SUBROUTINE NF01BY( CJTE, NSMP, NZ, L, IPAR, LIPAR, WB, LWB, Z,
$ LDZ, E, J, LDJ, JTE, DWORK, LDWORK, INFO )
C
C PURPOSE
C
C To compute the Jacobian of the error function for a neural network
C of the structure
C
C - tanh(w1*z+b1) -
C / : \
C z --- : --- sum(ws(i)*...)+ b(n+1) --- y,
C \ : /
C - tanh(wn*z+bn) -
C
C for the single-output case. The Jacobian has the form
C
C d e(1) / d WB(1) ... d e(1) / d WB(NWB)
C J = : : ,
C d e(NSMP) / d WB(1) ... d e(NSMP) / d WB(NWB)
C
C where e(z) is the error function, WB is the set of weights and
C biases of the network (for the considered output), and NWB is
C the number of elements of this set, NWB = IPAR(1)*(NZ+2)+1
C (see below).
C
C In the multi-output case, this routine should be called for each
C output.
C
C NOTE: this routine must have the same arguments as SLICOT Library
C routine NF01BD.
C
C ARGUMENTS
C
C Mode Parameters
C
C CJTE CHARACTER*1
C Specifies whether the matrix-vector product J'*e should be
C computed or not, as follows:
C = 'C' : compute J'*e;
C = 'N' : do not compute J'*e.
C
C Input/Output Parameters
C
C NSMP (input) INTEGER
C The number of training samples. NSMP >= 0.
C
C NZ (input) INTEGER
C The length of each input sample. NZ >= 0.
C
C L (input) INTEGER
C The length of each output sample.
C Currently, L must be 1.
C
C IPAR (input/output) INTEGER array, dimension (LIPAR)
C The integer parameters needed.
C On entry, the first element of this array must contain
C a value related to the number of neurons, n; specifically,
C n = abs(IPAR(1)), since setting IPAR(1) < 0 has a special
C meaning (see below).
C On exit, if IPAR(1) < 0 on entry, then no computations are
C performed, except the needed tests on input parameters,
C but the following values are returned:
C IPAR(1) contains the length of the array J, LJ;
C LDJ contains the leading dimension of array J.
C Otherwise, IPAR(1) and LDJ are unchanged on exit.
C
C LIPAR (input) INTEGER
C The length of the vector IPAR. LIPAR >= 1.
C
C WB (input) DOUBLE PRECISION array, dimension (LWB)
C The leading NWB = IPAR(1)*(NZ+2)+1 part of this array
C must contain the weights and biases of the network,
C WB = ( w(1,1), ..., w(1,NZ), ..., w(n,1), ..., w(n,NZ),
C ws(1), ..., ws(n), b(1), ..., b(n+1) ),
C where w(i,j) are the weights of the hidden layer,
C ws(i) are the weights of the linear output layer and
C b(i) are the biases.
C
C LWB (input) INTEGER
C The length of array WB. LWB >= NWB.
C
C Z (input) DOUBLE PRECISION array, dimension (LDZ, NZ)
C The leading NSMP-by-NZ part of this array must contain the
C set of input samples,
C Z = ( Z(1,1),...,Z(1,NZ); ...; Z(NSMP,1),...,Z(NSMP,NZ) ).
C
C LDZ INTEGER
C The leading dimension of array Z. LDZ >= MAX(1,NSMP).
C
C E (input) DOUBLE PRECISION array, dimension (NSMP)
C If CJTE = 'C', this array must contain the error vector e.
C If CJTE = 'N', this array is not referenced.
C
C J (output) DOUBLE PRECISION array, dimension (LDJ, NWB)
C The leading NSMP-by-NWB part of this array contains the
C Jacobian of the error function.
C
C LDJ INTEGER
C The leading dimension of array J. LDJ >= MAX(1,NSMP).
C Note that LDJ is an input parameter, except for
C IPAR(1) < 0 on entry, when it is an output parameter.
C
C JTE (output) DOUBLE PRECISION array, dimension (NWB)
C If CJTE = 'C', this array contains the matrix-vector
C product J'*e.
C If CJTE = 'N', this array is not referenced.
C
C Workspace
C
C DWORK DOUBLE PRECISION array, dimension (LDWORK)
C This argument is included for combatibility with SLICOT
C Library routine NF01BD.
C
C LDWORK INTEGER
C Normally, the length of the array DWORK. LDWORK >= 0.
C
C Error Indicator
C
C INFO INTEGER
C = 0: successful exit;
C < 0: if INFO = -i, the i-th argument had an illegal
C value.
C
C METHOD
C
C The Jacobian is computed analytically.
C
C CONTRIBUTORS
C
C A. Riedel, R. Schneider, Chemnitz University of Technology,
C Oct. 2000, during a stay at University of Twente, NL.
C V. Sima, Research Institute for Informatics, Bucharest, Mar. 2001.
C
C REVISIONS
C
C -
C
C KEYWORDS
C
C Input output description, neural network, nonlinear system,
C optimization, system response.
C
C ******************************************************************
C
C .. Parameters ..
DOUBLE PRECISION ZERO, ONE, TWO
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0 )
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(*)
C .. Local Scalars ..
LOGICAL WJTE
INTEGER BP1, DI, I, IB, K, M, NN, NWB, WS
DOUBLE PRECISION BIGNUM, SMLNUM, TMP
C .. External Functions ..
DOUBLE PRECISION DLAMCH
LOGICAL LSAME
EXTERNAL DLAMCH, LSAME
C .. External Subroutines ..
EXTERNAL DCOPY, DGEMM, DGEMV, DLABAD, XERBLA
C .. Intrinsic Functions ..
INTRINSIC ABS, EXP, LOG, MAX, MIN
C ..
C .. Executable Statements ..
C
WJTE = LSAME( CJTE, 'C' )
INFO = 0
NN = IPAR(1)
NWB = NN*( NZ + 2 ) + 1
IF( .NOT.( WJTE .OR. LSAME( CJTE, 'N' ) ) ) THEN
INFO = -1
ELSEIF ( NSMP.LT.0 ) THEN
INFO = -2
ELSEIF ( NZ.LT.0 ) THEN
INFO = -3
ELSEIF ( L.NE.1 ) THEN
INFO = -4
ELSEIF ( LIPAR.LT.1 ) THEN
INFO = -6
ELSEIF ( IPAR(1).LT.0 ) THEN
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'NF01BY', -INFO )
ELSE
IPAR(1) = NSMP*( ABS( NN )*( NZ + 2 ) + 1 )
LDJ = NSMP
ENDIF
RETURN
ELSEIF ( LWB.LT.NWB ) THEN
INFO = -8
ELSEIF ( LDZ.LT.MAX( 1, NSMP ) ) THEN
INFO = -10
ELSEIF ( LDJ.LT.MAX( 1, NSMP ) ) THEN
INFO = -13
ENDIF
C
C Return if there are illegal arguments.
C
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'NF01BY', -INFO )
RETURN
ENDIF
C
C Quick return if possible.
C
IF ( MIN( NSMP, NZ ).EQ.0 )
$ RETURN
C
C Set parameters to avoid overflows and increase accuracy for
C extreme values.
C
SMLNUM = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
BIGNUM = ONE / SMLNUM
CALL DLABAD( SMLNUM, BIGNUM )
SMLNUM = LOG( SMLNUM )
BIGNUM = LOG( BIGNUM )
C
WS = NZ*NN + 1
IB = WS + NN
BP1 = IB + NN
C
J(1, BP1) = ONE
CALL DCOPY( NSMP, J(1, BP1), 0, J(1, BP1), 1 )
C
DO 10 I = 0, NN - 1
CALL DCOPY( NSMP, WB(IB+I), 0, J(1, WS+I), 1 )
10 CONTINUE
C
CALL DGEMM( 'NoTranspose', 'NoTranspose', NSMP, NN, NZ, -TWO, Z,
$ LDZ, WB, NZ, -TWO, J(1, WS), LDJ )
DI = 1
C
DO 50 I = 0, NN - 1
C
DO 20 K = 1, NSMP
TMP = J(K, WS+I)
IF ( ABS( TMP ).GE.BIGNUM ) THEN
IF ( TMP.GT.ZERO ) THEN
J(K, WS+I) = -ONE
ELSE
J(K, WS+I) = ONE
END IF
ELSE IF ( ABS( TMP ).LE.SMLNUM ) THEN
J(K, WS+I) = ZERO
ELSE
J(K, WS+I) = TWO/( ONE + EXP( TMP ) ) - ONE
END IF
J(K, IB+I) = WB(WS+I)*( ONE - J(K, WS+I)**2 )
20 CONTINUE
C
DO 40 K = 0, NZ - 1
C
DO 30 M = 1, NSMP
J(M, DI+K) = J(M, IB+I)*Z(M, K+1)
30 CONTINUE
C
40 CONTINUE
C
DI = DI + NZ
50 CONTINUE
C
IF ( WJTE ) THEN
C
C Compute J'e.
C
CALL DGEMV( 'Transpose', NSMP, NWB, ONE, J, LDJ, E, 1, ZERO,
$ JTE, 1 )
END IF
C
RETURN
C
C *** Last line of NF01BY ***
END