#! /usr/bin/python3
# Last edited on 2021-04-03 14:59:46 by jstolfi

# Computes the combination of fertilizers to get 
# specified N-P-K amounts.

import rn
import rmxn
import sys
from math import sqrt, sin, cos, floor, ceil, exp, log, inf, nan, pi

def main():
  
  # Get the desired N,P,K amounts (grams)
  N = int(sys.argv[1])
  P = int(sys.argv[2])
  K = int(sys.argv[3])
  
  b = [ N, P, K ]
  
  # Define the matrix of NPK contents and names of available fertilizers:
  M = [
      [ 0.05, 0.15, 0.45 ],
      [ 0.30, 0.10, 0.10 ],
      [ 0.10, 0.54, 0.10 ],
      [ 0.45, 0.00, 0.00 ],
    ]
  Fname = [ 
      "Plantafol 05-15-45",
      "Plantafol 30-10-10",
      "Plantafol 10-54-10",
      "Urea"
    ]
    
  # Solve the system obtaining the two extreme solutions:
  x0, x1 = solve43(M, b)
  sys.stderr.write("Raw solutions:\n")
  printsol(sys.stderr, x0, x1, M, Fname)
  
  # Trim the solution interval to positive amounts:
  x0, x1 = clipsol(x0, x1)
  sys.stderr.write("Clipped solutions:\n")
  printsol(sys.stderr, x0, x1, M, Fname)
  return 0
  # ----------------------------------------------------------------------
  
def solve43(M, b):
  # Solves the system {x M = b} where {M} is 4 by 3, {x} is a 4-vector,
  # {b} is a 3-vector.
  
  assert len(M) == 4
  assert len(b) == 3
  
  # Solve using 0 of the last line:
  Q = M[0:3]
  Qinv = rmxn.inv_3(Q)
  x0 = rmxn.map_row(b, Qinv)
  x0 = x0 + [ 0, ]
  
  # Solve using 0 of the first line:
  P = M[1:]
  Pinv = rmxn.inv_3(P)
  x1 = rmxn.map_row(b, Pinv)
  x1 = [ 0, ] + x1
  return x0, x1
  # ----------------------------------------------------------------------

def clipsol(x0, x1):
  # Given two extreme solutions, clip the segment
  # to positive solutions:
  m = len(x0)
  assert len(x1) == m
  
  for k in range(m):
    if x0[k] < 0:
      r0 = -x0[k]/(x1[k]-x0[k])
      x0 = rn.mix(1-r0, x0, r0, x1)
    if x1[k] < 0:
      r1 = -x1[k]/(x0[k]-x1[k])
      x1 = rn.mix(1-r1, x1, r1, x0)

  return x0, x1
  # ----------------------------------------------------------------------
  
def printsol(wr, x0, x1, M, Fname):
  # Prints the amounts of each fertilizer, in the two extreme formulations.
  m = len(x0)
  assert len(x1) == m
  assert len(Fname) == m
  for k in range(m):
    wr.write("%5.1f %5.1f %s\n" % (x0[k], x1[k], Fname[k]))
  # Check the solutions:
  v0 = rmxn.map_row(x0, M)
  v1 = rmxn.map_row(x1, M)
  for k in range(3):
    wr.write("%5.1f %5.1f %s\n" % (v0[k], v1[k], "NPK"[k]))
  
  return
  # ----------------------------------------------------------------------
  
main()