class scipy.optimize.SR1(min_denominator=1e-08, init_scale='auto')[source]#

Symmetric-rank-1 Hessian update strategy.


This number, scaled by a normalization factor, defines the minimum denominator magnitude allowed in the update. When the condition is violated we skip the update. By default uses 1e-8.

init_scale{float, np.array, ‘auto’}, optional

This parameter can be used to initialize the Hessian or its inverse. When a float is given, the relevant array is initialized to np.eye(n) * init_scale, where n is the problem dimension. Alternatively, if a precisely (n, n) shaped, symmetric array is given, this array will be used. Otherwise an error is generated. Set it to ‘auto’ in order to use an automatic heuristic for choosing the initial scale. The heuristic is described in [1], p.143. The default is ‘auto’.


The update is based on the description in [1], p.144-146.


[1] (1,2)

Nocedal, Jorge, and Stephen J. Wright. “Numerical optimization” Second Edition (2006).



Compute the product of the internal matrix with the given vector.


Return the current internal matrix.

initialize(n, approx_type)

Initialize internal matrix.

update(delta_x, delta_grad)

Update internal matrix.