Source code for pharmpy.modeling.math
from __future__ import annotations
from pharmpy.deps import numpy as np
from pharmpy.deps import pandas as pd
from pharmpy.internals.math import cov2corr
[docs]
def calculate_se_from_cov(cov: pd.DataFrame):
"""Calculate standard errors from a covariance matrix
Parameters
----------
cov : pd.DataFrame
Input covariance matrix
Return
------
pd.Series
Standard errors
Examples
--------
>>> from pharmpy.modeling import calculate_se_from_cov
>>> from pharmpy.tools import load_example_modelfit_results
>>> results = load_example_modelfit_results("pheno")
>>> cov = results.covariance_matrix
>>> cov
POP_CL POP_VC COVAPGR IIV_CL IIV_VC SIGMA
POP_CL 4.408600e-08 4.761930e-08 -0.000002 -0.000001 1.552150e-07 8.042430e-08
POP_VC 4.761930e-08 7.233190e-04 -0.000804 0.000050 7.174490e-05 1.467290e-05
COVAPGR -1.679560e-06 -8.041750e-04 0.007015 -0.000108 -3.935790e-05 2.922260e-05
IIV_CL -1.090290e-06 4.989580e-05 -0.000108 0.000180 -1.863210e-05 5.049910e-06
IIV_VC 1.552150e-07 7.174490e-05 -0.000039 -0.000019 5.588920e-05 -4.497590e-07
SIGMA 8.042430e-08 1.467290e-05 0.000029 0.000005 -4.497590e-07 5.197970e-06
>>> calculate_se_from_cov(cov)
POP_CL 0.000210
POP_VC 0.026895
COVAPGR 0.083756
IIV_CL 0.013416
IIV_VC 0.007476
SIGMA 0.002280
dtype: float64
See also
--------
calculate_se_from_prec : Standard errors from precision matrix
calculate_corr_from_cov : Correlation matrix from covariance matrix
calculate_cov_from_prec : Covariance matrix from precision matrix
calculate_cov_from_corrse : Covariance matrix from correlation matrix and standard errors
calculate_prec_from_cov : Precision matrix from covariance matrix
calculate_prec_from_corrse : Precision matrix from correlation matrix and standard errors
calculate_corr_from_prec : Correlation matrix from precision matrix
"""
se = pd.Series(np.sqrt(np.diag(cov.values)), index=cov.index)
return se
[docs]
def calculate_se_from_prec(precision_matrix: pd.DataFrame):
"""Calculate standard errors from a precision matrix
Parameters
----------
precision_matrix : pd.DataFrame
Input precision matrix
Return
------
pd.Series
Standard errors
Examples
--------
>>> from pharmpy.modeling import calculate_se_from_prec
>>> from pharmpy.tools import load_example_modelfit_results
>>> results = load_example_modelfit_results("pheno")
>>> prec = results.precision_matrix
>>> prec
POP_CL POP_VC COVAPGR IIV_CL IIV_VC SIGMA
POP_CL 2.993428e+07 22261.039122 16027.859538 203633.930854 -39113.269503 -817314.801755
POP_VC 2.226104e+04 2129.852212 260.115313 -373.896066 -2799.330946 -7697.921603
COVAPGR 1.602786e+04 260.115313 187.053488 177.987340 -205.261483 -2224.522815
IIV_CL 2.036339e+05 -373.896066 177.987340 7542.279597 2472.034556 -10209.416944
IIV_VC -3.911327e+04 -2799.330946 -205.261483 2472.034556 22348.216559 9193.203130
SIGMA -8.173148e+05 -7697.921603 -2224.522815 -10209.416944 9193.203130 249978.454601
>>> calculate_se_from_prec(prec)
POP_CL 0.000210
POP_VC 0.026895
COVAPGR 0.083756
IIV_CL 0.013416
IIV_VC 0.007476
SIGMA 0.002280
dtype: float64
See also
--------
calculate_se_from_cov : Standard errors from covariance matrix
calculate_corr_from_cov : Correlation matrix from covariance matrix
calculate_cov_from_prec : Covariance matrix from precision matrix
calculate_cov_from_corrse : Covariance matrix from correlation matrix and standard errors
calculate_prec_from_cov : Precision matrix from covariance matrix
calculate_prec_from_corrse : Precision matrix from correlation matrix and standard errors
calculate_corr_from_prec : Correlation matrix from precision matrix
"""
se = pd.Series(
np.sqrt(np.diag(np.linalg.inv(precision_matrix.values))), index=precision_matrix.index
)
return se
[docs]
def calculate_corr_from_cov(cov: pd.DataFrame):
"""Calculate correlation matrix from a covariance matrix
Parameters
----------
cov : pd.DataFrame
Covariance matrix
Return
------
pd.DataFrame
Correlation matrix
Examples
--------
>>> from pharmpy.modeling import calculate_corr_from_cov
>>> from pharmpy.tools import load_example_modelfit_results
>>> results = load_example_modelfit_results("pheno")
>>> cov = results.covariance_matrix
>>> cov
POP_CL POP_VC COVAPGR IIV_CL IIV_VC SIGMA
POP_CL 4.408600e-08 4.761930e-08 -0.000002 -0.000001 1.552150e-07 8.042430e-08
POP_VC 4.761930e-08 7.233190e-04 -0.000804 0.000050 7.174490e-05 1.467290e-05
COVAPGR -1.679560e-06 -8.041750e-04 0.007015 -0.000108 -3.935790e-05 2.922260e-05
IIV_CL -1.090290e-06 4.989580e-05 -0.000108 0.000180 -1.863210e-05 5.049910e-06
IIV_VC 1.552150e-07 7.174490e-05 -0.000039 -0.000019 5.588920e-05 -4.497590e-07
SIGMA 8.042430e-08 1.467290e-05 0.000029 0.000005 -4.497590e-07 5.197970e-06
>>> calculate_corr_from_cov(cov)
POP_CL POP_VC COVAPGR IIV_CL IIV_VC SIGMA
POP_CL 1.000000 0.008433 -0.095506 -0.387063 0.098882 0.168004
POP_VC 0.008433 1.000000 -0.357003 0.138290 0.356831 0.239295
COVAPGR -0.095506 -0.357003 1.000000 -0.095767 -0.062857 0.153034
IIV_CL -0.387063 0.138290 -0.095767 1.000000 -0.185775 0.165104
IIV_VC 0.098882 0.356831 -0.062857 -0.185775 1.000000 -0.026388
SIGMA 0.168004 0.239295 0.153034 0.165104 -0.026388 1.000000
See also
--------
calculate_se_from_cov : Standard errors from covariance matrix
calculate_se_from_prec : Standard errors from precision matrix
calculate_cov_from_prec : Covariance matrix from precision matrix
calculate_cov_from_corrse : Covariance matrix from correlation matrix and standard errors
calculate_prec_from_cov : Precision matrix from covariance matrix
calculate_prec_from_corrse : Precision matrix from correlation matrix and standard errors
calculate_corr_from_prec : Correlation matrix from precision matrix
"""
corr = pd.DataFrame(cov2corr(cov.values), index=cov.index, columns=cov.columns)
return corr
[docs]
def calculate_cov_from_prec(precision_matrix: pd.DataFrame):
"""Calculate covariance matrix from a precision matrix
Parameters
----------
precision_matrix : pd.DataFrame
Precision matrix
Return
------
pd.DataFrame
Covariance matrix
Examples
--------
>>> from pharmpy.modeling import calculate_cov_from_prec
>>> from pharmpy.tools import load_example_modelfit_results
>>> results = load_example_modelfit_results("pheno")
>>> prec = results.precision_matrix
>>> prec
POP_CL POP_VC COVAPGR IIV_CL IIV_VC SIGMA
POP_CL 2.993428e+07 22261.039122 16027.859538 203633.930854 -39113.269503 -817314.801755
POP_VC 2.226104e+04 2129.852212 260.115313 -373.896066 -2799.330946 -7697.921603
COVAPGR 1.602786e+04 260.115313 187.053488 177.987340 -205.261483 -2224.522815
IIV_CL 2.036339e+05 -373.896066 177.987340 7542.279597 2472.034556 -10209.416944
IIV_VC -3.911327e+04 -2799.330946 -205.261483 2472.034556 22348.216559 9193.203130
SIGMA -8.173148e+05 -7697.921603 -2224.522815 -10209.416944 9193.203130 249978.454601
>>> calculate_cov_from_prec(prec)
POP_CL POP_VC COVAPGR IIV_CL IIV_VC SIGMA
POP_CL 4.408600e-08 4.761930e-08 -0.000002 -0.000001 1.552150e-07 8.042430e-08
POP_VC 4.761930e-08 7.233190e-04 -0.000804 0.000050 7.174490e-05 1.467290e-05
COVAPGR -1.679560e-06 -8.041750e-04 0.007015 -0.000108 -3.935790e-05 2.922260e-05
IIV_CL -1.090290e-06 4.989580e-05 -0.000108 0.000180 -1.863210e-05 5.049910e-06
IIV_VC 1.552150e-07 7.174490e-05 -0.000039 -0.000019 5.588920e-05 -4.497590e-07
SIGMA 8.042430e-08 1.467290e-05 0.000029 0.000005 -4.497590e-07 5.197970e-06
See also
--------
calculate_se_from_cov : Standard errors from covariance matrix
calculate_se_from_prec : Standard errors from precision matrix
calculate_corr_from_cov : Correlation matrix from covariance matrix
calculate_cov_from_corrse : Covariance matrix from correlation matrix and standard errors
calculate_prec_from_cov : Precision matrix from covariance matrix
calculate_prec_from_corrse : Precision matrix from correlation matrix and standard errors
calculate_corr_from_prec : Correlation matrix from precision matrix
"""
cov = pd.DataFrame(
np.linalg.inv(precision_matrix.values),
index=precision_matrix.index,
columns=precision_matrix.columns,
)
return cov
[docs]
def calculate_cov_from_corrse(corr: pd.DataFrame, se: pd.Series):
"""Calculate covariance matrix from a correlation matrix and standard errors
Parameters
----------
corr : pd.DataFrame
Correlation matrix
se : pd.Series
Standard errors
Return
------
pd.DataFrame
Covariance matrix
Examples
--------
>>> from pharmpy.modeling import calculate_cov_from_corrse
>>> from pharmpy.tools import load_example_modelfit_results
>>> results = load_example_modelfit_results("pheno")
>>> corr = results.correlation_matrix
>>> se = results.standard_errors
>>> corr
POP_CL POP_VC COVAPGR IIV_CL IIV_VC SIGMA
POP_CL 1.000000 0.008433 -0.095506 -0.387063 0.098882 0.168004
POP_VC 0.008433 1.000000 -0.357003 0.138290 0.356831 0.239295
COVAPGR -0.095506 -0.357003 1.000000 -0.095767 -0.062857 0.153034
IIV_CL -0.387063 0.138290 -0.095767 1.000000 -0.185775 0.165104
IIV_VC 0.098882 0.356831 -0.062857 -0.185775 1.000000 -0.026388
SIGMA 0.168004 0.239295 0.153034 0.165104 -0.026388 1.000000
>>> calculate_cov_from_corrse(corr, se)
POP_CL POP_VC COVAPGR IIV_CL IIV_VC SIGMA
POP_CL 4.408614e-08 4.761939e-08 -0.000002 -0.000001 1.552153e-07 8.042458e-08
POP_VC 4.761939e-08 7.233195e-04 -0.000804 0.000050 7.174494e-05 1.467293e-05
COVAPGR -1.679562e-06 -8.041749e-04 0.007015 -0.000108 -3.935789e-05 2.922264e-05
IIV_CL -1.090293e-06 4.989586e-05 -0.000108 0.000180 -1.863212e-05 5.049924e-06
IIV_VC 1.552153e-07 7.174494e-05 -0.000039 -0.000019 5.588923e-05 -4.497600e-07
SIGMA 8.042458e-08 1.467293e-05 0.000029 0.000005 -4.497600e-07 5.197990e-06
See also
--------
calculate_se_from_cov : Standard errors from covariance matrix
calculate_se_from_prec : Standard errors from precision matrix
calculate_corr_from_cov : Correlation matrix from covariance matrix
calculate_cov_from_prec : Covariance matrix from precision matrix
calculate_prec_from_cov : Precision matrix from covariance matrix
calculate_prec_from_corrse : Precision matrix from correlation matrix and standard errors
calculate_corr_from_prec : Correlation matrix from precision matrix
"""
sd_matrix = np.diag(se.values)
cov = sd_matrix @ corr.values @ sd_matrix
cov_df = pd.DataFrame(cov, index=corr.index, columns=corr.columns)
return cov_df
[docs]
def calculate_prec_from_cov(cov: pd.DataFrame):
"""Calculate precision matrix from a covariance matrix
Parameters
----------
cov : pd.DataFrame
Covariance matrix
Return
------
pd.DataFrame
Precision matrix
Examples
--------
>>> from pharmpy.modeling import calculate_prec_from_cov
>>> from pharmpy.tools import load_example_modelfit_results
>>> results = load_example_modelfit_results("pheno")
>>> cov = results.covariance_matrix
>>> cov
POP_CL POP_VC COVAPGR IIV_CL IIV_VC SIGMA
POP_CL 4.408600e-08 4.761930e-08 -0.000002 -0.000001 1.552150e-07 8.042430e-08
POP_VC 4.761930e-08 7.233190e-04 -0.000804 0.000050 7.174490e-05 1.467290e-05
COVAPGR -1.679560e-06 -8.041750e-04 0.007015 -0.000108 -3.935790e-05 2.922260e-05
IIV_CL -1.090290e-06 4.989580e-05 -0.000108 0.000180 -1.863210e-05 5.049910e-06
IIV_VC 1.552150e-07 7.174490e-05 -0.000039 -0.000019 5.588920e-05 -4.497590e-07
SIGMA 8.042430e-08 1.467290e-05 0.000029 0.000005 -4.497590e-07 5.197970e-06
>>> calculate_prec_from_cov(cov)
POP_CL POP_VC COVAPGR IIV_CL IIV_VC SIGMA
POP_CL 2.993428e+07 22261.039122 16027.859538 203633.930854 -39113.269503 -817314.801755
POP_VC 2.226104e+04 2129.852212 260.115313 -373.896066 -2799.330946 -7697.921603
COVAPGR 1.602786e+04 260.115313 187.053488 177.987340 -205.261483 -2224.522815
IIV_CL 2.036339e+05 -373.896066 177.987340 7542.279597 2472.034556 -10209.416944
IIV_VC -3.911327e+04 -2799.330946 -205.261483 2472.034556 22348.216559 9193.203130
SIGMA -8.173148e+05 -7697.921603 -2224.522815 -10209.416944 9193.203130 249978.454601
See also
--------
calculate_se_from_cov : Standard errors from covariance matrix
calculate_se_from_prec : Standard errors from precision matrix
calculate_corr_from_cov : Correlation matrix from covariance matrix
calculate_cov_from_prec : Covariance matrix from precision matrix
calculate_cov_from_corrse : Covariance matrix from correlation matrix and standard errors
calculate_prec_from_corrse : Precision matrix from correlation matrix and standard errors
calculate_corr_from_prec : Correlation matrix from precision matrix
"""
Pm = pd.DataFrame(np.linalg.inv(cov.values), index=cov.index, columns=cov.columns)
return Pm
[docs]
def calculate_prec_from_corrse(corr: pd.DataFrame, se: pd.Series):
"""Calculate precision matrix from a correlation matrix and standard errors
Parameters
----------
corr : pd.DataFrame
Correlation matrix
se : pd.Series
Standard errors
Return
------
pd.DataFrame
Precision matrix
Examples
--------
>>> from pharmpy.modeling import calculate_prec_from_corrse
>>> from pharmpy.tools import load_example_modelfit_results
>>> results = load_example_modelfit_results("pheno")
>>> corr = results.correlation_matrix
>>> se = results.standard_errors
>>> corr
POP_CL POP_VC COVAPGR IIV_CL IIV_VC SIGMA
POP_CL 1.000000 0.008433 -0.095506 -0.387063 0.098882 0.168004
POP_VC 0.008433 1.000000 -0.357003 0.138290 0.356831 0.239295
COVAPGR -0.095506 -0.357003 1.000000 -0.095767 -0.062857 0.153034
IIV_CL -0.387063 0.138290 -0.095767 1.000000 -0.185775 0.165104
IIV_VC 0.098882 0.356831 -0.062857 -0.185775 1.000000 -0.026388
SIGMA 0.168004 0.239295 0.153034 0.165104 -0.026388 1.000000
>>> calculate_prec_from_corrse(corr, se)
POP_CL POP_VC COVAPGR IIV_CL IIV_VC SIGMA
POP_CL 2.993418e+07 22260.995666 16027.840996 203633.422078 -39113.196303 -817311.952371
POP_VC 2.226100e+04 2129.850713 260.115336 -373.895598 -2799.329201 -7697.904374
COVAPGR 1.602784e+04 260.115336 187.053654 177.987259 -205.261518 -2224.519605
IIV_CL 2.036334e+05 -373.895598 177.987259 7542.266046 2472.031665 -10209.388516
IIV_VC -3.911320e+04 -2799.329201 -205.261518 2472.031665 22348.204432 9193.183296
SIGMA -8.173120e+05 -7697.904374 -2224.519605 -10209.388516 9193.183296 249977.511621
See also
--------
calculate_se_from_cov : Standard errors from covariance matrix
calculate_se_from_prec : Standard errors from precision matrix
calculate_corr_from_cov : Correlation matrix from covariance matrix
calculate_cov_from_prec : Covariance matrix from precision matrix
calculate_cov_from_corrse : Covariance matrix from correlation matrix and standard errors
calculate_prec_from_cov : Precision matrix from covariance matrix
calculate_corr_from_prec : Correlation matrix from precision matrix
"""
sd_matrix = np.diag(se.values)
cov = sd_matrix @ corr.values @ sd_matrix
Pm = pd.DataFrame(np.linalg.inv(cov), index=corr.index, columns=corr.columns)
return Pm
[docs]
def calculate_corr_from_prec(precision_matrix: pd.DataFrame):
"""Calculate correlation matrix from a precision matrix
Parameters
----------
precision_matrix : pd.DataFrame
Precision matrix
Return
------
pd.DataFrame
Correlation matrix
Examples
--------
>>> from pharmpy.modeling import calculate_corr_from_prec
>>> from pharmpy.tools import load_example_modelfit_results
>>> results = load_example_modelfit_results("pheno")
>>> prec = results.precision_matrix
>>> prec
POP_CL POP_VC COVAPGR IIV_CL IIV_VC SIGMA
POP_CL 2.993428e+07 22261.039122 16027.859538 203633.930854 -39113.269503 -817314.801755
POP_VC 2.226104e+04 2129.852212 260.115313 -373.896066 -2799.330946 -7697.921603
COVAPGR 1.602786e+04 260.115313 187.053488 177.987340 -205.261483 -2224.522815
IIV_CL 2.036339e+05 -373.896066 177.987340 7542.279597 2472.034556 -10209.416944
IIV_VC -3.911327e+04 -2799.330946 -205.261483 2472.034556 22348.216559 9193.203130
SIGMA -8.173148e+05 -7697.921603 -2224.522815 -10209.416944 9193.203130 249978.454601
>>> calculate_corr_from_prec(prec)
POP_CL POP_VC COVAPGR IIV_CL IIV_VC SIGMA
POP_CL 1.000000 0.008433 -0.095506 -0.387063 0.098882 0.168004
POP_VC 0.008433 1.000000 -0.357003 0.138290 0.356831 0.239295
COVAPGR -0.095506 -0.357003 1.000000 -0.095767 -0.062857 0.153034
IIV_CL -0.387063 0.138290 -0.095767 1.000000 -0.185775 0.165104
IIV_VC 0.098882 0.356831 -0.062857 -0.185775 1.000000 -0.026388
SIGMA 0.168004 0.239295 0.153034 0.165104 -0.026388 1.000000
See also
--------
calculate_se_from_cov : Standard errors from covariance matrix
calculate_se_from_prec : Standard errors from precision matrix
calculate_corr_from_cov : Correlation matrix from covariance matrix
calculate_cov_from_prec : Covariance matrix from precision matrix
calculate_cov_from_corrse : Covariance matrix from correlation matrix and standard errors
calculate_prec_from_cov : Precision matrix from covariance matrix
calculate_prec_from_corrse : Precision matrix from correlation matrix and standard errors
"""
corr = pd.DataFrame(
cov2corr(np.linalg.inv(precision_matrix.values)),
index=precision_matrix.index,
columns=precision_matrix.columns,
)
return corr
