vp.linalg.enorm

The Euclidean norm of x, with no overflow or underflow in the sum of squares (MINPACK enorm). An empty x has norm 0.

Part of the distribution vipyr; it runs from a checkout of the repository. Planned on PyPI as pip install vipyr.

Signature

vp.linalg.enorm(x)

Parameters

x : ndarray[float64], required

Range: rank 1.

Returns

A frozen EnormResult. Iterating it gives the fields below in order; it also has params, tests, log and check().

norm : float

Raises

vipyr.ParameterError

A ValueError: an argument outside its range, choices, rank or shape, or one of a group given without the rest; its .param names the argument.

TypeError

An argument of the wrong type, or an unknown keyword.

vipyr.VivBuildError

An ImportError: no C compiler, or the program's C does not build.

Examples

import numpy as np
import vipyr as vp
r = vp.linalg.enorm(x=np.array([3e200, 4e200]))
print(r.norm)
assert r.check()

4.9999999999999995e+200

Each example ran as written when these pages were generated, and the output shown is what it printed.

Checked against

Reference

mpmath at 50 digits, sqrt(sum x_i^2), at every scale from subnormal to 10³⁰⁰; scipy.linalg.norm where no partial sum overflows

Compared by

relative error

Tolerance

rel 10⁻¹⁴, vs_scipy 10⁻¹⁴

Why that tolerance

a sum of n <= 100 squares in three scaled accumulators, then a square root: the summation bound is about n u / 2 = 1.1 × 10⁻¹⁴ at n = 100, for enorm and for SciPy's norm alike

Credits

• A port of MINPACK (Argonne National Laboratory), under MINPACK's BSD-style copyright notice (1999, University of Chicago), which the port and the Fortran in lib/minpack/ref both carry. This product includes software developed by the University of Chicago, as Operator of Argonne National Laboratory.

Source

• Manifest: kernels/k1/k1.export.toml
• Viv: kernels/k1/norms.viv
• Viv: lib/minpack/enorm.viv
• The defs it reaches and the calls between them: map of the code