NF01BY

Computing the Jacobian of the error function for a neural network (one output variable)

Purpose

  To compute the Jacobian of the error function for a neural network
  of the structure

          - tanh(w1*z+b1) -
        /      :            \
      z ---    :          --- sum(ws(i)*...)+ b(n+1)  --- y,
        \      :            /
          - tanh(wn*z+bn) -

  for the single-output case. The Jacobian has the form

             d e(1)  / d WB(1)   ...    d e(1)  / d WB(NWB)
      J =            :                          :           ,
           d e(NSMP) / d WB(1)   ...  d e(NSMP) / d WB(NWB)

  where e(z) is the error function, WB is the set of weights and
  biases of the network (for the considered output), and NWB is
  the number of elements of this set, NWB = IPAR(1)*(NZ+2)+1
  (see below).

  In the multi-output case, this routine should be called for each
  output.

  NOTE: this routine must have the same arguments as SLICOT Library
  routine NF01BD.

      SUBROUTINE NF01BY( CJTE, NSMP, NZ, L, IPAR, LIPAR, WB, LWB, Z,
     $                   LDZ, E, J, LDJ, JTE, DWORK, LDWORK, INFO )
C     .. Scalar Arguments ..
      CHARACTER         CJTE
      INTEGER           INFO, L, LDJ, LDWORK, LDZ, LIPAR, LWB, NSMP, NZ
C     .. Array Arguments ..
      DOUBLE PRECISION  DWORK(*), E(*), J(LDJ,*), JTE(*), WB(*),
     $                  Z(LDZ,*)
      INTEGER           IPAR(*)

Mode Parameters

  CJTE    CHARACTER*1
          Specifies whether the matrix-vector product J'*e should be
          computed or not, as follows:
          = 'C' :  compute J'*e;
          = 'N' :  do not compute J'*e.

  NSMP    (input) INTEGER
          The number of training samples.  NSMP >= 0.

  NZ      (input) INTEGER
          The length of each input sample.  NZ >= 0.

  L       (input) INTEGER
          The length of each output sample.
          Currently, L must be 1.

  IPAR    (input/output) INTEGER array, dimension (LIPAR)
          The integer parameters needed.
          On entry, the first element of this array must contain
          a value related to the number of neurons, n; specifically,
          n = abs(IPAR(1)), since setting IPAR(1) < 0 has a special
          meaning (see below).
          On exit, if IPAR(1) < 0 on entry, then no computations are
          performed, except the needed tests on input parameters,
          but the following values are returned:
          IPAR(1) contains the length of the array J, LJ;
          LDJ     contains the leading dimension of array J.
          Otherwise, IPAR(1) and LDJ are unchanged on exit.

  LIPAR   (input) INTEGER
          The length of the vector IPAR.  LIPAR >= 1.

  WB      (input) DOUBLE PRECISION array, dimension (LWB)
          The leading NWB = IPAR(1)*(NZ+2)+1 part of this array
          must contain the weights and biases of the network,
          WB = ( w(1,1), ..., w(1,NZ), ..., w(n,1), ...,  w(n,NZ),
                 ws(1), ..., ws(n), b(1), ..., b(n+1) ),
          where w(i,j) are the weights of the hidden layer,
          ws(i) are the weights of the linear output layer and
          b(i) are the biases.

  LWB     (input) INTEGER
          The length of array WB.  LWB >= NWB.

  Z       (input) DOUBLE PRECISION array, dimension (LDZ, NZ)
          The leading NSMP-by-NZ part of this array must contain the
          set of input samples,
          Z = ( Z(1,1),...,Z(1,NZ); ...; Z(NSMP,1),...,Z(NSMP,NZ) ).

  LDZ     INTEGER
          The leading dimension of array Z.  LDZ >= MAX(1,NSMP).

  E       (input) DOUBLE PRECISION array, dimension (NSMP)
          If CJTE = 'C', this array must contain the error vector e.
          If CJTE = 'N', this array is not referenced.

  J       (output) DOUBLE PRECISION array, dimension (LDJ, NWB)
          The leading NSMP-by-NWB part of this array contains the
          Jacobian of the error function.

  LDJ     INTEGER
          The leading dimension of array J.  LDJ >= MAX(1,NSMP).
          Note that LDJ is an input parameter, except for
          IPAR(1) < 0 on entry, when it is an output parameter.

  JTE     (output) DOUBLE PRECISION array, dimension (NWB)
          If CJTE = 'C', this array contains the matrix-vector
          product J'*e.
          If CJTE = 'N', this array is not referenced.

  DWORK   DOUBLE PRECISION array, dimension (LDWORK)
          This argument is included for combatibility with SLICOT
          Library routine NF01BD.

  LDWORK  INTEGER
          Normally, the length of the array DWORK.  LDWORK >= 0.

  INFO    INTEGER
          = 0:  successful exit;
          < 0:  if INFO = -i, the i-th argument had an illegal
                value.

  The Jacobian is computed analytically.

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Program Text

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