/*
Copyright 2016 Ian Jauslin

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/

/*
  Base functions for root finding

  see integral_*.h for the values taken by ROOT_FUNC, etc...
*/


// compute the root of a real function of 1 variable using the Newton method
int ROOT_FUNC(root_newton_inplace) (ROOT_FLOAT_TYPE* out, int (*func)(ROOT_FLOAT_TYPE*, ROOT_FLOAT_TYPE, void*), int (*deriv_func)(ROOT_FLOAT_TYPE*, ROOT_FLOAT_TYPE, void*), ROOT_FLOAT_TYPE tolerance, unsigned int maxiter, void* extra_args){
  unsigned int count=0;
  ROOT_FLOAT_TYPE valf, valdf, delta, tmp;
  int ret;

  #ifdef ROOT_FLOAT_INIT
    ROOT_FLOAT_INIT(valf);
    ROOT_FLOAT_INIT(valdf);
    ROOT_FLOAT_INIT(delta);
    ROOT_FLOAT_INIT(tmp);
  #endif

  // evaluate at guess
  ret=(*func)(&valf, *out, extra_args);
  if(ret<0){
    #ifdef ROOT_FLOAT_FREE
      ROOT_FLOAT_FREE(valf);
      ROOT_FLOAT_FREE(valdf);
      ROOT_FLOAT_FREE(delta);
      ROOT_FLOAT_FREE(tmp);
    #endif
    return(ret);
  }
  // check that valf is a number
  if(! ROOT_FLOAT_ISNUMBER(valf)){
    #ifdef ROOT_FLOAT_FREE
      ROOT_FLOAT_FREE(valf);
      ROOT_FLOAT_FREE(valdf);
      ROOT_FLOAT_FREE(delta);
      ROOT_FLOAT_FREE(tmp);
    #endif
    return(LIBINUM_ERROR_NAN);
  }

  ROOT_FLOAT_ABS(delta, valf);

  // loop until tolerance is reached
  while(ROOT_FLOAT_CMP(delta, tolerance) > 0 && count < maxiter){
    // new guess
    (*deriv_func)(&valdf, *out, extra_args);
    if(ret<0){
      #ifdef ROOT_FLOAT_FREE
	ROOT_FLOAT_FREE(valf);
	ROOT_FLOAT_FREE(valdf);
	ROOT_FLOAT_FREE(delta);
	ROOT_FLOAT_FREE(tmp);
      #endif
      return(ret);
    }
    // check that valdf is a number that is not 0
    if(! ROOT_FLOAT_ISNUMBER(valdf) || ROOT_FLOAT_ISZERO(valdf)){
      #ifdef ROOT_FLOAT_FREE
	ROOT_FLOAT_FREE(valf);
	ROOT_FLOAT_FREE(valdf);
	ROOT_FLOAT_FREE(delta);
	ROOT_FLOAT_FREE(tmp);
      #endif
      return(LIBINUM_ERROR_NAN);
    }

    ROOT_FLOAT_DIV(tmp, valf, valdf);
    ROOT_FLOAT_SUB(*out, *out, tmp);
    
    // evaluate at new guess
    (*func)(&valf, *out, extra_args);
    if(ret<0){
      #ifdef ROOT_FLOAT_FREE
	ROOT_FLOAT_FREE(valf);
	ROOT_FLOAT_FREE(valdf);
	ROOT_FLOAT_FREE(delta);
	ROOT_FLOAT_FREE(tmp);
      #endif
      return(ret);
    }
    // check that valf is a number
    if(! ROOT_FLOAT_ISNUMBER(valf)){
      #ifdef ROOT_FLOAT_FREE
	ROOT_FLOAT_FREE(valf);
	ROOT_FLOAT_FREE(valdf);
	ROOT_FLOAT_FREE(delta);
	ROOT_FLOAT_FREE(tmp);
      #endif
      return(LIBINUM_ERROR_NAN);
    }

    ROOT_FLOAT_ABS(delta, valf);

    // increase counter
    count++;
  }

  // free variables
  #ifdef ROOT_FLOAT_FREE
    ROOT_FLOAT_FREE(valf);
    ROOT_FLOAT_FREE(valdf);
    ROOT_FLOAT_FREE(delta);
    ROOT_FLOAT_FREE(tmp);
  #endif

  // fail if maxiter was reached
  if(count==maxiter){
    return(LIBINUM_ERROR_MAXITER);
  }
  return(0);
}
int ROOT_FUNC(root_newton) (ROOT_FLOAT_TYPE* out, int (*func)(ROOT_FLOAT_TYPE*, ROOT_FLOAT_TYPE, void*), int (*deriv_func)(ROOT_FLOAT_TYPE*, ROOT_FLOAT_TYPE, void*), ROOT_FLOAT_TYPE init, ROOT_FLOAT_TYPE tolerance, unsigned int maxiter, void* extra_args){
  ROOT_FLOAT_SET(*out, init);
  ROOT_FUNC(root_newton_inplace) (out, func, deriv_func, tolerance, maxiter, extra_args);
  return(0);
}