nifty8.linearization module#

class Linearization(val, jac, metric=None, want_metric=False)[source]#

Bases: Operator

Let A be an operator and x a field. Linearization stores the value of the operator application (i.e. A(x)), the local Jacobian (i.e. dA(x)/dx) and, optionally, the local metric.

Parameters:

val (nifty8.field.Field or nifty8.multi_field.MultiField) – The value of the operator application.
jac (LinearOperator) – The Jacobian.
metric (LinearOperator or None) – The metric. Default: None.
want_metric (bool) – If True, the metric will be computed for other Linearizations derived from this one. Default: False.

__init__(val, jac, metric=None, want_metric=False)[source]#

add_metric(metric)[source]#

conjugate()[source]#

property domain#

the Jacobian’s domain

Type:: DomainTuple or MultiDomain

property gradient#

the gradient

Notes

Only available if target is a scalar

Type:: nifty8.field.Field or nifty8.multi_field.MultiField

property imag#

integrate(spaces=None)[source]#

Computes the (partial) integral over self

Parameters:

spaces (None, int or list of int) –

if None, integrate over the entire domain
else integrate over the specified subspaces

Returns:

the (partial) integral

Return type:

Linearization

property jac#

the Jacobian

Type:: LinearOperator

static make_const(field, want_metric=False)[source]#

Converts a Field to a Linearization, with a zero Jacobian

Parameters:

field (nifty8.field.Field or nifty8.multi_field.MultiField) – the field to be converted
want_metric (bool) – If True, the metric will be computed for other Linearizations derived from this one. Default: False.

Returns:

the requested Linearization

Return type:

Linearization

Notes

The Jacobian is square and contains only zeroes.

static make_const_empty_input(field, want_metric=False)[source]#

Converts a Field to a Linearization, with a zero Jacobian

Parameters:

field (nifty8.field.Field or nifty8.multi_field.MultiField) – the field to be converted
want_metric (bool) – If True, the metric will be computed for other Linearizations derived from this one. Default: False.

Returns:

the requested Linearization

Return type:

Linearization

Notes

The Jacobian has an empty input domain, i.e. its matrix representation has 0 columns.

static make_partial_var(field, constants, want_metric=False)[source]#

Converts a MultiField to a Linearization, with a Jacobian that is unity for some MultiField components and a zero matrix for others.

Parameters:

field (nifty8.multi_field.MultiField) – the field to be converted
constants (list of string) – the MultiField components for which the Jacobian should be a zero matrix.
want_metric (bool) – If True, the metric will be computed for other Linearizations derived from this one. Default: False.

Returns:

the requested Linearization

Return type:

Linearization

Notes

The Jacobian is square.

static make_var(field, want_metric=False)[source]#

Converts a Field to a Linearization, with a unity Jacobian

Parameters:

field (nifty8.field.Field or nifty8.multi_field.MultiField) – the field to be converted
want_metric (bool) – If True, the metric will be computed for other Linearizations derived from this one. Default: False.

Returns:

the requested Linearization

Return type:

Linearization

property metric#

the metric

Notes

Only available if target is a scalar

Type:: LinearOperator

new(val, jac, metric=None)[source]#

Create a new Linearization, taking the want_metric property from: this one.

Parameters:

val (nifty8.field.Field or nifty8.multi_field.MultiField) – the value of the operator application
jac (LinearOperator) – the Jacobian
metric (LinearOperator or None) – The metric. Default: None.

outer(other)[source]#

Computes the outer product of this Linearization with a Field or another Linearization

Parameters:: other (nifty8.field.Field or nifty8.multi_field.MultiField or Linearization)
Returns:: the outer product of self and other
Return type:: Linearization

prepend_jac(jac)[source]#

ptw(op, *args, **kwargs)[source]#

property real#

sum(spaces=None)[source]#

Computes the (partial) sum over self

Parameters:

spaces (None, int or list of int) –

if None, sum over the entire domain
else sum over the specified subspaces

Returns:

the (partial) sum

Return type:

Linearization

property target#

the Jacobian’s target (i.e. the value’s domain)

Type:: DomainTuple or MultiDomain

trivial_jac()[source]#

property val#

the value

Type:: nifty8.field.Field or nifty8.multi_field.MultiField

vdot(other)[source]#

Computes the inner product of this Linearization with a Field or another Linearization

Parameters:: other (nifty8.field.Field or nifty8.multi_field.MultiField or Linearization)
Returns:: the inner product of self and other
Return type:: Linearization

property want_metric#

True iff the metric was requested in the constructor

Type:: bool

with_want_metric()[source]#