Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

1-D interval location using Brent's method

`[a,gX,perf,retcode,delta,tol] = srchbre(net,X,Pd,Tl,Ai,Q,TS,dX,gX,perf,dperf,delta,tol,ch_perf)`

`srchbre`

is a linear search routine. It searches
in a given direction to locate the minimum of the performance function
in that direction. It uses a technique called Brent's technique.

`[a,gX,perf,retcode,delta,tol] = srchbre(net,X,Pd,Tl,Ai,Q,TS,dX,gX,perf,dperf,delta,tol,ch_perf)`

takes
these inputs,

`net` | Neural network |

`X` | Vector containing current values of weights and biases |

`Pd` | Delayed input vectors |

`Tl` | Layer target vectors |

`Ai` | Initial input delay conditions |

`Q` | Batch size |

`TS` | Time steps |

`dX` | Search direction vector |

`gX` | Gradient vector |

`perf` | Performance value at current |

`dperf` | Slope of performance value at current |

`delta` | Initial step size |

`tol` | Tolerance on search |

`ch_perf` | Change in performance on previous step |

and returns

`a` | Step size that minimizes performance |

`gX` | Gradient at new minimum point |

`perf` | Performance value at new minimum point |

`retcode` | Return code that has three elements. The first two elements correspond to the number of function evaluations in the two stages of the search. The third element is a return code. These have different meanings for different search algorithms. Some might not be used in this function. |

`0` Normal | |

`1` Minimum
step taken | |

`2` Maximum
step taken | |

`3` Beta
condition not met | |

`delta` | New initial step size, based on the current step size |

`tol` | New tolerance on search |

Parameters used for the Brent algorithm are

`alpha` | Scale factor that determines sufficient reduction in |

`beta` | Scale factor that determines sufficiently large step size |

`bmax` | Largest step size |

`scale_tol` | Parameter that relates the tolerance |

The defaults for these parameters are set in the training function
that calls them. See `traincgf`

, `traincgb`

, `traincgp`

, `trainbfg`

, and `trainoss`

.

Dimensions for these variables are

`Pd` |
| Each element |

`Tl` |
| Each element |

`Ai` |
| Each element |

where

`Ni ` | `=` | `net.numInputs` |

`Nl ` | `=` | `net.numLayers` |

`LD ` | `=` | `net.numLayerDelays` |

`Ri ` | `=` | `net.inputs{i}.size` |

`Si` | `=` | `net.layers{i}.size` |

`Vi` | `=` | ` net.targets{i}.size` |

`Dij` | `=` | `Ri * length(net.inputWeights{i,j}.delays)` |

Here is a problem consisting of inputs `p`

and
targets `t`

to be solved with a network.

p = [0 1 2 3 4 5]; t = [0 0 0 1 1 1];

A two-layer feed-forward network is created. The network's
input ranges from `[0 to 10]`

. The first layer has
two `tansig`

neurons, and the second layer has one `logsig`

neuron.
The `traincgf`

network training function and the `srchbac`

search
function are to be used.

net = newff([0 5],[2 1],{'tansig','logsig'},'traincgf'); a = sim(net,p)

net.trainParam.searchFcn = 'srchbre'; net.trainParam.epochs = 50; net.trainParam.show = 10; net.trainParam.goal = 0.1; net = train(net,p,t); a = sim(net,p)

You can create a standard network that uses `srchbre`

with `newff`

, `newcf`

,
or `newelm`

. To prepare a custom network to be trained
with `traincgf`

, using the line search function `srchbre`

,

Set

`net.trainFcn`

to`'traincgf'`

. This sets`net.trainParam`

to`traincgf`

's default parameters.Set

`net.trainParam.searchFcn`

to`'srchbre'`

.

The `srchbre`

function can be used with any
of the following training functions: `traincgf`

, `traincgb`

, `traincgp`

, `trainbfg`

, `trainoss`

.

`srchbre`

brackets the minimum of the performance
function in the search direction `dX`

, using Brent's
algorithm, described on page 46 of Scales (see reference below). It
is a hybrid algorithm based on the golden section search and the quadratic
approximation.

Scales, L.E., *Introduction to Non-Linear Optimization*,
New York, Springer-Verlag, 1985

Was this topic helpful?