Changeset 3349


Ignore:
Timestamp:
Sep 22, 2014 5:54:25 AM (6 years ago)
Author:
bradbell
Message:

Merge in fix to reverse documentation from trunk.

Location:
branches/cache
Files:
3 edited

Legend:

Unmodified
Added
Removed
  • branches/cache/cppad/local/reverse_sweep.hpp

    r3342 r3349  
    7777where \f$ n \f$ is the number of independent variables and
    7878\f$ m \f$ is the number of dependent variables.
     79We define \f$ u^{(k)} \f$ as the value of <code>x_k</code> in the previous call
     80of the form
     81<code>
     82        f.Forward(k, x_k)
     83</code>
     84We define
     85\f$ X : {\bf R}^{n \times d} \rightarrow {\bf R}^n \f$ by
     86\f[
     87        X(t, u) =  u^{(0)} + u^{(1)} t + \cdots + u^{(d)} t^d
     88\f]
     89We define
     90\f$ Y : {\bf R}^{n \times d} \rightarrow {\bf R}^m \f$ by
     91\f[
     92        Y(t, u) =  F[ X(t, u) ]
     93\f]
    7994We define the function
    80 \f$ G : {\bf R}^{n \times d} \rightarrow {\bf R} \f$ by
     95\f$ W : {\bf R}^{n \times d} \rightarrow {\bf R} \f$ by
    8196\f[
    82 G( u ) = \frac{1}{d !} \frac{ \partial^d }{ \partial t^d }
    83 \left[
    84         \sum_{i=1}^m w_i  F_i ( u^{(0)} + u^{(1)} t + \cdots + u^{(d)} t^d )
    85 \right]_{t=0}
     97W(u)
     98=
     99\sum_{k=0}^{d} ( w^{(k)} )^{\rm T}
     100        \frac{1}{k !} \frac{\partial^k}{\partial t^k} Y(0, u)
    86101\f]
    87 Note that the scale factor  1 / a d  converts
    88 the \a d-th partial derivative to the \a d-th order Taylor coefficient.
    89 This routine computes the derivative of \f$ G(u) \f$
     102(The matrix \f$ w \in {\bf R}^m \f$,
     103is defined below under the heading Partial.)
     104Note that the scale factor  1 / k  converts
     105the k-th partial derivative to the k-th order Taylor coefficient.
     106This routine computes the derivative of \f$ W(u) \f$
    90107with respect to all the Taylor coefficients
    91108\f$ u^{(k)} \f$ for \f$ k = 0 , ... , d \f$.
    92 The vector \f$ w \in {\bf R}^m \f$, and
    93 value of \f$ u \in {\bf R}^{n \times d} \f$
    94 at which the derivative is computed,
    95 are defined below.
    96109\n
    97110\n
     
    124137\b Input:
    125138The last \f$ m \f$ rows of \a Partial are inputs.
    126 The vector \f$ v \f$, used to define \f$ G(u) \f$,
     139The matrix \f$ w \f$, used to define \f$ W(u) \f$,
    127140is specified by these rows.
    128 For i = 0 , ... , m - 1, \a Partial [ ( \a num_var - m + i ) * K + d ] = v_i.
    129 For i = 0 , ... , m - 1 and for k = 0 , ... , d - 1,
    130 \a Partial [ ( \a num_var - m + i ) * K + k ] = 0.
     141For i = 0 , ... , m - 1,
     142for k = 0 , ... , d,
     143<code>Partial [ (num_var - m + i ) * K + k ] = w[i,k]</code>.
    131144\n
    132145\n
     
    140153For j = 1 , ... , n and for k = 0 , ... , d,
    141154\a Partial [ j * K + k ]
    142 is the partial derivative of \f$ G( u ) \f$ with
     155is the partial derivative of \f$ W( u ) \f$ with
    143156respect to \f$ u_j^{(k)} \f$.
    144157
  • branches/cache/omh/reverse/reverse_any.omh

    r3214 r3349  
    4949$head Notation$$
    5050
    51 $subhead x^(k)$$
     51$subhead u^(k)$$
    5252For $latex k = 0, \ldots , q-1$$,
    53 the vector $latex x^{(k)} \in B^n$$ is defined as the value of
     53the vector $latex u^{(k)} \in B^n$$ is defined as the value of
    5454$icode x_k$$ in the previous calls of the form
    5555$codei%
     
    5757%$$
    5858If there is no previous call with $latex k = 0$$,
    59 $latex x^{(0)}$$ is the value of the independent variables when the
     59$latex u^{(0)}$$ is the value of the independent variables when the
    6060corresponding
    6161AD of $icode Base$$
  • branches/cache/omh/whats_new/whats_new_14.omh

    r3339 r3349  
    5555The purpose of this section is to
    5656assist you in learning about changes between various versions of CppAD.
    57 
     57 
    5858$head cache branch$$
     59
     60$subhead 10-21$$
     61Fix a typo in documentation for
     62$cref/any order reverse/reverse_any/$$.
     63To be specific, $latex x^{(k)}$$ was changed to be $latex u^{(k)}$$.
     64
    5965$subhead 10-18$$
    6066An extra phantom (not used) variable was added to the end of the operation
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