#!/usr/bin/env python
# coding: utf-8

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# # The NRPy+ code required to generate the needed C code for the lowering operator: $g_{ij} \beta^i$, with the result set to C variables "`betaD0out`", "`betaD1out`", and "`betaD2out`" 
# 
# ## *Courtesy Zach Etienne*

# In[1]:


# The NRPy_param_funcs module sets up global structures that manage free parameters within NRPy+
import NRPy_param_funcs as par   # NRPy+: Parameter interface
# The indexedexp module defines various functions for defining and managing indexed quantities like tensors and pseudotensors
import indexedexp as ixp         # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support
# The grid module defines various parameters related to a numerical grid or the dimensionality of indexed expressions
# For example, it declares the parameter DIM, which specifies the dimensionality of the indexed expression
import grid as gri               # NRPy+: Functions having to do with numerical grids
from outputC import outputC      # NRPy+: Basic C code output functionality

# Set the dimension to 3
par.set_parval_from_str("DIM",3)

# Declare rank-1 contravariant ("U" and "D") vectors
betaU = ixp.declarerank1("betaU")
betaD = ixp.zerorank1()

# Declare h_{ij}=hDD[i][j] and h^{ij}=hUU[i][j]
hDD = ixp.declarerank2("hDD","sym01")

# Get the dimension we just set (should be set to 3).
DIM = par.parval_from_str("DIM")

for i in range(DIM):
    for j in range(DIM):
        betaD[j] += betaU[i]*hDD[i][j]

outputC(betaD,["betaD0out","betaD1out","betaD2out"])