT2With(a *ndarray.Array, o Options) (*ndarray.Array, error) { + return run(a, o, c2c, true, twoD) +} + +// RFFT2 is numpy.fft.rfft2. +func RFFT2(a *ndarray.Array) (*ndarray.Array, error) { return RFFT2With(a, Options{}) } + +// RFFT2With is numpy.fft.rfft2(a, s, axes, norm). +func RFFT2With(a *ndarray.Array, o Options) (*ndarray.Array, error) { + return run(a, o, r2c, false, twoD) +} + +// IRFFT2 is numpy.fft.irfft2. +func IRFFT2(a *ndarray.Array) (*ndarray.Array, error) { return IRFFT2With(a, Options{}) } + +// IRFFT2With is numpy.fft.irfft2(a, s, axes, norm). +func IRFFT2With(a *ndarray.Array, o Options) (*ndarray.Array, error) { + return run(a, o, c2r, true, twoD) +} + +// FFTN is numpy.fft.fftn: the transform over every axis. +func FFTN(a *ndarray.Array) (*ndarray.Array, error) { return FFTNWith(a, Options{}) } + +// FFTNWith is numpy.fft.fftn(a, s, axes, norm). +func FFTNWith(a *ndarray.Array, o Options) (*ndarray.Array, error) { + return run(a, o, c2c, false, allD) +} + +// IFFTN is numpy.fft.ifftn. +func IFFTN(a *ndarray.Array) (*ndarray.Array, error) { return IFFTNWith(a, Options{}) } + +// IFFTNWith is numpy.fft.ifftn(a, s, axes, norm). +func IFFTNWith(a *ndarray.Array, o Options) (*ndarray.Array, error) { + return run(a, o, c2c, true, allD) +} + +// RFFTN is numpy.fft.rfftn: the real transform runs along the last axis. +func RFFTN(a *ndarray.Array) (*ndarray.Array, error) { return RFFTNWith(a, Options{}) } + +// RFFTNWith is numpy.fft.rfftn(a, s, axes, norm). +func RFFTNWith(a *ndarray.Array, o Options) (*ndarray.Array, error) { + return run(a, o, r2c, false, allD) +} + +// IRFFTN is numpy.fft.irfftn. +func IRFFTN(a *ndarray.Array) (*ndarray.Array, error) { return IRFFTNWith(a, Options{}) } + +// IRFFTNWith is numpy.fft.irfftn(a, s, axes, norm). +func IRFFTNWith(a *ndarray.Array, o Options) (*ndarray.Array, error) { + return run(a, o, c2r, true, allD) +} + +// rank is how many axes a transform family takes by default. +type rank uint8 + +const ( + oneD rank = iota + twoD + allD +) + +// run resolves the arguments, pads or truncates the input, and calls go-fft. +func run(a *ndarray.Array, o Options, k kind, inverse bool, r rank) (*ndarray.Array, error) { + if (k == r2c || k == iherm) && a.DType().IsComplex() { + return nil, fmt.Errorf("%w: a real transform of a %v array", ErrArgs, a.DType()) + } + axes, dup, err := resolveAxes(a, o, r) + if err != nil { + return nil, err + } + out, err := outLengths(a, o, k, axes) + if err != nil { + return nil, err + } + if dup { + return sequential(a, axes, out, o.Norm, k, inverse) + } + // The input is cut or padded to the lengths the transform reads: for the + // half-spectrum inverses the last axis holds out/2+1 bins. + in := append([]int(nil), out...) + if k == c2r || k == herm { + in[len(in)-1] = out[len(out)-1]/2 + 1 + } + x := a + for i, ax := range axes { + x = resize(x, ax, in[i]) + } + single := a.DType() == ndarray.Float32 || a.DType() == ndarray.Complex64 + shape := x.Shape() + switch k { + case c2c: + return complexTransform(x, shape, axes, o.Norm, inverse, single), nil + case r2c: + return realForward(x, shape, axes, o.Norm, single), nil + case c2r: + shape[axes[len(axes)-1]] = out[len(out)-1] + return realInverse(x, shape, axes, o.Norm, single), nil + case herm: + // numpy: hfft(a, n) = irfft(conj(a), n) scaled as a forward transform. + shape[axes[len(axes)-1]] = out[len(out)-1] + return realInverse(x.Conj(), shape, axes, opposite(o.Norm), single), nil + } + // iherm: ihfft(a, n) = conj(rfft(a, n)) scaled as an inverse transform. + return realForward(x, shape, axes, opposite(o.Norm), single).Conj(), nil +} + +// sequential runs a multi-axis transform one axis at a time, in the order +// numpy.fft does, for an axis list that names an axis twice: that axis is then +// transformed twice, each time cut or padded to its own length. (go-fft +// refuses a repeated axis.) fftn goes from the last axis to the first; rfftn +// does the real transform along the last axis first, then the others; irfftn +// does the others first and the real inverse last. +func sequential(a *ndarray.Array, axes, out []int, norm Norm, k kind, inverse bool) (*ndarray.Array, error) { + one := func(x *ndarray.Array, i int, k kind) (*ndarray.Array, error) { + return run(x, Options{S: []int{out[i]}, Axes: []int{axes[i]}, Norm: norm}, k, inverse, oneD) + } + last := len(axes) - 1 + x := a + var err error + switch k { + case c2c: + for i := last; i >= 0 && err == nil; i-- { + x, err = one(x, i, c2c) + } + case r2c: + x, err = one(x, last, r2c) + for i := 0; i < last && err == nil; i++ { + x, err = one(x, i, c2c) + } + default: // c2r: herm and iherm are 1-D and cannot repeat an axis + for i := 0; i < last && err == nil; i++ { + x, err = one(x, i, c2c) + } + if err == nil { + x, err = one(x, last, c2r) + } + } + return x, err +} + +// opposite swaps the forward and inverse scalings. +func opposite(n Norm) Norm { + switch n { + case Backward: + return Forward + case Forward: + return Backward + } + return n +} + +// resolveAxes returns the normalised axes to transform, and whether one is +// listed twice. +func resolveAxes(a *ndarray.Array, o Options, r rank) (axes []int, dup bool, err error) { + nd := a.Ndim() + axes = o.Axes + if axes == nil { + switch { + case r == oneD: + axes = []int{-1} + case r == twoD: + axes = []int{-2, -1} + case o.S != nil: + axes = make([]int, len(o.S)) + for i := range axes { + axes[i] = i - len(o.S) + } + default: + axes = make([]int, nd) + for i := range axes { + axes[i] = i + } + } + } + if r == oneD && len(axes) != 1 { + return nil, false, fmt.Errorf("%w: a 1-D transform takes one axis, got %v", ErrArgs, axes) + } + if len(axes) == 0 { + return nil, false, fmt.Errorf("%w: no axis to transform", ErrArgs) + } + seen := make([]bool, nd) + out := make([]int, len(axes)) + for i, ax := range axes { + n := ax + if n < 0 { + n += nd + } + if n < 0 || n >= nd { + return nil, false, fmt.Errorf("%w: axis %d out of range for %d-dimensional array", ErrArgs, ax, nd) + } + dup = dup || seen[n] + seen[n] = true + out[i] = n + } + return out, dup, nil +} + +// outLengths returns the length of each transformed axis of the result's +// real or complex signal (before r2c halves the last one). +func outLengths(a *ndarray.Array, o Options, k kind, axes []int) ([]int, error) { + shape := a.Shape() + if o.S != nil && len(o.S) != len(axes) { + return nil, fmt.Errorf("%w: %d lengths for %d axes", ErrArgs, len(o.S), len(axes)) + } + out := make([]int, len(axes)) + for i, ax := range axes { + switch { + case o.S != nil: + out[i] = o.S[i] + case (k == c2r || k == herm) && i == len(axes)-1: + out[i] = 2 * (shape[ax] - 1) + default: + out[i] = shape[ax] + } + if out[i] < 1 { + return nil, fmt.Errorf("%w: length %d along axis %d", ErrArgs, out[i], ax) + } + } + return out, nil +} + +// resize cuts or zero-pads a to length n along axis ax. +func resize(a *ndarray.Array, ax, n int) *ndarray.Array { + shape := a.Shape() + m := shape[ax] + if n == m { + return a + } + idx := make([]ndarray.Index, len(shape)) + for i := range idx { + idx[i] = ndarray.All() + } + if n < m { + idx[ax] = ndarray.To(n) + v, _ := a.Slice(idx...) // a range within the axis: cannot fail + return v + } + shape[ax] = n - m + pad, _ := ndarray.ZerosOf(a.DType(), shape...) // a's shape with one axis grown: valid + r, _ := ndarray.Concatenate([]*ndarray.Array{a, pad}, ax) + return r +} + +// complexTransform runs FFTN/IFFTN along axes. +func complexTransform(x *ndarray.Array, shape, axes []int, norm Norm, inverse, single bool) *ndarray.Array { + o := gofft.Options{Axes: axes, Norm: norm} + if single { + d, _ := ndarray.Data[complex64](x.AsType(ndarray.Complex64)) + var r []complex64 + if inverse { + r = gofft.IFFTN32With(d, shape, o) + } else { + r = gofft.FFTN32With(d, shape, o) + } + return wrap(r, shape) + } + d, _ := ndarray.Data[complex128](x.AsType(ndarray.Complex128)) + var r []complex128 + if inverse { + r = gofft.IFFTNWith(d, shape, o) + } else { + r = gofft.FFTNWith(d, shape, o) + } + return wrap(r, shape) +} + +// realForward runs RFFTN along axes; the last axis of the result holds +// n/2+1 bins. +func realForward(x *ndarray.Array, shape, axes []int, norm Norm, single bool) *ndarray.Array { + o := gofft.Options{Axes: axes, Norm: norm} + outShape := append([]int(nil), shape...) + last := axes[len(axes)-1] + outShape[last] = shape[last]/2 + 1 + if single { + d, _ := ndarray.Data[float32](x.Real().AsType(ndarray.Float32)) + return wrap(gofft.RFFTN32With(d, shape, o), outShape) + } + d, _ := ndarray.Data[float64](x.Real().AsType(ndarray.Float64)) + return wrap(gofft.RFFTNWith(d, shape, o), outShape) +} + +// realInverse runs IRFFTN along axes into a real array of the given shape. +func realInverse(x *ndarray.Array, shape, axes []int, norm Norm, single bool) *ndarray.Array { + o := gofft.Options{Axes: axes, Norm: norm} + if single { + d, _ := ndarray.Data[complex64](x.AsType(ndarray.Complex64)) + return wrap(gofft.IRFFTN32With(d, shape, o), shape) + } + d, _ := ndarray.Data[complex128](x.AsType(ndarray.Complex128)) + return wrap(gofft.IRFFTNWith(d, shape, o), shape) +} + +// wrap makes an array of a transform's output. The lengths always match. +func wrap[T float32 | float64 | complex64 | complex128](d []T, shape []int) *ndarray.Array { + r, _ := ndarray.FromSlice(d, shape...) + return r +} + +// FFTFreq is numpy.fft.fftfreq: the sample frequencies of an n-point FFT with +// sample spacing d. +func FFTFreq(n int, d float64) (*ndarray.Array, error) { + if n < 1 { + return nil, fmt.Errorf("%w: fftfreq of %d points", ErrArgs, n) + } + return wrap(gofft.FFTFreq(n, d), []int{n}), nil +} + +// RFFTFreq is numpy.fft.rfftfreq: the n/2+1 non-negative frequencies of an +// n-point RFFT. +func RFFTFreq(n int, d float64) (*ndarray.Array, error) { + if n < 1 { + return nil, fmt.Errorf("%w: rfftfreq of %d points", ErrArgs, n) + } + return wrap(gofft.RFFTFreq(n, d), []int{n/2 + 1}), nil +} + +// FFTShift is numpy.fft.fftshift: it rotates each of the given axes (every +// axis when none is given) by half its length, moving the zero frequency to +// the centre. +func FFTShift(a *ndarray.Array, axes ...int) (*ndarray.Array, error) { + return shift(a, axes, false) +} + +// IFFTShift is numpy.fft.ifftshift, the inverse of FFTShift. +func IFFTShift(a *ndarray.Array, axes ...int) (*ndarray.Array, error) { + return shift(a, axes, true) +} + +// shift rolls each axis by n/2 (FFTShift) or -(n/2) (IFFTShift), for any +// dtype, by taking the two halves and joining them the other way round. +func shift(a *ndarray.Array, axes []int, inverse bool) (*ndarray.Array, error) { + if axes == nil { + axes = make([]int, a.Ndim()) + for i := range axes { + axes[i] = i + } + } + var norm []int + if len(axes) > 0 { + var err error + if norm, _, err = resolveAxes(a, Options{Axes: axes}, allD); err != nil { + return nil, err + } + } + x := a + shape := a.Shape() + for _, ax := range norm { + n := shape[ax] + cut := n - n/2 // fftshift moves the last n/2 to the front + if inverse { + cut = n / 2 + } + idx := make([]ndarray.Index, len(shape)) + for i := range idx { + idx[i] = ndarray.All() + } + idx[ax] = ndarray.From(cut) + tail, _ := x.Slice(idx...) + idx[ax] = ndarray.To(cut) + head, _ := x.Slice(idx...) + x, _ = ndarray.Concatenate([]*ndarray.Array{tail, head}, ax) + } + if x == a { + return a.Copy(), nil + } + return x, nil +} diff --git a/fft/fft_test.go b/fft/fft_test.go new file mode 100644 index 0000000..e8c0c9f --- /dev/null +++ b/fft/fft_test.go @@ -0,0 +1,267 @@ +package fft + +import ( + _ "embed" + "encoding/json" + "errors" + "math" + "strconv" + "testing" + + "github.com/go-ndarray/ndarray" +) + +// cases.json holds numpy.fft's results for every transform on several +// dtypes, shapes and argument sets, generated by testdata/cases.py. +// +//go:embed testdata/cases.json +var casesJSON []byte + +type fftCase struct { + Fn string `json:"fn"` + DType string `json:"dtype"` + Shape []int `json:"shape"` + X []json.RawMessage `json:"x"` + N *int `json:"n"` + S []int `json:"s"` + Axis *int `json:"axis"` + Axes []int `json:"axes"` + Norm *string `json:"norm"` + RDType string `json:"rdtype"` + RShape []int `json:"rshape"` + R []json.RawMessage `json:"r"` + Error string `json:"error"` +} + +func parseValues(t *testing.T, raw []json.RawMessage) []complex128 { + t.Helper() + out := make([]complex128, len(raw)) + for i, r := range raw { + var pair []string + if json.Unmarshal(r, &pair) == nil { + out[i] = complex(num(t, pair[0]), num(t, pair[1])) + continue + } + var s string + if err := json.Unmarshal(r, &s); err != nil { + t.Fatal(err) + } + out[i] = complex(num(t, s), 0) + } + return out +} + +func num(t *testing.T, s string) float64 { + t.Helper() + f, err := strconv.ParseFloat(s, 64) + if err != nil { + t.Fatal(err) + } + return f +} + +var norms = map[string]Norm{"ortho": Ortho, "forward": Forward, "backward": Backward} + +type transform func(*ndarray.Array, Options) (*ndarray.Array, error) + +var transforms = map[string]transform{ + "fft": FFTWith, "ifft": IFFTWith, "rfft": RFFTWith, "irfft": IRFFTWith, + "hfft": HFFTWith, "ihfft": IHFFTWith, + "fft2": FFT2With, "ifft2": IFFT2With, "rfft2": RFFT2With, "irfft2": IRFFT2With, + "fftn": FFTNWith, "ifftn": IFFTNWith, "rfftn": RFFTNWith, "irfftn": IRFFTNWith, +} + +// TestMatchesNumPy runs every case of the fixture and compares dtype, shape +// and values (within 64 epsilons of the largest magnitude of the result, in +// the result's precision: the two libraries use different algorithms). +func TestMatchesNumPy(t *testing.T) { + var fx struct { + NumPy string `json:"numpy"` + Cases []fftCase `json:"cases"` + } + if err := json.Unmarshal(casesJSON, &fx); err != nil { + t.Fatal(err) + } + checked := 0 + for i, c := range fx.Cases { + got, err := runCase(t, c) + if c.Error != "" { + if err == nil { + t.Errorf("case %d %s %s %v: got %v, NumPy raises %s", i, c.Fn, c.DType, c.Shape, got.Shape(), c.Error) + } + continue + } + if err != nil { + t.Errorf("case %d %s %s %v: %v", i, c.Fn, c.DType, c.Shape, err) + continue + } + if got.DType().String() != c.RDType || !sameInts(got.Shape(), c.RShape) { + t.Errorf("case %d %s %s %v: %v %v, NumPy %s %v", i, c.Fn, c.DType, c.Shape, + got.DType(), got.Shape(), c.RDType, c.RShape) + continue + } + want := parseValues(t, c.R) + gc := got.AsType(ndarray.Complex128) + g, _ := ndarray.Data[complex128](gc) + scale := 0.0 + for _, w := range want { + scale = math.Max(scale, math.Hypot(real(w), imag(w))) + } + eps := 0x1p-52 + if c.RDType == "complex64" || c.RDType == "float32" { + eps = 0x1p-23 + } + for j := range want { + d := g[j] - want[j] + if math.Hypot(real(d), imag(d)) > 64*eps*math.Max(scale, 1) { + t.Errorf("case %d %s %s %v [%d] = %v, NumPy %v", i, c.Fn, c.DType, c.Shape, j, g[j], want[j]) + break + } + } + checked++ + } + t.Logf("%d of %d cases checked against NumPy %s", checked, len(fx.Cases), fx.NumPy) +} + +func sameInts(a, b []int) bool { + if len(a) != len(b) { + return false + } + for i := range a { + if a[i] != b[i] { + return false + } + } + return true +} + +// runCase builds the input of a case and calls the matching function. +func runCase(t *testing.T, c fftCase) (*ndarray.Array, error) { + t.Helper() + switch c.Fn { + case "fftfreq": + return FFTFreq(*c.N, 0.1) + case "rfftfreq": + return RFFTFreq(*c.N, 0.1) + } + dt, err := ndarray.ParseDType(c.DType) + if err != nil { + t.Fatal(err) + } + vals := parseValues(t, c.X) + x, _ := ndarray.FromSlice(vals, c.Shape...) + x = x.AsType(dt) + switch c.Fn { + case "fftshift": + return FFTShift(x, c.Axes...) + case "ifftshift": + return IFFTShift(x, c.Axes...) + } + o := Options{S: c.S, Axes: c.Axes} + if c.N != nil { + o.S = []int{*c.N} + } + if c.Axis != nil { + o.Axes = []int{*c.Axis} + } + if c.Norm != nil { + o.Norm = norms[*c.Norm] + } + return transforms[c.Fn](x, o) +} + +func TestDefaultsEqualWith(t *testing.T) { + x, _ := ndarray.FromSlice([]float64{1, 2, 3, 4, 5, 6}, 2, 3) + pairs := []struct { + name string + f func(*ndarray.Array) (*ndarray.Array, error) + g transform + }{ + {"FFT", FFT, FFTWith}, {"IFFT", IFFT, IFFTWith}, {"RFFT", RFFT, RFFTWith}, {"IRFFT", IRFFT, IRFFTWith}, + {"HFFT", HFFT, HFFTWith}, {"IHFFT", IHFFT, IHFFTWith}, {"FFT2", FFT2, FFT2With}, {"IFFT2", IFFT2, IFFT2With}, + {"RFFT2", RFFT2, RFFT2With}, {"IRFFT2", IRFFT2, IRFFT2With}, {"FFTN", FFTN, FFTNWith}, + {"IFFTN", IFFTN, IFFTNWith}, {"RFFTN", RFFTN, RFFTNWith}, {"IRFFTN", IRFFTN, IRFFTNWith}, + } + for _, p := range pairs { + a, err1 := p.f(x) + b, err2 := p.g(x, Options{}) + if err1 != nil || err2 != nil || a.String() != b.String() { + t.Errorf("%s differs from its With form: %v %v", p.name, err1, err2) + } + } +} + +func TestArgumentErrors(t *testing.T) { + x, _ := ndarray.Zeros(4, 4) + for name, o := range map[string]Options{ + "two axes for 1-D": {Axes: []int{0, 1}}, + "S/axes length": {S: []int{2, 2}, Axes: []int{0}}, + } { + if _, err := FFTWith(x, o); !errors.Is(err, ErrArgs) { + t.Errorf("%s: err = %v", name, err) + } + } + if _, err := FFTNWith(x, Options{Axes: []int{}}); !errors.Is(err, ErrArgs) { + t.Errorf("no axes: err = %v", err) + } + // A repeated axis is transformed twice, in numpy's order, with the lengths + // numpy fixes before the first pass (so the 3 bins are padded back to 4). + y, _ := ndarray.FromSlice([]float64{1, 2, 3, 4, 5, 6, 7, 8}, 2, 4) + r, err := RFFTNWith(y, Options{Axes: []int{1, 1}}) + step, _ := RFFTWith(y, Options{Axes: []int{1}}) + step, _ = FFTWith(step, Options{Axes: []int{1}, S: []int{4}}) + if err != nil || r.String() != step.String() { + t.Errorf("rfftn over a repeated axis = %v, %v; want %v", r, err, step) + } + r, err = IRFFTNWith(step, Options{Axes: []int{1, 1}, S: []int{3, 4}}) + inv, _ := IFFTWith(step, Options{Axes: []int{1}, S: []int{3}}) + inv, _ = IRFFTWith(inv, Options{Axes: []int{1}, S: []int{4}}) + if err != nil || r.String() != inv.String() { + t.Errorf("irfftn over a repeated axis = %v, %v; want %v", r, err, inv) + } + if _, err := RFFTNWith(y, Options{Axes: []int{1, 1}, S: []int{4, 0}}); !errors.Is(err, ErrArgs) { + t.Errorf("repeated axis with a zero length: err = %v", err) + } + if _, err := FFTNWith(x, Options{S: []int{4}}); err != nil { + t.Errorf("S selects the last axis: %v", err) + } + for _, n := range []int{0, -1} { + if _, err := FFTFreq(n, 1); !errors.Is(err, ErrArgs) { + t.Errorf("FFTFreq(%d) err = %v", n, err) + } + if _, err := RFFTFreq(n, 1); !errors.Is(err, ErrArgs) { + t.Errorf("RFFTFreq(%d) err = %v", n, err) + } + } + if _, err := FFTShift(x, 2); !errors.Is(err, ErrArgs) { + t.Errorf("FFTShift axis err = %v", err) + } + s, _ := ndarray.FromSlice([]int8{3}, []int{}...) + if r, err := FFTShift(s); err != nil || r == s || r.String() != s.String() { + t.Errorf("FFTShift of a 0-d array = %v, %v", r, err) + } + if r, _ := FFTShift(x, []int{}...); r == x { + t.Error("FFTShift returned its input") + } +} + +// TestNormsAreInverse checks the round trip under each scaling, in both +// precisions. +func TestNormsAreInverse(t *testing.T) { + for _, dt := range []ndarray.DType{ndarray.Float64, ndarray.Float32} { + x, _ := ndarray.FromSlice([]float64{1, -2, 3, 0.5, 4, -1}, 6) + x = x.AsType(dt) + for _, n := range []Norm{Backward, Ortho, Forward} { + f, _ := RFFTWith(x, Options{Norm: n}) + b, _ := IRFFTWith(f, Options{S: []int{6}, Norm: n}) + if b.DType() != dt { + t.Fatalf("%v round trip gives %v", dt, b.DType()) + } + for i := range 6 { + if math.Abs(b.At(i)-x.At(i)) > 1e-5 { + t.Errorf("%v %v: [%d] %g != %g", dt, n, i, b.At(i), x.At(i)) + } + } + } + } +} diff --git a/fft/testdata/cases.json b/fft/testdata/cases.json new file mode 100644 index 0000000..2d5012a --- /dev/null +++ b/fft/testdata/cases.json @@ -0,0 +1 @@ +{"numpy": "2.5.3", "cases": [{"fn": "fft", "dtype": "float64", "shape": [8], "x": ["0.5455202066613396", "0.6749019794879405", "0.9636266787187049", "0.8793944555824906", "-0.20213024291774995", "-0.49103170125446743", "-0.8948263981778347", "-1.1144878557384363"], "n": null, "s": null, "axis": null, "axes": null, "norm": null, "rdtype": "complex128", "rshape": [8], "r": 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"r": ["0.0", "1.4285714285714284", "2.8571428571428568", "4.285714285714285", "-4.285714285714285", "-2.8571428571428568", "-1.4285714285714284"]}, {"fn": "rfftfreq", "n": 7, "rdtype": "float64", "rshape": [4], "r": ["0.0", "1.4285714285714284", "2.8571428571428568", "4.285714285714285"]}]} diff --git a/fft/testdata/cases.py b/fft/testdata/cases.py new file mode 100644 index 0000000..8d9da60 --- /dev/null +++ b/fft/testdata/cases.py @@ -0,0 +1,65 @@ +# Generates fft/testdata/cases.json: `uv run --with numpy python fft/testdata/cases.py > fft/testdata/cases.json` +# Inputs are a fixed formula, not a random generator, and are stored with the +# results; numbers are repr strings, complex numbers [re, im]. +import json, math +import numpy as np + +def signal(shape, dt): + n = int(np.prod(shape)) + i = np.arange(n, dtype=np.float64) + re = np.sin(0.7 * i + 0.3) + 0.25 * np.cos(2.3 * i) + im = np.cos(1.1 * i - 0.2) * 0.5 + if np.dtype(dt).kind == 'c': + return (re + 1j * im).astype(dt).reshape(shape) + if np.dtype(dt).kind == 'i': + return np.round(re * 10).astype(dt).reshape(shape) + return re.astype(dt).reshape(shape) + +def enc(v): + v = np.asarray(v) + if v.dtype.kind == 'c': + return [[repr(float(z.real)), repr(float(z.imag))] for z in v.ravel()] + return [repr(float(z)) for z in v.ravel()] + +calls = [ + ("fft", {}), ("fft", {"n": 6}), ("fft", {"n": 3, "axis": 0}), ("fft", {"norm": "ortho"}), + ("ifft", {}), ("ifft", {"norm": "forward"}), + ("rfft", {}), ("rfft", {"n": 7}), ("rfft", {"axis": 0, "norm": "ortho"}), + ("irfft", {}), ("irfft", {"n": 9}), ("irfft", {"axis": 0}), + ("hfft", {}), ("hfft", {"n": 5, "norm": "ortho"}), ("ihfft", {}), ("ihfft", {"norm": "forward"}), + ("fft2", {}), ("fft2", {"s": [3, 6]}), ("ifft2", {"norm": "ortho"}), + ("rfft2", {}), ("irfft2", {}), ("irfft2", {"s": [4, 7]}), + ("fftn", {}), ("fftn", {"axes": [0]}), ("fftn", {"s": [2, 8], "axes": [0, -1]}), + ("ifftn", {"axes": [-1, 0]}), + ("rfftn", {}), ("rfftn", {"axes": [-1, 0]}), ("irfftn", {}), ("irfftn", {"s": [3, 5], "axes": [0, 1]}), + ("fft", {"axis": 3}), ("fftn", {"axes": [0, 0]}), ("fft", {"n": 0}), +] +cases = [] +for dt in ["float64", "float32", "complex128", "complex64", "int32"]: + for shape in [(8,), (5,), (3, 4), (2, 3, 5)]: + x = signal(shape, dt) + for fn, kw in calls: + if fn.endswith("2") and len(shape) < 2: + continue + c = {"fn": fn, "dtype": dt, "shape": list(shape), "x": enc(x), + "n": kw.get("n"), "s": kw.get("s"), "axis": kw.get("axis"), + "axes": kw.get("axes"), "norm": kw.get("norm")} + try: + r = np.asarray(getattr(np.fft, fn)(x, **kw)) + c.update(rdtype=str(r.dtype), rshape=list(r.shape), r=enc(r)) + except Exception as e: + c["error"] = type(e).__name__ + cases.append(c) +for fn, kw in [("fftshift", {}), ("fftshift", {"axes": [1]}), ("ifftshift", {}), ("ifftshift", {"axes": [0]})]: + for shape in [(5,), (3, 4), (2, 3, 5)]: + x = signal(shape, "float64") + if kw.get("axes") and kw["axes"][0] >= len(shape): + continue + r = getattr(np.fft, fn)(x, **kw) + cases.append({"fn": fn, "dtype": "float64", "shape": list(shape), "x": enc(x), "axes": kw.get("axes"), + "rdtype": str(r.dtype), "rshape": list(r.shape), "r": enc(r)}) +for n in [1, 4, 7]: + for fn in ["fftfreq", "rfftfreq"]: + r = getattr(np.fft, fn)(n, 0.1) + cases.append({"fn": fn, "n": n, "rdtype": str(r.dtype), "rshape": list(r.shape), "r": enc(r)}) +print(json.dumps({"numpy": np.__version__, "cases": cases})) diff --git a/go.mod b/go.mod index 94f5256..0c5ccd6 100644 --- a/go.mod +++ b/go.mod @@ -1,3 +1,5 @@ module github.com/go-ndarray/ndarray go 1.27.2 + +require github.com/go-fft/fft v0.23.0 diff --git a/go.sum b/go.sum new file mode 100644 index 0000000..83a6b8b --- /dev/null +++ b/go.sum @@ -0,0 +1,2 @@ +github.com/go-fft/fft v0.23.0 h1:SBQmOliIthFyRz1MbnrT/HnJejmLJxoWdLXkXsGMCis= +github.com/go-fft/fft v0.23.0/go.mod h1:GN5V4TWCjV05ECqH1ONfjFM6Z1m2shqCdssxKGqQ41s=