Streamlit - 没有名为 'seaborn' 的模块错误
Streamlit - No module named 'seaborn' error
我在 python 和 Streamlit 中创建了一个使用 seaborn 的应用程序，但是当我将它部署到 Streamlit 云时，我收到一条错误消息 No module named 'seaborn' 。如果我注释掉 seaborn，其他模块（例如 matplotlib）也会出现同样的错误。当我在本地启动该应用程序进行测试时，该应用程序运行良好。我已将错误作为屏幕截图和我的代码提供（它很长 - 我对 python 还是个新手，做事相当直截了当）。如果有人能解释我如何修复这个错误，我将不胜感激。
谢谢
错误截图：
代码示例：
import streamlit as st
import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
st.title("Rayleigh Fractionation Model")
st.write("-------------")
st.write("")
#####################################################################################################
# Initial melt composition
#####################################################################################################
st.subheader("Initial Composition and Model Results")
st.write("")
with st.expander("Starting silicate melt composition (Default is OIB)"):
col1_a, col2_a, col3_a, col4_a = st.columns([1, 1, 1, 1])
with col1_a:
Th_sil_i = st.number_input("Th (ppm)", min_value = 0.0, value = 4.0)
Nb_sil_i = st.number_input("Nb (ppm)", min_value = 0.0, value = 48.0)
La_sil_i = st.number_input("La (ppm)", min_value = 0.0, value = 37.0)
Ce_sil_i = st.number_input("Ce (ppm)", min_value = 0.0, value = 80.0)
Pr_sil_i = st.number_input("Pr (ppm)", min_value = 0.0, value = 9.7)
Nd_sil_i = st.number_input("Nd (ppm)", min_value = 0.0, value = 38.5)
with col2_a:
Zr_sil_i = st.number_input("Zr (ppm)", min_value = 0.0, value = 280.0)
Hf_sil_i = st.number_input("Hf (ppm)", min_value = 0.0, value = 7.8)
Sm_sil_i = st.number_input("Sm (ppm)", min_value = 0.0, value = 10.0)
Eu_sil_i = st.number_input("Eu (ppm)", min_value = 0.0, value = 3.0)
Ti_sil_i = st.number_input("Ti (ppm)", min_value = 0.0, value = 17200.0)
Gd_sil_i = st.number_input("Gd (ppm)", min_value = 0.0, value = 7.62)
with col3_a:
Tb_sil_i = st.number_input("Tb (ppm)", min_value = 0.0, value = 1.05)
Dy_sil_i = st.number_input("Dy (ppm)", min_value = 0.0, value = 5.6)
Y_sil_i = st.number_input("Y (ppm)", min_value = 0.0, value = 29.0)
Ho_sil_i = st.number_input("Ho (ppm)", min_value = 0.0, value = 1.06)
Er_sil_i = st.number_input("Er (ppm)", min_value = 0.0, value = 2.62)
Tm_sil_i = st.number_input("Tm (ppm)", min_value = 0.0, value = 0.35)
with col4_a:
Yb_sil_i = st.number_input("Yb (ppm)", min_value = 0.0, value = 2.16)
Lu_sil_i = st.number_input("Lu (ppm)", min_value = 0.0, value = 0.3)
V_sil_i = st.number_input("V (ppm)", min_value = 0.0, value = 500.0)
Sc_sil_i = st.number_input("Sc (ppm)", min_value = 0.0, value = 100.0)
initial_melt = {
"Elements":["Th", "Nb", "La", "Ce", "Pr", "Nd", "Zr", "Hf", "Sm", "Eu", "Ti", "Gd", "Tb", "Dy", "Y", "Ho", "Er", "Tm", "Yb", "Lu", "V", "Sc"],
"Concentration (ppm)":[Th_sil_i, Nb_sil_i, La_sil_i, Ce_sil_i, Pr_sil_i, Nd_sil_i, Zr_sil_i, Hf_sil_i, Sm_sil_i, Eu_sil_i, Ti_sil_i, Gd_sil_i, Tb_sil_i, Dy_sil_i, Y_sil_i, Ho_sil_i, Er_sil_i, Tm_sil_i, Yb_sil_i, Lu_sil_i, V_sil_i, Sc_sil_i]
}
initial_melt_df = pd.DataFrame(data = initial_melt)
#####################################################################################################
# Fractionating minerals
#####################################################################################################
F_sil_remaining = np.arange(0.1, 1.0+0.001, 0.001)
st.sidebar.write("**Choose the minerals that are fractionating**")
P_Cpx = st.sidebar.number_input("Clinopyroxene", 0.0, 1.0, 0.0, 0.05)
P_Pl = st.sidebar.number_input("Plagioclase", 0.0, 1.0, 0.0, 0.05)
P_Opx = st.sidebar.number_input("Orthopyroxene", 0.0, 1.0, 0.0, 0.05)
P_Ol = st.sidebar.number_input("Olivine", 0.0, 1.0, 0.0, 0.05)
P_Mt = st.sidebar.number_input("Magnetite", 0.0, 1.0, 0.0, 0.05)
P_Ilm = st.sidebar.number_input("Ilmenite", 0.0, 1.0, 0.0, 0.05)
P_Ap = st.sidebar.number_input("Apatite", 0.0, 1.0, 0.0, 0.05)
P_Chr = st.sidebar.number_input("Chromite", 0.0, 1.0, 0.0, 0.05)
P_Maj_gn = st.sidebar.number_input("Majorite garnet", 0.0, 1.0, 0.0, 0.05)
P_Amp = st.sidebar.number_input("Amphibole", 0.0, 1.0, 0.0, 0.05)
Total = P_Cpx + P_Pl + P_Opx + P_Ol + P_Mt + P_Ilm + P_Ap + P_Chr + P_Maj_gn + P_Amp
st.sidebar.write(f"Total minerals fractionating = {Total}")
st.sidebar.write("*The total minerals fractionating should not be greater than 1*")
st.sidebar.write("--------------")
st.sidebar.write("")
st.sidebar.write("**Created by:**")
st.sidebar.write("***Matthew Brzozowski, PhD***")
st.sidebar.write("***matt.brzozow@gmail.com***")
#####################################################################################################
# Partition coefficients
#####################################################################################################
# Partition coefficients for different minerals
# Kd values from Bedard et al. (2009) --> Most minerals
# The D values are appropriate for a system corresponding to a rock with molar An = 0.709, clinopyroxene Aliv = 0.04, and melt MgO = 5.47 and SiO2 = 53.6 wt.%.
# Kd values from Corgne and Wood (2004) --> Majorite garnet
# Fe-, Al-rich peridotite
# Kd values from McKenzie and O'Nions (1991) --> Amphibole
# Basalt
D_Th_Cpx = 0.0225 # Bedard et al. (2009)
D_Nb_Cpx = 0.0098 # Bedard et al. (2009)
D_La_Cpx = 0.1 # Bedard et al. (2009)
D_Ce_Cpx = 0.16 # Bedard et al. (2009)
D_Nd_Cpx = 0.338 # Bedard et al. (2009)
D_Zr_Cpx = 0.022 # Bedard et al. (2009)
D_Sm_Cpx = 0.53 # Bedard et al. (2009)
D_Eu_Cpx = 0.04 # Bedard et al. (2009)
D_Ti_Cpx = 0.213 # Bedard et al. (2009)
D_Gd_Cpx = 0.673 # Bedard et al. (2009)
D_Tb_Cpx = 0.721 # Bedard et al. (2009)
D_Y_Cpx = 0.752 # Bedard et al. (2009)
D_Yb_Cpx = 0.678 # Bedard et al. (2009)
D_Lu_Cpx = 0.642 # Bedard et al. (2009)
D_V_Cpx = 0.49 # Bedard et al. (2009)
D_Pr_Cpx = 0.240 # Bedard et al. (2009)
D_Dy_Cpx = 0.747 # Bedard et al. (2009)
D_Ho_Cpx = 0.751 # Bedard et al. (2009)
D_Er_Cpx = 0.737 # Bedard et al. (2009)
D_Tm_Cpx = 0.711 # Bedard et al. (2009)
D_Sc_Cpx = 1.11 # Bedard et al. (2009)
D_Hf_Cpx = 0.050 # Bedard et al. (2009)
D_Th_Pl = 0.0162 # Bedard et al. (2009)
D_Nb_Pl = 0.00328 # Bedard et al. (2009)
D_La_Pl = 0.0238 # Bedard et al. (2009)
D_Ce_Pl = 0.036 # Bedard et al. (2009)
D_Nd_Pl = 0.0111 # Bedard et al. (2009)
D_Zr_Pl = 0.00048 # Bedard et al. (2009)
D_Sm_Pl = 0.0141 # Bedard et al. (2009)
D_Eu_Pl = 0.0872 # Bedard et al. (2009)
D_Ti_Pl = 0.0243 # Bedard et al. (2009)
D_Gd_Pl = 0.0223 # Bedard et al. (2009)
D_Tb_Pl = 0.0118 # Bedard et al. (2009)
D_Y_Pl = 0.0087 # Bedard et al. (2009)
D_Yb_Pl = 0.0039 # Bedard et al. (2009)
D_Lu_Pl = 0.0038 # Bedard et al. (2009)
D_V_Pl = 0 # Bedard et al. (2009)
D_Pr_Pl = 0.0271 # Bedard et al. (2009)
D_Dy_Pl = 0.0159 # Bedard et al. (2009)
D_Ho_Pl = 0.0256 # Bedard et al. (2009)
D_Er_Pl = 0.0115 # Bedard et al. (2009)
D_Tm_Pl = 0.0192 # Bedard et al. (2009)
D_Sc_Pl = 0.00106 # Bedard et al. (2009)
D_Hf_Pl = 0.0042 # Bedard et al. (2009)
D_Th_Opx = 0.0064 # Bedard et al. (2009)
D_Nb_Opx = 0.015 # Bedard et al. (2009)
D_La_Opx = 0.00328 # Bedard et al. (2009)
D_Ce_Opx = 0.00552 # Bedard et al. (2009)
D_Nd_Opx = 0.0142 # Bedard et al. (2009)
D_Zr_Opx = 0.0167 # Bedard et al. (2009)
D_Sm_Opx = 0.0293 # Bedard et al. (2009)
D_Eu_Opx = 0.0227 # Bedard et al. (2009)
D_Ti_Opx = 0.201 # Bedard et al. (2009)
D_Gd_Opx = 0.051 # Bedard et al. (2009)
D_Tb_Opx = 0.0656 # Bedard et al. (2009)
D_Y_Opx = 0.0953 # Bedard et al. (2009)
D_Yb_Opx = 0.16 # Bedard et al. (2009)
D_Lu_Opx = 0.177 # Bedard et al. (2009)
D_V_Opx = 0.453 # Bedard et al. (2009)
D_Pr_Opx = 0.0090 # Bedard et al. (2009)
D_Dy_Opx = 0.0831 # Bedard et al. (2009)
D_Ho_Opx = 0.102 # Bedard et al. (2009)
D_Er_Opx = 0.121 # Bedard et al. (2009)
D_Tm_Opx = 0.141 # Bedard et al. (2009)
D_Sc_Opx = 1.068 # Bedard et al. (2009)
D_Hf_Opx = 0.0408 # Bedard et al. (2009)
D_Th_Ol = 0.0346 # Bedard et al. (2009)
D_Nb_Ol = 0.00491 # Bedard et al. (2009)
D_La_Ol = 0.00008 # Bedard et al. (2009)
D_Ce_Ol = 0.00019 # Bedard et al. (2009)
D_Nd_Ol = 0.00093 # Bedard et al. (2009)
D_Zr_Ol = 0.0319 # Bedard et al. (2009)
D_Sm_Ol = 0.0031 # Bedard et al. (2009)
D_Eu_Ol = 0.0111 # Bedard et al. (2009)
D_Ti_Ol = 0.0334 # Bedard et al. (2009)
D_Gd_Ol = 0.00784 # Bedard et al. (2009)
D_Tb_Ol = 0.0119 # Bedard et al. (2009)
D_Y_Ol = 0.0222 # Bedard et al. (2009)
D_Yb_Ol = 0.0521 # Bedard et al. (2009)
D_Lu_Ol = 0.0621 # Bedard et al. (2009)
D_V_Ol = 0.15 # Bedard et al. (2009)
D_Pr_Ol = 0.00043 # Bedard et al. (2009)
D_Dy_Ol = 0.0177 # Bedard et al. (2009)
D_Ho_Ol = 0.0247 # Bedard et al. (2009)
D_Er_Ol = 0.0330 # Bedard et al. (2009)
D_Tm_Ol = 0.0423 # Bedard et al. (2009)
D_Sc_Ol = 0.29 # Bedard et al. (2009)
D_Hf_Ol = 0.0139 # Bedard et al. (2009)
D_Th_Mt = 0.0077 # Bedard et al. (2009)
D_Nb_Mt = 0.0764 # Bedard et al. (2009)
D_La_Mt = 0.015 # Bedard et al. (2009)
D_Ce_Mt = 0.016 # Bedard et al. (2009)
D_Nd_Mt = 0.026 # Bedard et al. (2009)
D_Zr_Mt = 0.084 # Bedard et al. (2009)
D_Sm_Mt = 0.024 # Bedard et al. (2009)
D_Eu_Mt = 0.025 # Bedard et al. (2009)
D_Ti_Mt = 1.49 # Bedard et al. (2009)
D_Gd_Mt = 0.018 # Bedard et al. (2009)
D_Tb_Mt = 0.019 # Bedard et al. (2009)
D_Y_Mt = 0.018 # Bedard et al. (2009)
D_Yb_Mt = 0.018 # Bedard et al. (2009)
D_Lu_Mt = 0.018 # Bedard et al. (2009)
D_V_Mt = 0.64 # Bedard et al. (2009)
D_Pr_Mt = 0.018 # Bedard et al. (2009)
D_Dy_Mt = 0.018 # Bedard et al. (2009)
D_Ho_Mt = 0.018 # Bedard et al. (2009)
D_Er_Mt = 0.018 # Bedard et al. (2009)
D_Tm_Mt = 0.018 # Bedard et al. (2009)
D_Sc_Mt = 1.10 # Bedard et al. (2009)
D_Hf_Mt = 0.076 # Bedard et al. (2009)
D_Th_Ilm = 0.105 # Bedard et al. (2009)
D_Nb_Ilm = 1.62 # Bedard et al. (2009)
D_La_Ilm = 0.0027 # Bedard et al. (2009)
D_Ce_Ilm = 0.0046 # Bedard et al. (2009)
D_Nd_Ilm = 0.012 # Bedard et al. (2009)
D_Zr_Ilm = 0.35 # Bedard et al. (2009)
D_Sm_Ilm = 0.025 # Bedard et al. (2009)
D_Eu_Ilm = 0.0028 # Bedard et al. (2009)
D_Ti_Ilm = float()
D_Gd_Ilm = 0.0428 # Bedard et al. (2009)
D_Tb_Ilm = 0.0546 # Bedard et al. (2009)
D_Y_Ilm = 0.0777 # Bedard et al. (2009)
D_Yb_Ilm = 0.125 # Bedard et al. (2009)
D_Lu_Ilm = 0.137 # Bedard et al. (2009)
D_V_Ilm = 10.3 # Bedard et al. (2009)
D_Pr_Ilm = 0.0076 # Bedard et al. (2009)
D_Dy_Ilm = 0.0683 # Bedard et al. (2009)
D_Ho_Ilm = 0.0827 # Bedard et al. (2009)
D_Er_Ilm = 0.0971 # Bedard et al. (2009)
D_Tm_Ilm = 0.111 # Bedard et al. (2009)
D_Sc_Ilm = 1.91 # Bedard et al. (2009)
D_Hf_Ilm = 0.42 # Bedard et al. (2009)
D_Th_Ap = 0.835 # Bedard et al. (2009)
D_Nb_Ap = 0.00295 # Bedard et al. (2009)
D_La_Ap = 2.425 # Bedard et al. (2009)
D_Ce_Ap = 2.78 # Bedard et al. (2009)
D_Nd_Ap = 16.8 # Bedard et al. (2009)
D_Zr_Ap = 0.067 # Bedard et al. (2009)
D_Sm_Ap = 4.67 # Bedard et al. (2009)
D_Eu_Ap = 7.36 # Bedard et al. (2009)
D_Ti_Ap = 0.047 # Bedard et al. (2009)
D_Gd_Ap = 4.05 # Bedard et al. (2009)
D_Tb_Ap = 15.2 # Bedard et al. (2009)
D_Y_Ap = 2.285 # Bedard et al. (2009)
D_Yb_Ap = 1.5 # Bedard et al. (2009)
D_Lu_Ap = 0.96 # Bedard et al. (2009)
D_V_Ap = 0.022 # Bedard et al. (2009)
D_Pr_Ap = 14.0 # Bedard et al. (2009)
D_Dy_Ap = 12.9 # Bedard et al. (2009)
D_Ho_Ap = 10.8 # Bedard et al. (2009)
D_Er_Ap = 8.79 # Bedard et al. (2009)
D_Tm_Ap = 7.14 # Bedard et al. (2009)
D_Sc_Ap = 0.0258 # Bedard et al. (2009)
D_Hf_Ap = 89 # Bedard et al. (2009)
D_Th_Chr = 0.001 # Bedard et al. (2009)
D_Nb_Chr = 0.01 # Bedard et al. (2009)
D_La_Chr = 0.0006 # Bedard et al. (2009)
D_Ce_Chr = 0.0006 # Bedard et al. (2009)
D_Nd_Chr = 0.0006 # Bedard et al. (2009)
D_Zr_Chr = 0.015 # Bedard et al. (2009)
D_Sm_Chr = 0.0006 # Bedard et al. (2009)
D_Eu_Chr = 0.0006 # Bedard et al. (2009)
D_Ti_Chr = 0.125 # Bedard et al. (2009)
D_Gd_Chr = 0.0006 # Bedard et al. (2009)
D_Tb_Chr = 0.0011 # Bedard et al. (2009)
D_Y_Chr = 0.002 # Bedard et al. (2009)
D_Yb_Chr = 0.0045 # Bedard et al. (2009)
D_Lu_Chr = 0.0045 # Bedard et al. (2009)
D_V_Chr = 10 # Bedard et al. (2009)
D_Pr_Chr = 0.0006 # Bedard et al. (2009)
D_Dy_Chr = 0.0015 # Bedard et al. (2009)
D_Ho_Chr = 0.0023 # Bedard et al. (2009)
D_Er_Chr = 0.003 # Bedard et al. (2009)
D_Tm_Chr = 0.0038 # Bedard et al. (2009)
D_Sc_Chr = 0.1 # Bedard et al. (2009)
D_Hf_Chr = 0.015 # Bedard et al. (2009)
D_Th_Maj_gn = float()
D_Nb_Maj_gn = 0.0022 # Bobrov et al. (2014) --> run 2322
D_La_Maj_gn = 0.0011 # Bobrov et al. (2014) --> run 2322
D_Ce_Maj_gn = 0.0016 # Bobrov et al. (2014) --> run 2322
D_Nd_Maj_gn = 0.0058 # Bobrov et al. (2014) --> run 2322
D_Zr_Maj_gn = 0.174 # Bobrov et al. (2014) --> run 2322
D_Sm_Maj_gn = 0.027 # Bobrov et al. (2014) --> run 2322
D_Eu_Maj_gn = 0.059 # Bobrov et al. (2014) --> run 2322
D_Ti_Maj_gn = float()
D_Gd_Maj_gn = 0.099 # Bobrov et al. (2014) --> run 2322
D_Tb_Maj_gn = 0.201 # Bobrov et al. (2014) --> run 2322
D_Y_Maj_gn = 0.556 # Bobrov et al. (2014) --> run 2322
D_Yb_Maj_gn = 1.62 # Bobrov et al. (2014) --> run 2322
D_Lu_Maj_gn = 1.97 # Bobrov et al. (2014) --> run 2322
D_V_Maj_gn = float()
D_Pr_Maj_gn = 0.0022 # Bobrov et al. (2014) --> run 2322
D_Dy_Maj_gn = 0.342 # Bobrov et al. (2014) --> run 2322
D_Ho_Maj_gn = 0.551 # Bobrov et al. (2014) --> run 2322
D_Er_Maj_gn = 0.848 # Bobrov et al. (2014) --> run 2322
D_Tm_Maj_gn = 1.17 # Bobrov et al. (2014) --> run 2322
D_Sc_Maj_gn = 2.69 # Bobrov et al. (2014) --> run 2322
D_Hf_Maj_gn = 0.144 # Bobrov et al. (2014) --> run 2322
D_Th_Amp = float()
D_Nb_Amp = float()
D_La_Amp = 0.17 # McKenzie and O'Nions (1991)
D_Ce_Amp = 0.26 # McKenzie and O'Nions (1991)
D_Nd_Amp = 0.44 # McKenzie and O'Nions (1991)
D_Zr_Amp = float() # McKenzie and O'Nions (1991)
D_Sm_Amp = 0.76 # McKenzie and O'Nions (1991)
D_Eu_Amp = 0.88 # McKenzie and O'Nions (1991)
D_Ti_Amp = 0.69 # McKenzie and O'Nions (1991)
D_Gd_Amp = 0.86 # McKenzie and O'Nions (1991)
D_Tb_Amp = 0.83 # McKenzie and O'Nions (1991)
D_Y_Amp = float()
D_Yb_Amp = 0.59 # McKenzie and O'Nions (1991)
D_Lu_Amp = 0.51 # McKenzie and O'Nions (1991)
D_V_Amp = float()
D_Pr_Amp = 0.35 # McKenzie and O'Nions (1991)
D_Dy_Amp = 0.78 # McKenzie and O'Nions (1991)
D_Ho_Amp = 0.73 # McKenzie and O'Nions (1991)
D_Er_Amp = 0.68 # McKenzie and O'Nions (1991)
D_Tm_Amp = 0.64 # McKenzie and O'Nions (1991)
D_Sc_Amp = float()
D_Hf_Amp = float()
#####################################################################################################
# Bulk partition coefficients
#####################################################################################################
D_Th_bulk = (P_Cpx * D_Th_Cpx) + (P_Pl * D_Th_Pl) + (P_Opx * D_Th_Opx) + (P_Ol * D_Th_Ol) + (P_Mt * D_Th_Mt) + (P_Ilm * D_Th_Ilm) + (P_Ap * D_Th_Ap) + (P_Chr * D_Th_Chr) + (P_Maj_gn * D_Th_Maj_gn) + (P_Amp * D_Th_Amp)
D_Nb_bulk = (P_Cpx * D_Nb_Cpx) + (P_Pl * D_Nb_Pl) + (P_Opx * D_Nb_Opx) + (P_Ol * D_Nb_Ol) + (P_Mt * D_Nb_Mt) + (P_Ilm * D_Nb_Ilm) + (P_Ap * D_Nb_Ap) + (P_Chr * D_Nb_Chr) + (P_Maj_gn * D_Nb_Maj_gn) + (P_Amp * D_Nb_Amp)
D_La_bulk = (P_Cpx * D_La_Cpx) + (P_Pl * D_La_Pl) + (P_Opx * D_La_Opx) + (P_Ol * D_La_Ol) + (P_Mt * D_La_Mt) + (P_Ilm * D_La_Ilm) + (P_Ap * D_La_Ap) + (P_Chr * D_La_Chr) + (P_Maj_gn * D_La_Maj_gn) + (P_Amp * D_La_Amp)
D_Ce_bulk = (P_Cpx * D_Ce_Cpx) + (P_Pl * D_Ce_Pl) + (P_Opx * D_Ce_Opx) + (P_Ol * D_Ce_Ol) + (P_Mt * D_Ce_Mt) + (P_Ilm * D_Ce_Ilm) + (P_Ap * D_Ce_Ap) + (P_Chr * D_Ce_Chr) + (P_Maj_gn * D_Ce_Maj_gn) + (P_Amp * D_Ce_Amp)
D_Pr_bulk = (P_Cpx * D_Pr_Cpx) + (P_Pl * D_Pr_Pl) + (P_Opx * D_Pr_Opx) + (P_Ol * D_Pr_Ol) + (P_Mt * D_Pr_Mt) + (P_Ilm * D_Pr_Ilm) + (P_Ap * D_Pr_Ap) + (P_Chr * D_Pr_Chr) + (P_Maj_gn * D_Pr_Maj_gn) + (P_Amp * D_Pr_Amp)
D_Nd_bulk = (P_Cpx * D_Nd_Cpx) + (P_Pl * D_Nd_Pl) + (P_Opx * D_Nd_Opx) + (P_Ol * D_Nd_Ol) + (P_Mt * D_Nd_Mt) + (P_Ilm * D_Nd_Ilm) + (P_Ap * D_Nd_Ap) + (P_Chr * D_Nd_Chr) + (P_Maj_gn * D_Nd_Maj_gn) + (P_Amp * D_Nd_Amp)
D_Zr_bulk = (P_Cpx * D_Zr_Cpx) + (P_Pl * D_Zr_Pl) + (P_Opx * D_Zr_Opx) + (P_Ol * D_Zr_Ol) + (P_Mt * D_Zr_Mt) + (P_Ilm * D_Zr_Ilm) + (P_Ap * D_Zr_Ap) + (P_Chr * D_Zr_Chr) + (P_Maj_gn * D_Zr_Maj_gn) + (P_Amp * D_Zr_Amp)
D_Hf_bulk = (P_Cpx * D_Hf_Cpx) + (P_Pl * D_Hf_Pl) + (P_Opx * D_Hf_Opx) + (P_Ol * D_Hf_Ol) + (P_Mt * D_Hf_Mt) + (P_Ilm * D_Hf_Ilm) + (P_Ap * D_Hf_Ap) + (P_Chr * D_Hf_Chr) + (P_Maj_gn * D_Hf_Maj_gn) + (P_Amp * D_Hf_Amp)
D_Sm_bulk = (P_Cpx * D_Sm_Cpx) + (P_Pl * D_Sm_Pl) + (P_Opx * D_Sm_Opx) + (P_Ol * D_Sm_Ol) + (P_Mt * D_Sm_Mt) + (P_Ilm * D_Sm_Ilm) + (P_Ap * D_Sm_Ap) + (P_Chr * D_Sm_Chr) + (P_Maj_gn * D_Sm_Maj_gn) + (P_Amp * D_Sm_Amp)
D_Eu_bulk = (P_Cpx * D_Eu_Cpx) + (P_Pl * D_Eu_Pl) + (P_Opx * D_Eu_Opx) + (P_Ol * D_Eu_Ol) + (P_Mt * D_Eu_Mt) + (P_Ilm * D_Eu_Ilm) + (P_Ap * D_Eu_Ap) + (P_Chr * D_Eu_Chr) + (P_Maj_gn * D_Eu_Maj_gn) + (P_Amp * D_Eu_Amp)
D_Ti_bulk = (P_Cpx * D_Ti_Cpx) + (P_Pl * D_Ti_Pl) + (P_Opx * D_Ti_Opx) + (P_Ol * D_Ti_Ol) + (P_Mt * D_Ti_Mt) + (P_Ilm * D_Ti_Ilm) + (P_Ap * D_Ti_Ap) + (P_Chr * D_Ti_Chr) + (P_Maj_gn * D_Ti_Maj_gn) + (P_Amp * D_Ti_Amp)
D_Gd_bulk = (P_Cpx * D_Gd_Cpx) + (P_Pl * D_Gd_Pl) + (P_Opx * D_Gd_Opx) + (P_Ol * D_Gd_Ol) + (P_Mt * D_Gd_Mt) + (P_Ilm * D_Gd_Ilm) + (P_Ap * D_Gd_Ap) + (P_Chr * D_Gd_Chr) + (P_Maj_gn * D_Gd_Maj_gn) + (P_Amp * D_Gd_Amp)
D_Tb_bulk = (P_Cpx * D_Tb_Cpx) + (P_Pl * D_Tb_Pl) + (P_Opx * D_Tb_Opx) + (P_Ol * D_Tb_Ol) + (P_Mt * D_Tb_Mt) + (P_Ilm * D_Tb_Ilm) + (P_Ap * D_Tb_Ap) + (P_Chr * D_Tb_Chr) + (P_Maj_gn * D_Tb_Maj_gn) + (P_Amp * D_Tb_Amp)
D_Dy_bulk = (P_Cpx * D_Dy_Cpx) + (P_Pl * D_Dy_Pl) + (P_Opx * D_Dy_Opx) + (P_Ol * D_Dy_Ol) + (P_Mt * D_Dy_Mt) + (P_Ilm * D_Dy_Ilm) + (P_Ap * D_Dy_Ap) + (P_Chr * D_Dy_Chr) + (P_Maj_gn * D_Dy_Maj_gn) + (P_Amp * D_Dy_Amp)
D_Y_bulk = (P_Cpx * D_Y_Cpx) + (P_Pl * D_Y_Pl) + (P_Opx * D_Y_Opx) + (P_Ol * D_Y_Ol) + (P_Mt * D_Y_Mt) + (P_Ilm * D_Y_Ilm) + (P_Ap * D_Y_Ap) + (P_Chr * D_Y_Chr) + (P_Maj_gn * D_Y_Maj_gn) + (P_Amp * D_Y_Amp)
D_Ho_bulk = (P_Cpx * D_Ho_Cpx) + (P_Pl * D_Ho_Pl) + (P_Opx * D_Ho_Opx) + (P_Ol * D_Ho_Ol) + (P_Mt * D_Ho_Mt) + (P_Ilm * D_Ho_Ilm) + (P_Ap * D_Ho_Ap) + (P_Chr * D_Ho_Chr) + (P_Maj_gn * D_Ho_Maj_gn) + (P_Amp * D_Ho_Amp)
D_Er_bulk = (P_Cpx * D_Er_Cpx) + (P_Pl * D_Er_Pl) + (P_Opx * D_Er_Opx) + (P_Ol * D_Er_Ol) + (P_Mt * D_Er_Mt) + (P_Ilm * D_Er_Ilm) + (P_Ap * D_Er_Ap) + (P_Chr * D_Er_Chr) + (P_Maj_gn * D_Er_Maj_gn) + (P_Amp * D_Er_Amp)
D_Tm_bulk = (P_Cpx * D_Tm_Cpx) + (P_Pl * D_Tm_Pl) + (P_Opx * D_Tm_Opx) + (P_Ol * D_Tm_Ol) + (P_Mt * D_Tm_Mt) + (P_Ilm * D_Tm_Ilm) + (P_Ap * D_Tm_Ap) + (P_Chr * D_Tm_Chr) + (P_Maj_gn * D_Tm_Maj_gn) + (P_Amp * D_Tm_Amp)
D_Yb_bulk = (P_Cpx * D_Yb_Cpx) + (P_Pl * D_Yb_Pl) + (P_Opx * D_Yb_Opx) + (P_Ol * D_Yb_Ol) + (P_Mt * D_Yb_Mt) + (P_Ilm * D_Yb_Ilm) + (P_Ap * D_Yb_Ap) + (P_Chr * D_Yb_Chr) + (P_Maj_gn * D_Yb_Maj_gn) + (P_Amp * D_Yb_Amp)
D_Lu_bulk = (P_Cpx * D_Lu_Cpx) + (P_Pl * D_Lu_Pl) + (P_Opx * D_Lu_Opx) + (P_Ol * D_Lu_Ol) + (P_Mt * D_Lu_Mt) + (P_Ilm * D_Lu_Ilm) + (P_Ap * D_Lu_Ap) + (P_Chr * D_Lu_Chr) + (P_Maj_gn * D_Lu_Maj_gn) + (P_Amp * D_Lu_Amp)
D_V_bulk = (P_Cpx * D_V_Cpx) + (P_Pl * D_V_Pl) + (P_Opx * D_V_Opx) + (P_Ol * D_V_Ol) + (P_Mt * D_V_Mt) + (P_Ilm * D_V_Ilm) + (P_Ap * D_V_Ap) + (P_Chr * D_V_Chr) + (P_Maj_gn * D_V_Maj_gn) + (P_Amp * D_V_Amp)
D_Sc_bulk = (P_Cpx * D_Sc_Cpx) + (P_Pl * D_Sc_Pl) + (P_Opx * D_Sc_Opx) + (P_Ol * D_Sc_Ol) + (P_Mt * D_Sc_Mt) + (P_Ilm * D_Sc_Ilm) + (P_Ap * D_Sc_Ap) + (P_Chr * D_Sc_Chr) + (P_Maj_gn * D_Sc_Maj_gn) + (P_Amp * D_Sc_Amp)
#####################################################################################################
# Residual melt calculation
#####################################################################################################
Th_sil_f = Th_sil_i * (F_sil_remaining ** (D_Th_bulk - 1))
Nb_sil_f = Nb_sil_i * (F_sil_remaining ** (D_Nb_bulk - 1))
La_sil_f = La_sil_i * (F_sil_remaining ** (D_La_bulk - 1))
Ce_sil_f = Ce_sil_i * (F_sil_remaining ** (D_Ce_bulk - 1))
Pr_sil_f = Pr_sil_i * (F_sil_remaining ** (D_Pr_bulk - 1))
Nd_sil_f = Nd_sil_i * (F_sil_remaining ** (D_Nd_bulk - 1))
Zr_sil_f = Zr_sil_i * (F_sil_remaining ** (D_Zr_bulk - 1))
Hf_sil_f = Hf_sil_i * (F_sil_remaining ** (D_Hf_bulk - 1))
Sm_sil_f = Sm_sil_i * (F_sil_remaining ** (D_Sm_bulk - 1))
Eu_sil_f = Eu_sil_i * (F_sil_remaining ** (D_Eu_bulk - 1))
Ti_sil_f = Ti_sil_i * (F_sil_remaining ** (D_Ti_bulk - 1))
Gd_sil_f = Gd_sil_i * (F_sil_remaining ** (D_Gd_bulk - 1))
Tb_sil_f = Tb_sil_i * (F_sil_remaining ** (D_Tb_bulk - 1))
Dy_sil_f = Dy_sil_i * (F_sil_remaining ** (D_Dy_bulk - 1))
Y_sil_f = Y_sil_i * (F_sil_remaining ** (D_Y_bulk - 1))
Ho_sil_f = Ho_sil_i * (F_sil_remaining ** (D_Ho_bulk - 1))
Er_sil_f = Er_sil_i * (F_sil_remaining ** (D_Er_bulk - 1))
Tm_sil_f = Tm_sil_i * (F_sil_remaining ** (D_Tm_bulk - 1))
Yb_sil_f = Yb_sil_i * (F_sil_remaining ** (D_Yb_bulk - 1))
Lu_sil_f = Lu_sil_i * (F_sil_remaining ** (D_Lu_bulk - 1))
V_sil_f = V_sil_i * (F_sil_remaining ** (D_V_bulk - 1))
Sc_sil_f = Sc_sil_i * (F_sil_remaining ** (D_Sc_bulk - 1))
#####################################################################################################
# Cumulate melt calculation
#####################################################################################################
Th_sol = ((1 - (F_sil_remaining ** D_Th_bulk)) / (1 - F_sil_remaining)) * Th_sil_i
Nb_sol = ((1 - (F_sil_remaining ** D_Nb_bulk)) / (1 - F_sil_remaining)) * Nb_sil_i
La_sol = ((1 - (F_sil_remaining ** D_La_bulk)) / (1 - F_sil_remaining)) * La_sil_i
Ce_sol = ((1 - (F_sil_remaining ** D_Ce_bulk)) / (1 - F_sil_remaining)) * Ce_sil_i
Pr_sol = ((1 - (F_sil_remaining ** D_Pr_bulk)) / (1 - F_sil_remaining)) * Pr_sil_i
Nd_sol = ((1 - (F_sil_remaining ** D_Nd_bulk)) / (1 - F_sil_remaining)) * Nd_sil_i
Zr_sol = ((1 - (F_sil_remaining ** D_Zr_bulk)) / (1 - F_sil_remaining)) * Zr_sil_i
Hf_sol = ((1 - (F_sil_remaining ** D_Hf_bulk)) / (1 - F_sil_remaining)) * Hf_sil_i
Sm_sol = ((1 - (F_sil_remaining ** D_Sm_bulk)) / (1 - F_sil_remaining)) * Sm_sil_i
Eu_sol = ((1 - (F_sil_remaining ** D_Eu_bulk)) / (1 - F_sil_remaining)) * Eu_sil_i
Ti_sol = ((1 - (F_sil_remaining ** D_Ti_bulk)) / (1 - F_sil_remaining)) * Ti_sil_i
Gd_sol = ((1 - (F_sil_remaining ** D_Gd_bulk)) / (1 - F_sil_remaining)) * Gd_sil_i
Tb_sol = ((1 - (F_sil_remaining ** D_Tb_bulk)) / (1 - F_sil_remaining)) * Tb_sil_i
Dy_sol = ((1 - (F_sil_remaining ** D_Dy_bulk)) / (1 - F_sil_remaining)) * Dy_sil_i
Y_sol = ((1 - (F_sil_remaining ** D_Y_bulk)) / (1 - F_sil_remaining)) * Y_sil_i
Ho_sol = ((1 - (F_sil_remaining ** D_Ho_bulk)) / (1 - F_sil_remaining)) * Ho_sil_i
Er_sol = ((1 - (F_sil_remaining ** D_Er_bulk)) / (1 - F_sil_remaining)) * Er_sil_i
Tm_sol = ((1 - (F_sil_remaining ** D_Tm_bulk)) / (1 - F_sil_remaining)) * Tm_sil_i
Yb_sol = ((1 - (F_sil_remaining ** D_Yb_bulk)) / (1 - F_sil_remaining)) * Yb_sil_i
Lu_sol = ((1 - (F_sil_remaining ** D_Lu_bulk)) / (1 - F_sil_remaining)) * Lu_sil_i
V_sol = ((1 - (F_sil_remaining ** D_V_bulk)) / (1 - F_sil_remaining)) * V_sil_i
Sc_sol = ((1 - (F_sil_remaining ** D_Sc_bulk)) / (1 - F_sil_remaining)) * Sc_sil_i
您可能需要安装它。
python --version
python -m pip install seaborn
您需要根据 Streamlit 文档指明您的 App dependencies。
The main reason that apps fail to build properly is because Streamlit Cloud can't find your dependencies! So make sure you:
- Add a requirements file for Python dependencies.
- (optional) Add a packages.txt file to manage any external dependencies (i.e Linux dependencies outside Python environment).
Note: Python requirements files should be placed either in the root of your repository or in the same directory as your Streamlit app
我在 python 和 Streamlit 中创建了一个使用 seaborn 的应用程序，但是当我将它部署到 Streamlit 云时，我收到一条错误消息 No module named 'seaborn' 。如果我注释掉 seaborn，其他模块（例如 matplotlib）也会出现同样的错误。当我在本地启动该应用程序进行测试时，该应用程序运行良好。我已将错误作为屏幕截图和我的代码提供（它很长 - 我对 python 还是个新手，做事相当直截了当）。如果有人能解释我如何修复这个错误，我将不胜感激。
谢谢
错误截图：
代码示例：
import streamlit as st
import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
st.title("Rayleigh Fractionation Model")
st.write("-------------")
st.write("")
#####################################################################################################
# Initial melt composition
#####################################################################################################
st.subheader("Initial Composition and Model Results")
st.write("")
with st.expander("Starting silicate melt composition (Default is OIB)"):
col1_a, col2_a, col3_a, col4_a = st.columns([1, 1, 1, 1])
with col1_a:
Th_sil_i = st.number_input("Th (ppm)", min_value = 0.0, value = 4.0)
Nb_sil_i = st.number_input("Nb (ppm)", min_value = 0.0, value = 48.0)
La_sil_i = st.number_input("La (ppm)", min_value = 0.0, value = 37.0)
Ce_sil_i = st.number_input("Ce (ppm)", min_value = 0.0, value = 80.0)
Pr_sil_i = st.number_input("Pr (ppm)", min_value = 0.0, value = 9.7)
Nd_sil_i = st.number_input("Nd (ppm)", min_value = 0.0, value = 38.5)
with col2_a:
Zr_sil_i = st.number_input("Zr (ppm)", min_value = 0.0, value = 280.0)
Hf_sil_i = st.number_input("Hf (ppm)", min_value = 0.0, value = 7.8)
Sm_sil_i = st.number_input("Sm (ppm)", min_value = 0.0, value = 10.0)
Eu_sil_i = st.number_input("Eu (ppm)", min_value = 0.0, value = 3.0)
Ti_sil_i = st.number_input("Ti (ppm)", min_value = 0.0, value = 17200.0)
Gd_sil_i = st.number_input("Gd (ppm)", min_value = 0.0, value = 7.62)
with col3_a:
Tb_sil_i = st.number_input("Tb (ppm)", min_value = 0.0, value = 1.05)
Dy_sil_i = st.number_input("Dy (ppm)", min_value = 0.0, value = 5.6)
Y_sil_i = st.number_input("Y (ppm)", min_value = 0.0, value = 29.0)
Ho_sil_i = st.number_input("Ho (ppm)", min_value = 0.0, value = 1.06)
Er_sil_i = st.number_input("Er (ppm)", min_value = 0.0, value = 2.62)
Tm_sil_i = st.number_input("Tm (ppm)", min_value = 0.0, value = 0.35)
with col4_a:
Yb_sil_i = st.number_input("Yb (ppm)", min_value = 0.0, value = 2.16)
Lu_sil_i = st.number_input("Lu (ppm)", min_value = 0.0, value = 0.3)
V_sil_i = st.number_input("V (ppm)", min_value = 0.0, value = 500.0)
Sc_sil_i = st.number_input("Sc (ppm)", min_value = 0.0, value = 100.0)
initial_melt = {
"Elements":["Th", "Nb", "La", "Ce", "Pr", "Nd", "Zr", "Hf", "Sm", "Eu", "Ti", "Gd", "Tb", "Dy", "Y", "Ho", "Er", "Tm", "Yb", "Lu", "V", "Sc"],
"Concentration (ppm)":[Th_sil_i, Nb_sil_i, La_sil_i, Ce_sil_i, Pr_sil_i, Nd_sil_i, Zr_sil_i, Hf_sil_i, Sm_sil_i, Eu_sil_i, Ti_sil_i, Gd_sil_i, Tb_sil_i, Dy_sil_i, Y_sil_i, Ho_sil_i, Er_sil_i, Tm_sil_i, Yb_sil_i, Lu_sil_i, V_sil_i, Sc_sil_i]
}
initial_melt_df = pd.DataFrame(data = initial_melt)
#####################################################################################################
# Fractionating minerals
#####################################################################################################
F_sil_remaining = np.arange(0.1, 1.0+0.001, 0.001)
st.sidebar.write("**Choose the minerals that are fractionating**")
P_Cpx = st.sidebar.number_input("Clinopyroxene", 0.0, 1.0, 0.0, 0.05)
P_Pl = st.sidebar.number_input("Plagioclase", 0.0, 1.0, 0.0, 0.05)
P_Opx = st.sidebar.number_input("Orthopyroxene", 0.0, 1.0, 0.0, 0.05)
P_Ol = st.sidebar.number_input("Olivine", 0.0, 1.0, 0.0, 0.05)
P_Mt = st.sidebar.number_input("Magnetite", 0.0, 1.0, 0.0, 0.05)
P_Ilm = st.sidebar.number_input("Ilmenite", 0.0, 1.0, 0.0, 0.05)
P_Ap = st.sidebar.number_input("Apatite", 0.0, 1.0, 0.0, 0.05)
P_Chr = st.sidebar.number_input("Chromite", 0.0, 1.0, 0.0, 0.05)
P_Maj_gn = st.sidebar.number_input("Majorite garnet", 0.0, 1.0, 0.0, 0.05)
P_Amp = st.sidebar.number_input("Amphibole", 0.0, 1.0, 0.0, 0.05)
Total = P_Cpx + P_Pl + P_Opx + P_Ol + P_Mt + P_Ilm + P_Ap + P_Chr + P_Maj_gn + P_Amp
st.sidebar.write(f"Total minerals fractionating = {Total}")
st.sidebar.write("*The total minerals fractionating should not be greater than 1*")
st.sidebar.write("--------------")
st.sidebar.write("")
st.sidebar.write("**Created by:**")
st.sidebar.write("***Matthew Brzozowski, PhD***")
st.sidebar.write("***matt.brzozow@gmail.com***")
#####################################################################################################
# Partition coefficients
#####################################################################################################
# Partition coefficients for different minerals
# Kd values from Bedard et al. (2009) --> Most minerals
# The D values are appropriate for a system corresponding to a rock with molar An = 0.709, clinopyroxene Aliv = 0.04, and melt MgO = 5.47 and SiO2 = 53.6 wt.%.
# Kd values from Corgne and Wood (2004) --> Majorite garnet
# Fe-, Al-rich peridotite
# Kd values from McKenzie and O'Nions (1991) --> Amphibole
# Basalt
D_Th_Cpx = 0.0225 # Bedard et al. (2009)
D_Nb_Cpx = 0.0098 # Bedard et al. (2009)
D_La_Cpx = 0.1 # Bedard et al. (2009)
D_Ce_Cpx = 0.16 # Bedard et al. (2009)
D_Nd_Cpx = 0.338 # Bedard et al. (2009)
D_Zr_Cpx = 0.022 # Bedard et al. (2009)
D_Sm_Cpx = 0.53 # Bedard et al. (2009)
D_Eu_Cpx = 0.04 # Bedard et al. (2009)
D_Ti_Cpx = 0.213 # Bedard et al. (2009)
D_Gd_Cpx = 0.673 # Bedard et al. (2009)
D_Tb_Cpx = 0.721 # Bedard et al. (2009)
D_Y_Cpx = 0.752 # Bedard et al. (2009)
D_Yb_Cpx = 0.678 # Bedard et al. (2009)
D_Lu_Cpx = 0.642 # Bedard et al. (2009)
D_V_Cpx = 0.49 # Bedard et al. (2009)
D_Pr_Cpx = 0.240 # Bedard et al. (2009)
D_Dy_Cpx = 0.747 # Bedard et al. (2009)
D_Ho_Cpx = 0.751 # Bedard et al. (2009)
D_Er_Cpx = 0.737 # Bedard et al. (2009)
D_Tm_Cpx = 0.711 # Bedard et al. (2009)
D_Sc_Cpx = 1.11 # Bedard et al. (2009)
D_Hf_Cpx = 0.050 # Bedard et al. (2009)
D_Th_Pl = 0.0162 # Bedard et al. (2009)
D_Nb_Pl = 0.00328 # Bedard et al. (2009)
D_La_Pl = 0.0238 # Bedard et al. (2009)
D_Ce_Pl = 0.036 # Bedard et al. (2009)
D_Nd_Pl = 0.0111 # Bedard et al. (2009)
D_Zr_Pl = 0.00048 # Bedard et al. (2009)
D_Sm_Pl = 0.0141 # Bedard et al. (2009)
D_Eu_Pl = 0.0872 # Bedard et al. (2009)
D_Ti_Pl = 0.0243 # Bedard et al. (2009)
D_Gd_Pl = 0.0223 # Bedard et al. (2009)
D_Tb_Pl = 0.0118 # Bedard et al. (2009)
D_Y_Pl = 0.0087 # Bedard et al. (2009)
D_Yb_Pl = 0.0039 # Bedard et al. (2009)
D_Lu_Pl = 0.0038 # Bedard et al. (2009)
D_V_Pl = 0 # Bedard et al. (2009)
D_Pr_Pl = 0.0271 # Bedard et al. (2009)
D_Dy_Pl = 0.0159 # Bedard et al. (2009)
D_Ho_Pl = 0.0256 # Bedard et al. (2009)
D_Er_Pl = 0.0115 # Bedard et al. (2009)
D_Tm_Pl = 0.0192 # Bedard et al. (2009)
D_Sc_Pl = 0.00106 # Bedard et al. (2009)
D_Hf_Pl = 0.0042 # Bedard et al. (2009)
D_Th_Opx = 0.0064 # Bedard et al. (2009)
D_Nb_Opx = 0.015 # Bedard et al. (2009)
D_La_Opx = 0.00328 # Bedard et al. (2009)
D_Ce_Opx = 0.00552 # Bedard et al. (2009)
D_Nd_Opx = 0.0142 # Bedard et al. (2009)
D_Zr_Opx = 0.0167 # Bedard et al. (2009)
D_Sm_Opx = 0.0293 # Bedard et al. (2009)
D_Eu_Opx = 0.0227 # Bedard et al. (2009)
D_Ti_Opx = 0.201 # Bedard et al. (2009)
D_Gd_Opx = 0.051 # Bedard et al. (2009)
D_Tb_Opx = 0.0656 # Bedard et al. (2009)
D_Y_Opx = 0.0953 # Bedard et al. (2009)
D_Yb_Opx = 0.16 # Bedard et al. (2009)
D_Lu_Opx = 0.177 # Bedard et al. (2009)
D_V_Opx = 0.453 # Bedard et al. (2009)
D_Pr_Opx = 0.0090 # Bedard et al. (2009)
D_Dy_Opx = 0.0831 # Bedard et al. (2009)
D_Ho_Opx = 0.102 # Bedard et al. (2009)
D_Er_Opx = 0.121 # Bedard et al. (2009)
D_Tm_Opx = 0.141 # Bedard et al. (2009)
D_Sc_Opx = 1.068 # Bedard et al. (2009)
D_Hf_Opx = 0.0408 # Bedard et al. (2009)
D_Th_Ol = 0.0346 # Bedard et al. (2009)
D_Nb_Ol = 0.00491 # Bedard et al. (2009)
D_La_Ol = 0.00008 # Bedard et al. (2009)
D_Ce_Ol = 0.00019 # Bedard et al. (2009)
D_Nd_Ol = 0.00093 # Bedard et al. (2009)
D_Zr_Ol = 0.0319 # Bedard et al. (2009)
D_Sm_Ol = 0.0031 # Bedard et al. (2009)
D_Eu_Ol = 0.0111 # Bedard et al. (2009)
D_Ti_Ol = 0.0334 # Bedard et al. (2009)
D_Gd_Ol = 0.00784 # Bedard et al. (2009)
D_Tb_Ol = 0.0119 # Bedard et al. (2009)
D_Y_Ol = 0.0222 # Bedard et al. (2009)
D_Yb_Ol = 0.0521 # Bedard et al. (2009)
D_Lu_Ol = 0.0621 # Bedard et al. (2009)
D_V_Ol = 0.15 # Bedard et al. (2009)
D_Pr_Ol = 0.00043 # Bedard et al. (2009)
D_Dy_Ol = 0.0177 # Bedard et al. (2009)
D_Ho_Ol = 0.0247 # Bedard et al. (2009)
D_Er_Ol = 0.0330 # Bedard et al. (2009)
D_Tm_Ol = 0.0423 # Bedard et al. (2009)
D_Sc_Ol = 0.29 # Bedard et al. (2009)
D_Hf_Ol = 0.0139 # Bedard et al. (2009)
D_Th_Mt = 0.0077 # Bedard et al. (2009)
D_Nb_Mt = 0.0764 # Bedard et al. (2009)
D_La_Mt = 0.015 # Bedard et al. (2009)
D_Ce_Mt = 0.016 # Bedard et al. (2009)
D_Nd_Mt = 0.026 # Bedard et al. (2009)
D_Zr_Mt = 0.084 # Bedard et al. (2009)
D_Sm_Mt = 0.024 # Bedard et al. (2009)
D_Eu_Mt = 0.025 # Bedard et al. (2009)
D_Ti_Mt = 1.49 # Bedard et al. (2009)
D_Gd_Mt = 0.018 # Bedard et al. (2009)
D_Tb_Mt = 0.019 # Bedard et al. (2009)
D_Y_Mt = 0.018 # Bedard et al. (2009)
D_Yb_Mt = 0.018 # Bedard et al. (2009)
D_Lu_Mt = 0.018 # Bedard et al. (2009)
D_V_Mt = 0.64 # Bedard et al. (2009)
D_Pr_Mt = 0.018 # Bedard et al. (2009)
D_Dy_Mt = 0.018 # Bedard et al. (2009)
D_Ho_Mt = 0.018 # Bedard et al. (2009)
D_Er_Mt = 0.018 # Bedard et al. (2009)
D_Tm_Mt = 0.018 # Bedard et al. (2009)
D_Sc_Mt = 1.10 # Bedard et al. (2009)
D_Hf_Mt = 0.076 # Bedard et al. (2009)
D_Th_Ilm = 0.105 # Bedard et al. (2009)
D_Nb_Ilm = 1.62 # Bedard et al. (2009)
D_La_Ilm = 0.0027 # Bedard et al. (2009)
D_Ce_Ilm = 0.0046 # Bedard et al. (2009)
D_Nd_Ilm = 0.012 # Bedard et al. (2009)
D_Zr_Ilm = 0.35 # Bedard et al. (2009)
D_Sm_Ilm = 0.025 # Bedard et al. (2009)
D_Eu_Ilm = 0.0028 # Bedard et al. (2009)
D_Ti_Ilm = float()
D_Gd_Ilm = 0.0428 # Bedard et al. (2009)
D_Tb_Ilm = 0.0546 # Bedard et al. (2009)
D_Y_Ilm = 0.0777 # Bedard et al. (2009)
D_Yb_Ilm = 0.125 # Bedard et al. (2009)
D_Lu_Ilm = 0.137 # Bedard et al. (2009)
D_V_Ilm = 10.3 # Bedard et al. (2009)
D_Pr_Ilm = 0.0076 # Bedard et al. (2009)
D_Dy_Ilm = 0.0683 # Bedard et al. (2009)
D_Ho_Ilm = 0.0827 # Bedard et al. (2009)
D_Er_Ilm = 0.0971 # Bedard et al. (2009)
D_Tm_Ilm = 0.111 # Bedard et al. (2009)
D_Sc_Ilm = 1.91 # Bedard et al. (2009)
D_Hf_Ilm = 0.42 # Bedard et al. (2009)
D_Th_Ap = 0.835 # Bedard et al. (2009)
D_Nb_Ap = 0.00295 # Bedard et al. (2009)
D_La_Ap = 2.425 # Bedard et al. (2009)
D_Ce_Ap = 2.78 # Bedard et al. (2009)
D_Nd_Ap = 16.8 # Bedard et al. (2009)
D_Zr_Ap = 0.067 # Bedard et al. (2009)
D_Sm_Ap = 4.67 # Bedard et al. (2009)
D_Eu_Ap = 7.36 # Bedard et al. (2009)
D_Ti_Ap = 0.047 # Bedard et al. (2009)
D_Gd_Ap = 4.05 # Bedard et al. (2009)
D_Tb_Ap = 15.2 # Bedard et al. (2009)
D_Y_Ap = 2.285 # Bedard et al. (2009)
D_Yb_Ap = 1.5 # Bedard et al. (2009)
D_Lu_Ap = 0.96 # Bedard et al. (2009)
D_V_Ap = 0.022 # Bedard et al. (2009)
D_Pr_Ap = 14.0 # Bedard et al. (2009)
D_Dy_Ap = 12.9 # Bedard et al. (2009)
D_Ho_Ap = 10.8 # Bedard et al. (2009)
D_Er_Ap = 8.79 # Bedard et al. (2009)
D_Tm_Ap = 7.14 # Bedard et al. (2009)
D_Sc_Ap = 0.0258 # Bedard et al. (2009)
D_Hf_Ap = 89 # Bedard et al. (2009)
D_Th_Chr = 0.001 # Bedard et al. (2009)
D_Nb_Chr = 0.01 # Bedard et al. (2009)
D_La_Chr = 0.0006 # Bedard et al. (2009)
D_Ce_Chr = 0.0006 # Bedard et al. (2009)
D_Nd_Chr = 0.0006 # Bedard et al. (2009)
D_Zr_Chr = 0.015 # Bedard et al. (2009)
D_Sm_Chr = 0.0006 # Bedard et al. (2009)
D_Eu_Chr = 0.0006 # Bedard et al. (2009)
D_Ti_Chr = 0.125 # Bedard et al. (2009)
D_Gd_Chr = 0.0006 # Bedard et al. (2009)
D_Tb_Chr = 0.0011 # Bedard et al. (2009)
D_Y_Chr = 0.002 # Bedard et al. (2009)
D_Yb_Chr = 0.0045 # Bedard et al. (2009)
D_Lu_Chr = 0.0045 # Bedard et al. (2009)
D_V_Chr = 10 # Bedard et al. (2009)
D_Pr_Chr = 0.0006 # Bedard et al. (2009)
D_Dy_Chr = 0.0015 # Bedard et al. (2009)
D_Ho_Chr = 0.0023 # Bedard et al. (2009)
D_Er_Chr = 0.003 # Bedard et al. (2009)
D_Tm_Chr = 0.0038 # Bedard et al. (2009)
D_Sc_Chr = 0.1 # Bedard et al. (2009)
D_Hf_Chr = 0.015 # Bedard et al. (2009)
D_Th_Maj_gn = float()
D_Nb_Maj_gn = 0.0022 # Bobrov et al. (2014) --> run 2322
D_La_Maj_gn = 0.0011 # Bobrov et al. (2014) --> run 2322
D_Ce_Maj_gn = 0.0016 # Bobrov et al. (2014) --> run 2322
D_Nd_Maj_gn = 0.0058 # Bobrov et al. (2014) --> run 2322
D_Zr_Maj_gn = 0.174 # Bobrov et al. (2014) --> run 2322
D_Sm_Maj_gn = 0.027 # Bobrov et al. (2014) --> run 2322
D_Eu_Maj_gn = 0.059 # Bobrov et al. (2014) --> run 2322
D_Ti_Maj_gn = float()
D_Gd_Maj_gn = 0.099 # Bobrov et al. (2014) --> run 2322
D_Tb_Maj_gn = 0.201 # Bobrov et al. (2014) --> run 2322
D_Y_Maj_gn = 0.556 # Bobrov et al. (2014) --> run 2322
D_Yb_Maj_gn = 1.62 # Bobrov et al. (2014) --> run 2322
D_Lu_Maj_gn = 1.97 # Bobrov et al. (2014) --> run 2322
D_V_Maj_gn = float()
D_Pr_Maj_gn = 0.0022 # Bobrov et al. (2014) --> run 2322
D_Dy_Maj_gn = 0.342 # Bobrov et al. (2014) --> run 2322
D_Ho_Maj_gn = 0.551 # Bobrov et al. (2014) --> run 2322
D_Er_Maj_gn = 0.848 # Bobrov et al. (2014) --> run 2322
D_Tm_Maj_gn = 1.17 # Bobrov et al. (2014) --> run 2322
D_Sc_Maj_gn = 2.69 # Bobrov et al. (2014) --> run 2322
D_Hf_Maj_gn = 0.144 # Bobrov et al. (2014) --> run 2322
D_Th_Amp = float()
D_Nb_Amp = float()
D_La_Amp = 0.17 # McKenzie and O'Nions (1991)
D_Ce_Amp = 0.26 # McKenzie and O'Nions (1991)
D_Nd_Amp = 0.44 # McKenzie and O'Nions (1991)
D_Zr_Amp = float() # McKenzie and O'Nions (1991)
D_Sm_Amp = 0.76 # McKenzie and O'Nions (1991)
D_Eu_Amp = 0.88 # McKenzie and O'Nions (1991)
D_Ti_Amp = 0.69 # McKenzie and O'Nions (1991)
D_Gd_Amp = 0.86 # McKenzie and O'Nions (1991)
D_Tb_Amp = 0.83 # McKenzie and O'Nions (1991)
D_Y_Amp = float()
D_Yb_Amp = 0.59 # McKenzie and O'Nions (1991)
D_Lu_Amp = 0.51 # McKenzie and O'Nions (1991)
D_V_Amp = float()
D_Pr_Amp = 0.35 # McKenzie and O'Nions (1991)
D_Dy_Amp = 0.78 # McKenzie and O'Nions (1991)
D_Ho_Amp = 0.73 # McKenzie and O'Nions (1991)
D_Er_Amp = 0.68 # McKenzie and O'Nions (1991)
D_Tm_Amp = 0.64 # McKenzie and O'Nions (1991)
D_Sc_Amp = float()
D_Hf_Amp = float()
#####################################################################################################
# Bulk partition coefficients
#####################################################################################################
D_Th_bulk = (P_Cpx * D_Th_Cpx) + (P_Pl * D_Th_Pl) + (P_Opx * D_Th_Opx) + (P_Ol * D_Th_Ol) + (P_Mt * D_Th_Mt) + (P_Ilm * D_Th_Ilm) + (P_Ap * D_Th_Ap) + (P_Chr * D_Th_Chr) + (P_Maj_gn * D_Th_Maj_gn) + (P_Amp * D_Th_Amp)
D_Nb_bulk = (P_Cpx * D_Nb_Cpx) + (P_Pl * D_Nb_Pl) + (P_Opx * D_Nb_Opx) + (P_Ol * D_Nb_Ol) + (P_Mt * D_Nb_Mt) + (P_Ilm * D_Nb_Ilm) + (P_Ap * D_Nb_Ap) + (P_Chr * D_Nb_Chr) + (P_Maj_gn * D_Nb_Maj_gn) + (P_Amp * D_Nb_Amp)
D_La_bulk = (P_Cpx * D_La_Cpx) + (P_Pl * D_La_Pl) + (P_Opx * D_La_Opx) + (P_Ol * D_La_Ol) + (P_Mt * D_La_Mt) + (P_Ilm * D_La_Ilm) + (P_Ap * D_La_Ap) + (P_Chr * D_La_Chr) + (P_Maj_gn * D_La_Maj_gn) + (P_Amp * D_La_Amp)
D_Ce_bulk = (P_Cpx * D_Ce_Cpx) + (P_Pl * D_Ce_Pl) + (P_Opx * D_Ce_Opx) + (P_Ol * D_Ce_Ol) + (P_Mt * D_Ce_Mt) + (P_Ilm * D_Ce_Ilm) + (P_Ap * D_Ce_Ap) + (P_Chr * D_Ce_Chr) + (P_Maj_gn * D_Ce_Maj_gn) + (P_Amp * D_Ce_Amp)
D_Pr_bulk = (P_Cpx * D_Pr_Cpx) + (P_Pl * D_Pr_Pl) + (P_Opx * D_Pr_Opx) + (P_Ol * D_Pr_Ol) + (P_Mt * D_Pr_Mt) + (P_Ilm * D_Pr_Ilm) + (P_Ap * D_Pr_Ap) + (P_Chr * D_Pr_Chr) + (P_Maj_gn * D_Pr_Maj_gn) + (P_Amp * D_Pr_Amp)
D_Nd_bulk = (P_Cpx * D_Nd_Cpx) + (P_Pl * D_Nd_Pl) + (P_Opx * D_Nd_Opx) + (P_Ol * D_Nd_Ol) + (P_Mt * D_Nd_Mt) + (P_Ilm * D_Nd_Ilm) + (P_Ap * D_Nd_Ap) + (P_Chr * D_Nd_Chr) + (P_Maj_gn * D_Nd_Maj_gn) + (P_Amp * D_Nd_Amp)
D_Zr_bulk = (P_Cpx * D_Zr_Cpx) + (P_Pl * D_Zr_Pl) + (P_Opx * D_Zr_Opx) + (P_Ol * D_Zr_Ol) + (P_Mt * D_Zr_Mt) + (P_Ilm * D_Zr_Ilm) + (P_Ap * D_Zr_Ap) + (P_Chr * D_Zr_Chr) + (P_Maj_gn * D_Zr_Maj_gn) + (P_Amp * D_Zr_Amp)
D_Hf_bulk = (P_Cpx * D_Hf_Cpx) + (P_Pl * D_Hf_Pl) + (P_Opx * D_Hf_Opx) + (P_Ol * D_Hf_Ol) + (P_Mt * D_Hf_Mt) + (P_Ilm * D_Hf_Ilm) + (P_Ap * D_Hf_Ap) + (P_Chr * D_Hf_Chr) + (P_Maj_gn * D_Hf_Maj_gn) + (P_Amp * D_Hf_Amp)
D_Sm_bulk = (P_Cpx * D_Sm_Cpx) + (P_Pl * D_Sm_Pl) + (P_Opx * D_Sm_Opx) + (P_Ol * D_Sm_Ol) + (P_Mt * D_Sm_Mt) + (P_Ilm * D_Sm_Ilm) + (P_Ap * D_Sm_Ap) + (P_Chr * D_Sm_Chr) + (P_Maj_gn * D_Sm_Maj_gn) + (P_Amp * D_Sm_Amp)
D_Eu_bulk = (P_Cpx * D_Eu_Cpx) + (P_Pl * D_Eu_Pl) + (P_Opx * D_Eu_Opx) + (P_Ol * D_Eu_Ol) + (P_Mt * D_Eu_Mt) + (P_Ilm * D_Eu_Ilm) + (P_Ap * D_Eu_Ap) + (P_Chr * D_Eu_Chr) + (P_Maj_gn * D_Eu_Maj_gn) + (P_Amp * D_Eu_Amp)
D_Ti_bulk = (P_Cpx * D_Ti_Cpx) + (P_Pl * D_Ti_Pl) + (P_Opx * D_Ti_Opx) + (P_Ol * D_Ti_Ol) + (P_Mt * D_Ti_Mt) + (P_Ilm * D_Ti_Ilm) + (P_Ap * D_Ti_Ap) + (P_Chr * D_Ti_Chr) + (P_Maj_gn * D_Ti_Maj_gn) + (P_Amp * D_Ti_Amp)
D_Gd_bulk = (P_Cpx * D_Gd_Cpx) + (P_Pl * D_Gd_Pl) + (P_Opx * D_Gd_Opx) + (P_Ol * D_Gd_Ol) + (P_Mt * D_Gd_Mt) + (P_Ilm * D_Gd_Ilm) + (P_Ap * D_Gd_Ap) + (P_Chr * D_Gd_Chr) + (P_Maj_gn * D_Gd_Maj_gn) + (P_Amp * D_Gd_Amp)
D_Tb_bulk = (P_Cpx * D_Tb_Cpx) + (P_Pl * D_Tb_Pl) + (P_Opx * D_Tb_Opx) + (P_Ol * D_Tb_Ol) + (P_Mt * D_Tb_Mt) + (P_Ilm * D_Tb_Ilm) + (P_Ap * D_Tb_Ap) + (P_Chr * D_Tb_Chr) + (P_Maj_gn * D_Tb_Maj_gn) + (P_Amp * D_Tb_Amp)
D_Dy_bulk = (P_Cpx * D_Dy_Cpx) + (P_Pl * D_Dy_Pl) + (P_Opx * D_Dy_Opx) + (P_Ol * D_Dy_Ol) + (P_Mt * D_Dy_Mt) + (P_Ilm * D_Dy_Ilm) + (P_Ap * D_Dy_Ap) + (P_Chr * D_Dy_Chr) + (P_Maj_gn * D_Dy_Maj_gn) + (P_Amp * D_Dy_Amp)
D_Y_bulk = (P_Cpx * D_Y_Cpx) + (P_Pl * D_Y_Pl) + (P_Opx * D_Y_Opx) + (P_Ol * D_Y_Ol) + (P_Mt * D_Y_Mt) + (P_Ilm * D_Y_Ilm) + (P_Ap * D_Y_Ap) + (P_Chr * D_Y_Chr) + (P_Maj_gn * D_Y_Maj_gn) + (P_Amp * D_Y_Amp)
D_Ho_bulk = (P_Cpx * D_Ho_Cpx) + (P_Pl * D_Ho_Pl) + (P_Opx * D_Ho_Opx) + (P_Ol * D_Ho_Ol) + (P_Mt * D_Ho_Mt) + (P_Ilm * D_Ho_Ilm) + (P_Ap * D_Ho_Ap) + (P_Chr * D_Ho_Chr) + (P_Maj_gn * D_Ho_Maj_gn) + (P_Amp * D_Ho_Amp)
D_Er_bulk = (P_Cpx * D_Er_Cpx) + (P_Pl * D_Er_Pl) + (P_Opx * D_Er_Opx) + (P_Ol * D_Er_Ol) + (P_Mt * D_Er_Mt) + (P_Ilm * D_Er_Ilm) + (P_Ap * D_Er_Ap) + (P_Chr * D_Er_Chr) + (P_Maj_gn * D_Er_Maj_gn) + (P_Amp * D_Er_Amp)
D_Tm_bulk = (P_Cpx * D_Tm_Cpx) + (P_Pl * D_Tm_Pl) + (P_Opx * D_Tm_Opx) + (P_Ol * D_Tm_Ol) + (P_Mt * D_Tm_Mt) + (P_Ilm * D_Tm_Ilm) + (P_Ap * D_Tm_Ap) + (P_Chr * D_Tm_Chr) + (P_Maj_gn * D_Tm_Maj_gn) + (P_Amp * D_Tm_Amp)
D_Yb_bulk = (P_Cpx * D_Yb_Cpx) + (P_Pl * D_Yb_Pl) + (P_Opx * D_Yb_Opx) + (P_Ol * D_Yb_Ol) + (P_Mt * D_Yb_Mt) + (P_Ilm * D_Yb_Ilm) + (P_Ap * D_Yb_Ap) + (P_Chr * D_Yb_Chr) + (P_Maj_gn * D_Yb_Maj_gn) + (P_Amp * D_Yb_Amp)
D_Lu_bulk = (P_Cpx * D_Lu_Cpx) + (P_Pl * D_Lu_Pl) + (P_Opx * D_Lu_Opx) + (P_Ol * D_Lu_Ol) + (P_Mt * D_Lu_Mt) + (P_Ilm * D_Lu_Ilm) + (P_Ap * D_Lu_Ap) + (P_Chr * D_Lu_Chr) + (P_Maj_gn * D_Lu_Maj_gn) + (P_Amp * D_Lu_Amp)
D_V_bulk = (P_Cpx * D_V_Cpx) + (P_Pl * D_V_Pl) + (P_Opx * D_V_Opx) + (P_Ol * D_V_Ol) + (P_Mt * D_V_Mt) + (P_Ilm * D_V_Ilm) + (P_Ap * D_V_Ap) + (P_Chr * D_V_Chr) + (P_Maj_gn * D_V_Maj_gn) + (P_Amp * D_V_Amp)
D_Sc_bulk = (P_Cpx * D_Sc_Cpx) + (P_Pl * D_Sc_Pl) + (P_Opx * D_Sc_Opx) + (P_Ol * D_Sc_Ol) + (P_Mt * D_Sc_Mt) + (P_Ilm * D_Sc_Ilm) + (P_Ap * D_Sc_Ap) + (P_Chr * D_Sc_Chr) + (P_Maj_gn * D_Sc_Maj_gn) + (P_Amp * D_Sc_Amp)
#####################################################################################################
# Residual melt calculation
#####################################################################################################
Th_sil_f = Th_sil_i * (F_sil_remaining ** (D_Th_bulk - 1))
Nb_sil_f = Nb_sil_i * (F_sil_remaining ** (D_Nb_bulk - 1))
La_sil_f = La_sil_i * (F_sil_remaining ** (D_La_bulk - 1))
Ce_sil_f = Ce_sil_i * (F_sil_remaining ** (D_Ce_bulk - 1))
Pr_sil_f = Pr_sil_i * (F_sil_remaining ** (D_Pr_bulk - 1))
Nd_sil_f = Nd_sil_i * (F_sil_remaining ** (D_Nd_bulk - 1))
Zr_sil_f = Zr_sil_i * (F_sil_remaining ** (D_Zr_bulk - 1))
Hf_sil_f = Hf_sil_i * (F_sil_remaining ** (D_Hf_bulk - 1))
Sm_sil_f = Sm_sil_i * (F_sil_remaining ** (D_Sm_bulk - 1))
Eu_sil_f = Eu_sil_i * (F_sil_remaining ** (D_Eu_bulk - 1))
Ti_sil_f = Ti_sil_i * (F_sil_remaining ** (D_Ti_bulk - 1))
Gd_sil_f = Gd_sil_i * (F_sil_remaining ** (D_Gd_bulk - 1))
Tb_sil_f = Tb_sil_i * (F_sil_remaining ** (D_Tb_bulk - 1))
Dy_sil_f = Dy_sil_i * (F_sil_remaining ** (D_Dy_bulk - 1))
Y_sil_f = Y_sil_i * (F_sil_remaining ** (D_Y_bulk - 1))
Ho_sil_f = Ho_sil_i * (F_sil_remaining ** (D_Ho_bulk - 1))
Er_sil_f = Er_sil_i * (F_sil_remaining ** (D_Er_bulk - 1))
Tm_sil_f = Tm_sil_i * (F_sil_remaining ** (D_Tm_bulk - 1))
Yb_sil_f = Yb_sil_i * (F_sil_remaining ** (D_Yb_bulk - 1))
Lu_sil_f = Lu_sil_i * (F_sil_remaining ** (D_Lu_bulk - 1))
V_sil_f = V_sil_i * (F_sil_remaining ** (D_V_bulk - 1))
Sc_sil_f = Sc_sil_i * (F_sil_remaining ** (D_Sc_bulk - 1))
#####################################################################################################
# Cumulate melt calculation
#####################################################################################################
Th_sol = ((1 - (F_sil_remaining ** D_Th_bulk)) / (1 - F_sil_remaining)) * Th_sil_i
Nb_sol = ((1 - (F_sil_remaining ** D_Nb_bulk)) / (1 - F_sil_remaining)) * Nb_sil_i
La_sol = ((1 - (F_sil_remaining ** D_La_bulk)) / (1 - F_sil_remaining)) * La_sil_i
Ce_sol = ((1 - (F_sil_remaining ** D_Ce_bulk)) / (1 - F_sil_remaining)) * Ce_sil_i
Pr_sol = ((1 - (F_sil_remaining ** D_Pr_bulk)) / (1 - F_sil_remaining)) * Pr_sil_i
Nd_sol = ((1 - (F_sil_remaining ** D_Nd_bulk)) / (1 - F_sil_remaining)) * Nd_sil_i
Zr_sol = ((1 - (F_sil_remaining ** D_Zr_bulk)) / (1 - F_sil_remaining)) * Zr_sil_i
Hf_sol = ((1 - (F_sil_remaining ** D_Hf_bulk)) / (1 - F_sil_remaining)) * Hf_sil_i
Sm_sol = ((1 - (F_sil_remaining ** D_Sm_bulk)) / (1 - F_sil_remaining)) * Sm_sil_i
Eu_sol = ((1 - (F_sil_remaining ** D_Eu_bulk)) / (1 - F_sil_remaining)) * Eu_sil_i
Ti_sol = ((1 - (F_sil_remaining ** D_Ti_bulk)) / (1 - F_sil_remaining)) * Ti_sil_i
Gd_sol = ((1 - (F_sil_remaining ** D_Gd_bulk)) / (1 - F_sil_remaining)) * Gd_sil_i
Tb_sol = ((1 - (F_sil_remaining ** D_Tb_bulk)) / (1 - F_sil_remaining)) * Tb_sil_i
Dy_sol = ((1 - (F_sil_remaining ** D_Dy_bulk)) / (1 - F_sil_remaining)) * Dy_sil_i
Y_sol = ((1 - (F_sil_remaining ** D_Y_bulk)) / (1 - F_sil_remaining)) * Y_sil_i
Ho_sol = ((1 - (F_sil_remaining ** D_Ho_bulk)) / (1 - F_sil_remaining)) * Ho_sil_i
Er_sol = ((1 - (F_sil_remaining ** D_Er_bulk)) / (1 - F_sil_remaining)) * Er_sil_i
Tm_sol = ((1 - (F_sil_remaining ** D_Tm_bulk)) / (1 - F_sil_remaining)) * Tm_sil_i
Yb_sol = ((1 - (F_sil_remaining ** D_Yb_bulk)) / (1 - F_sil_remaining)) * Yb_sil_i
Lu_sol = ((1 - (F_sil_remaining ** D_Lu_bulk)) / (1 - F_sil_remaining)) * Lu_sil_i
V_sol = ((1 - (F_sil_remaining ** D_V_bulk)) / (1 - F_sil_remaining)) * V_sil_i
Sc_sol = ((1 - (F_sil_remaining ** D_Sc_bulk)) / (1 - F_sil_remaining)) * Sc_sil_i
您可能需要安装它。
python --version
python -m pip install seaborn
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