# Test of the adjoint (adj-tl_test / std)¶

## Description¶

This mode is dedicated to testing the adjoint of the observation operator for a given configuration set-up.

For every inversion case study, it is necessary to compute a test of the adjoint before running a full variational inversion. It allows to detect any error specific to your test case and that were never met before. If the computation costs of the inversion set-up are very high, it is possible to execute a adjoint test with a simplified set-up (e.g. with a shorter period), but it is important to include configurations that can generate errors (month of February, several months/years in a row, etc.).

This test consists in checking that: $$\langle \mathcal{H}(\delta \mathbf{x}) \vert \mathcal{H}(\delta \mathbf{x}) \rangle = \langle \delta \mathbf{x} \vert \mathcal{H}^* \circ \mathcal{H}(\delta \mathbf{x}) \rangle$$.

$$\mathcal{H}(\delta \mathbf{x})$$ is computed with the tangent linear model, and then $$\mathcal{H}^*\circ \mathcal{H}(\delta \mathbf{x})$$ is calculated with the adjoint.

In principle, the two terms of the equation are never exactly equal. Nevertheless, the difference should never exceed several times the machine accuracy.

## Yaml arguments¶

The following arguments are used to configure the plugin. pyCIF will return an exception at the initialization if mandatory arguments are not specified, or if any argument does not fit accepted values or type:

### Mandatory arguments¶

increments: (mandatory)

Scale of the increments to do the test. The following equation is used: $$\delta x = \delta i \;.\; \sigma_\mathbf{x}$$

accepted type: float

### Optional arguments¶

incrmode: (optional): cst

Type of increments to use in the test.

accepted values:

• cst: Increments are the same for all dimensions of the control vector

• rand: Increments are selected randomly with a Normal distribution centered to zero with standard deviation \${increments}

testspace: (optional): control

Reference space to apply the test of the adjoint

accepted values:

• control: The test is applied in the control space

• chi:

The test is applied is the reduction $$\chi$$ space; this includes multiplication by the square root of the matrix $$\mathbf{B}$$; it is recommended to do this test before an inversion using error correlations

Which type of test to run

accepted values:

• tltaylor: Taylor test

• tllinearity: Test the linearity of the tangent linear

Reload results from previously compiled test. If True does not recomputed the tangent-linear and/or the adjoint

accepted type: bool

random_seed: (optional): 0

Seed to use in the test of the adjoint for generating random numbers; used only with incrmode = rand

accepted type: int

check_transforms: (optional): False

Check whether individual transformation pass the test of the adjoint. Transformations are printed out in the order they are run in forward.

For each transformation, the output reads as follows:

transformation_ID, transformation_name, sub-simulation date: $$\langle \mathcal{H}(\delta \mathbf{x}) \vert \mathcal{H}(\delta \mathbf{x}) \rangle$$ / $$\langle \delta \mathbf{x} \vert \mathcal{H}^* \circ \mathcal{H}(\delta \mathbf{x}) \rangle$$

The output is printed out both in the main pyCIF log file and in a dedicated file check_transforms.log in your work directory.

accepted type: bool

use_forward: (optional): False

Force using the forward model instead of the tangent linear. WARNING: this works only if the model is linear

accepted type: bool

taylor_iter: (optional): 1

Number of iterations for the Taylor test

accepted type: int

lambdalin: (optional): 0.1

Factor to use to perturb increments in the Taylor and linearity tests

accepted type: float

## Requirements¶

The current plugin requires the present plugins to run properly:

Requirement name

Requirement type

Explicit definition

Any valid

Default name

Default version

obsvect

ObsVect

False

True

standard

std

controlvect

ControlVect

True

True

standard

std

obsoperator

ObsOperator

True

True

standard

std

## Yaml template¶

Please find below a template for a Yaml configuration:

 1mode:
2  plugin:
4    version: std
5    type: mode
6
7  # Mandatory arguments
8  increments: XXXXX  # float
9
10  # Optional arguments
11  incrmode: XXXXX  # cst|rand
12  testspace: XXXXX  # control|chi