Supported Operations¶

Dualpy registers derivative rules for the NumPy operations listed below. Any operation not on this list will raise NotImplementedError when called on dual-number inputs. Coverage is expanded in each release.

Ufuncs¶

Arithmetic¶

NumPy ufunc	Notes
`add`
`subtract`
`multiply`
`divide` / `true_divide`
`power`
`float_power`
`negative`
`positive`
`absolute` / `abs`
`fabs`
`square`
`reciprocal`
`cbrt`
`fmod`
`remainder` / `mod`
`copysign`
`matmul`
`maximum`
`minimum`

Trigonometric¶

NumPy ufunc	Notes
`sin`
`cos`
`tan`
`arcsin`
`arccos`
`arctan`
`arctan2`
`hypot`
`degrees`
`radians`
`deg2rad`
`rad2deg`

Hyperbolic¶

NumPy ufunc	Notes
`sinh`
`cosh`
`tanh`
`arcsinh`
`arccosh`
`arctanh`

Exponential & logarithmic¶

NumPy ufunc	Notes
`exp`
`exp2`
`expm1`
`log`
`log2`
`log10`
`log1p`
`logaddexp`
`logaddexp2`
`sqrt`

Comparison¶

NumPy ufunc	Notes
`equal`	Returns plain array (no tangent)
`not_equal`	Returns plain array
`greater`	Returns plain array
`greater_equal`	Returns plain array
`less`	Returns plain array
`less_equal`	Returns plain array

Logical & query¶

NumPy ufunc	Notes
`logical_and`	Returns plain array
`logical_or`	Returns plain array
`logical_xor`	Returns plain array
`logical_not`	Returns plain array
`isnan`	Returns plain array
`isinf`	Returns plain array
`isfinite`	Returns plain array
`signbit`	Returns plain array

Rounding¶

NumPy ufunc	Notes
`sign`	Zero tangent (piecewise constant)
`heaviside`	Zero tangent
`floor`	Zero tangent
`ceil`	Zero tangent
`trunc`	Zero tangent
`rint`	Zero tangent

Array routines¶

Linear algebra¶

NumPy function	Notes
`np.dot`
`np.inner`
`np.outer`
`np.tensordot`
`np.einsum`	Arbitrary number of operands
`np.trace`
`np.cross`
`np.vdot`
`np.kron`
`np.linalg.norm`	Supports `ord`, `axis`, `keepdims`
`np.linalg.det`
`np.linalg.inv`
`np.linalg.solve`	Both A and b may be dual
`np.linalg.cholesky`
`np.linalg.eigh`	Symmetric/Hermitian eigendecomposition
`np.linalg.svd`	Full and reduced modes
`np.linalg.qr`
`np.linalg.lstsq`
`np.linalg.matrix_power`	Positive, negative, and zero exponents
`np.linalg.multi_dot`

Reductions¶

NumPy function	Notes
`np.sum`
`np.mean`
`np.prod`
`np.max`
`np.min`
`np.var`	Supports `ddof`
`np.std`	Supports `ddof`
`np.cumsum`
`np.cumprod`
`np.argmax`	Returns plain integer (no tangent)
`np.argmin`	Returns plain integer
`np.nansum`
`np.nanmean`
`np.nanvar`
`np.nanstd`
`np.nanmax`
`np.nanmin`
`np.average`	Supports `weights`
`np.median`
`np.all`	Returns plain array
`np.any`	Returns plain array
`np.count_nonzero`	Returns plain integer

Shape manipulation¶

NumPy function	Notes
`np.concatenate`
`np.stack`
`np.hstack`
`np.vstack`
`np.dstack`
`np.column_stack`
`np.reshape`
`np.transpose`
`np.swapaxes`
`np.moveaxis`
`np.squeeze`
`np.expand_dims`
`np.ravel`
`np.split`
`np.array_split`
`np.tile`
`np.repeat`
`np.flip`
`np.fliplr`
`np.flipud`
`np.roll`
`np.broadcast_to`
`np.atleast_1d`
`np.atleast_2d`
`np.atleast_3d`
`np.pad`	Tangent padded with zeros
`np.rot90`
`np.take`
`np.take_along_axis`
`np.insert`
`np.delete`
`np.append`
`np.select`

Construction¶

NumPy function	Notes
`np.array`	From list of dual arrays
`np.zeros_like`
`np.ones_like`
`np.full_like`
`np.empty_like`	Returns zeros (safe default)
`np.copy`
`np.linspace`
`np.arange`
`np.eye`
`np.identity`
`np.diag`
`np.diagonal`
`np.meshgrid`
`np.triu`
`np.tril`

Searching & sorting¶

NumPy function	Notes
`np.where`
`np.clip`
`np.sort`
`np.argsort`	Returns plain integer array
`np.searchsorted`	Returns plain integer array
`np.nonzero`	Returns plain index arrays
`np.flatnonzero`	Returns plain index array
`np.extract`

Numerical¶

NumPy function	Notes
`np.diff`
`np.convolve`
`np.correlate`
`np.interp`
`np.trapezoid`	Supports `x` and `dx`
`np.sinc`
`np.gradient`	Numerical gradient (not to be confused with `dualpy.gradient`)