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title spatial

The stdlib_spatial module

This module provides implementations of algorithms for spatial data processing.

[TOC]

kabsch_umeyama - Finding optimal rotation matrix

Status

Experimental

Description

Compute the optimal similarity transform (Kabsch–Umeyama): [ P \approx c , R , Q + t ] where:

  • R is an orthogonal rotation matrix,
  • c is an optional scaling factor,
  • t is a translation vector.

The transformation minimizes the root-mean-square deviation (RMSD) between corresponding columns of P and Q, optionally using weights and with optional scaling. The implementation is based on the algorithm described here: Aligning point patterns with Kabsch–Umeyama algorithm

Syntax

call [[stdlib_spatial(module):kabsch_umeyama(interface)]] (P, Q, R, t, c, rmsd [, W, scale])

Arguments

P: Shall be a real or complex rank-2 array. It is an intent(in) argument.

Q: Shall be a rank-2 array with same kind as P. It is an intent(in) argument.

R: Shall be a rank-2 array with same kind as P. For real kinds, the algorithm returns a proper rotation matrix, meaning det(R) = 1. It is an intent(out) argument.

t: Shall be a rank-1 array with same kind as P. It is an intent(out) argument.

c: Scalar value of the same type as P. It is an intent(out) argument. If scale is disabled c will be returned with a value of 1.

rmsd: Scalar value of real kind. It is an intent(out) argument.

W (optional): Shall be a rank-1 array of real kind. It is an intent(in) argument. By default, W is an array of 1s.

scale (optional): Shall be a logical type. It is an intent(in) argument. By default, scale = .true..

Example

{!example/spatial/example_kabsch_umeyama.f90!}