Metadata-Version: 2.1
Name: gmat
Version: 2020.4.9
Summary: Genomic Multivariate Analysis Tools
Home-page: https://github.com/chaoning/GMAT
Author: Chao Ning
Author-email: ningchao91@gmail.com
License: UNKNOWN
Description: 
        # Contents
        * [1 Contact](#1-Contact)
        * [2 Install](#2-Install)
          * [2.1 Dependencies](#21-Dependencies)
          * [2.2 Quick install](#22-Quick-install)
          * [2.3 Detailed Package Install Instructions](#23-Detailed-Package-Install-Instructions)
        * [3 REMMAX function](#3-REMMAX-function)
          * [3.1 Format of the input file](#31-Format-of-the-input-file)
          * [3.2 Exhaustive additive by addtive epistatis](#32-Exhaustive-additive-by-addtive-epistatis)
            * [3.2.1 Include additive and additive by additive genomic relationship matrix](#321-Include-additive-and-additive-by-additive-genomic-relationship-matrix)
            * [3.2.2 Include additive, dominance and additive by additive genomic relationship matrix](#322-Include-additive-dominance-and-additive-by-additive-genomic-relationship-matrix)
            * [3.2.3 Include additive, dominance and three kinds of epistatic genomic relationship matrix](#323-Include-additive-dominance-and-three-kinds-of-epistatic-genomic-relationship-matrix)
          * [3.3 Exhaustive additive by dominance epistatis](#33-Exhaustive-additive-by-dominance-epistatis)
          * [3.4 Exhaustive dominance by dominance epistatis](#34-Exhaustive-dominance-by-dominance-epistatis)
        
        # 1 Contact
        Chao Ning  
        ningchao(at)sdau(dot)edu(dot)cn  
        ningchao91(at)gmail(dot)com  
        
        # 2 Install
        We will keep GMAT updated. Please uninstall older version to obtain the latest functions. The easiest uninstall way:  
        \> pip uninstall gmat
        
        ## 2.1 Dependencies
        * numpy>=1.16.0  
        * pandas>=0.19.0  
        * scipy>=1.1.1  
        * cffi>=1.12.0  
        * pandas_plink>=2.0.0  
        * tqdm>=4.43.0  
        
        We recommend using a Python distribution such as [Anaconda](https://www.anaconda.com/distribution/) (Python 3.7 version). This distribution can be used on Linux and Windows. It is the easiest way to get all the required package dependencies. 
        
        ## 2.2 Quick install
        \> pip install gmat  
        
        ## 2.3 Detailed Package Install Instructions
        (1) Install the dependent packages  
        (2) Go to the directory of GMAT and type  
        \> python setup.py install  
        
        # 3 REMMAX function  
        Rapid Epistatic Mixed Model Association Studies
        
        ***Cite***:  
        * Dan Wang, Hui Tang, Jian-Feng Liu, Shizhong Xu, Qin Zhang and Chao Ning. Rapid Epistatic Mixed Model Association Studies by Controlling Multiple Polygenic Effects. *BioRxiv*, 2020. doi: https://doi.org/10.1101/2020.03.05.976498  
        * Chao Ning, Dan Wang, Huimin Kang, Raphael Mrode, Lei Zhou, Shizhong Xu, Jian-Feng Liu. A rapid epistatic mixed-model association analysis by linear retransformations of genomic estimated values. *Bioinformatics*, 2018, 34(11): 1817-1825.  
        
        ## 3.1 Format of the input file
        * Plink binary file including \*.bed, \*.bim and \*.fam.  
        Missing genotypes are recommended to impute with Beagle or other softwares, although they will be imputed according the frequency of occurrence.   
        
        * phenotypic file:  
        (1) Delimited by blanks or tabs;  
        (2) All individuals in the plink file must have phenotypic values. If no, please remove these individuals from the plink binary file;  
        (3) The fisrt column is the family id and the second column is the individual id. The first two columns are the same to plink fam file, but order can be different;  
        (4) The last column is the phenotypic values. **Miss values are not allowed**;  
        (5) The covariates (including population means) are put before the phenotypic column. A column of 1’s must be contained.  
        (6) Repeated mesures are allowed for individuals.  
        An example phenotypic file with four covariates (population mean, sex, age, treatmeant or untreatmeant) is as follows:  
        12659	14462	1	0	126	0	0.58  
        12659	14463	1	0	91	1	0.39  
        12659	14464	1	1	126	0	0.37  
        12659	14465	1	0	91	1	0.9  
        12659	14466	1	0	91	1	0.84  
        12659	14467	1	0	91	1	0.61  
        12659	14468	1	1	91	1	0.84  
        An example phenotypic file with repeated mesures is as follows:  
        0 01_01 1 -2.25383070574996  
        0 01_02 1 -1.88774565927855  
        0 01_03 1 2.4150679267528  
        0 01_03 1 -0.320697695608065  
        0 01_04 1 2.41743663901475  
        0 01_06 1 -0.634513668596019  
        0 01_06 1 -1.4489729404784  
        0 01_07 1 1.92328500921367  
        0 01_07 1 1.54547583777757  
          
        ## 3.2 Exhaustive additive by addtive epistatis  
        Data: Mouse data in directory of GMAT/examples/data/mouse    
        
        ### 3.2.1 Include additive and additive by additive genomic relationship matrix
        #### (1)  Exact test (for small data)
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.gmatrix import agmat
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        from gmat.remma.remma_epiAA import remma_epiAA
        from gmat.remma import annotation_snp_pos
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file) 
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        gmat_lst = [ag, ag*ag]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var_a_axa.txt')
        
        # Step 3: Test
        var_com = np.loadtxt('var_a_axa.txt')  # numpy array： [0] addtive variance; [1] additive by additive variance; [2] residual variance
        remma_epiAA(pheno_file, bed_file, gmat_lst, var_com, p_cut=1.0e-5, out_file='epiAA_a_axa')
        
        # Step 4: Select top SNPs and add the SNP position
        res_file = 'epiAA_a_axa'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        ```
        
        #### (2) Parallel exact test  (for small data)
        Analysis can be subdivided with remma_epiAA_parallel and run parallelly on different machines.
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.gmatrix import agmat
        from gmat.uvlmm.design_matrix import design_matrix_wemai_multi_gmat
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file) 
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        gmat_lst = [ag, ag*ag]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var_a_axa.txt')
        
        # Step 3: parallel test. Write codes of thist step in separate scripts and run parallelly
        
        ## parallel 1
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAA import remma_epiAA_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var_a_axa.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        gmat_lst = [ag, ag*ag]
        # parallel=[3, 1] means divide total tests into three parts and run part 1
        remma_epiAA_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 1], p_cut=1.0e-5, out_file='epiAA_parallel_a_axa')
        
        ## parallel 2
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAA import remma_epiAA_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var_a_axa.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        gmat_lst = [ag, ag*ag]
        # parallel=[3, 2] means divide total tests into three parts and run part 2
        remma_epiAA_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 2], p_cut=1.0e-5, out_file='epiAA_parallel_a_axa')
        
        ## parallel 3
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAA import remma_epiAA_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var_a_axa.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        gmat_lst = [ag, ag*ag]
        # parallel=[3, 3] means divide total tests into three parts and run part 3
        remma_epiAA_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 3], p_cut=1.0e-5, out_file='epiAA_parallel_a_axa')
        
        # Step 4: Merge files 'epiAA_parallel_a_axa.*' with the following codes.
        import os
        prefix = 'epiAA_parallel_a_axa'
        parallel_num = 3  # the number of parallels
        with open(prefix + ".merge", 'w') as fout:
            with open(prefix + '.1') as fin:
                head_line = fin.readline()
                fout.write(head_line)
            for i in range(1, parallel_num+1):
                with open(prefix + '.' + str(i)) as fin:
                    head_line = fin.readline()
                    for line in fin:
                        fout.write(line)
                os.remove(prefix + '.' + str(i))
        
        # Step 5: Select top SNPs and add the SNP position
        from gmat.remma import annotation_snp_pos
        res_file = 'epiAA_parallel_a_axa.merge'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        
        ```
        
        #### (3) approximate test (recommended for big data)
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        import pandas as pd
        from gmat.gmatrix import agmat
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        from gmat.remma.remma_epiAA import remma_epiAA_approx
        from gmat.remma import annotation_snp_pos
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file) 
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        gmat_lst = [ag, ag*ag]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var_a_axa.txt')
        
        # Step 3: Approximate test
        var_com = np.loadtxt('var_a_axa.txt')  # numpy array： [0] addtive variance; [1] additive by additive variance; [2] residual variance
        remma_epiAA_approx(pheno_file, bed_file, gmat_lst, var_com, p_cut=1.0e-5, num_random_pair=100000, out_file='epiAA_approx_a_axa')
        
        # Step 4: Select top SNPs and add the SNP position
        res_file = 'epiAA_approx_a_axa'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        ```
        
        #### (4) Parallel approximate test (recommended for big data)
        Analysis can be subdivided with remma_epiAA_approx_parallel and run parallelly on different machines.
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        import pandas as pd
        from gmat.gmatrix import agmat
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file) 
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        gmat_lst = [ag, ag*ag]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var_a_axa.txt')
        
        # Step 3: parallel approximate test. Write codes of thist step in separate scripts and run parallelly
        
        ## parallel 1
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAA import remma_epiAA_approx_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var_a_axa.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        gmat_lst = [ag, ag*ag]
        # parallel=[3, 1] means divide total tests into three parts and run part 1
        remma_epiAA_approx_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 1], p_cut=1.0e-5, out_file='epiAA_approx_parallel_a_axa')
        
        ## parallel 2
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAA import remma_epiAA_approx_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var_a_axa.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        gmat_lst = [ag, ag*ag]
        # parallel=[3, 2] means divide total tests into three parts and run part 2
        remma_epiAA_approx_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 2], p_cut=1.0e-5, out_file='epiAA_approx_parallel_a_axa')
        
        ## parallel 3
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAA import remma_epiAA_approx_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var_a_axa.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        gmat_lst = [ag, ag*ag]
        # parallel=[3, 3] means divide total tests into three parts and run part 3
        remma_epiAA_approx_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 3], p_cut=1.0e-5, out_file='epiAA_approx_parallel_a_axa')
        
        # Step 4: Merge files 'epiAA_approx_parallel_a_axa.*' 
        # with the following codes.
        import os
        prefix = 'epiAA_approx_parallel_a_axa'
        parallel_num = 3  # the number of parallels
        with open(prefix + '.merge', 'w') as fout:
            with open(prefix + '.1') as fin:
                head_line = fin.readline()
                fout.write(head_line)
            for i in range(1, parallel_num+1):
                with open(prefix + '.' + str(i)) as fin:
                    head_line = fin.readline()
                    for line in fin:
                        fout.write(line)
                os.remove(prefix + '.' + str(i))
        
        # Step 5: Select top SNPs and add the SNP position
        from gmat.remma import annotation_snp_pos                   
        res_file = 'epiAA_approx_parallel_a_axa.merge'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        ```
        
        ### 3.2.2 Include additive, dominance and additive by additive genomic relationship matrix
        #### (1) Exact test (for small data)
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.gmatrix import agmat, dgmat_as
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        from gmat.remma.remma_epiAA import remma_epiAA
        from gmat.remma import annotation_snp_pos
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file)  # additive genomic relationship matrix
        dgmat_as(bed_file)  # dominance genomic relationship matrix
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        dg = np.loadtxt(bed_file + '.dgrm_as0')  # load the dominance genomic relationship matrix
        gmat_lst = [ag, dg, ag*ag]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var_a_d_axa.txt')
        
        # Step 3: Test
        var_com = np.loadtxt('var_a_d_axa.txt')  # numpy array： [0] addtive variance; [1] dominance variance; [2] additive by additive variance; [3] residual variance
        remma_epiAA(pheno_file, bed_file, gmat_lst, var_com, p_cut=1.0e-5, out_file='epiAA_a_d_axa')
        
        # Step 4: Select top SNPs and add the SNP position
        res_file = 'epiAA_a_d_axa'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        
        ```
        
        #### (2) Parallel exact test (for small data)
        Analysis can be subdivided with remma_epiAA_parallel and run parallelly on different machines.
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.gmatrix import agmat, dgmat_as
        from gmat.uvlmm.design_matrix import design_matrix_wemai_multi_gmat
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file)  # additive genomic relationship matrix
        dgmat_as(bed_file)  # dominance genomic relationship matrix
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        dg = np.loadtxt(bed_file + '.dgrm_as0')  # load the dominance genomic relationship matrix
        gmat_lst = [ag, dg, ag*ag]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var_a_d_axa.txt')
        
        # Step 3: parallel test. Write codes of thist step in separate scripts and run parallelly
        
        ## parallel 1
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAA import remma_epiAA_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var_a_d_axa.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag] 
        # parallel=[3, 1] means divide total tests into three parts and run part 1
        remma_epiAA_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 1], p_cut=1.0e-5, out_file='epiAA_parallel_a_d_axa')
        
        ## parallel 2
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAA import remma_epiAA_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var_a_d_axa.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag] 
        # parallel=[3, 2] means divide total tests into three parts and run part 2
        remma_epiAA_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 2], p_cut=1.0e-5, out_file='epiAA_parallel_a_d_axa')
        
        ## parallel 3
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAA import remma_epiAA_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var_a_d_axa.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag] 
        # parallel=[3, 3] means divide total tests into three parts and run part 3
        remma_epiAA_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 3], p_cut=1.0e-5, out_file='epiAA_parallel_a_d_axa')
        
        # Step 4: Merge files 'epiAA_parallel_a_d_axa.*' with the following codes.
        import os
        prefix = 'epiAA_parallel_a_d_axa'
        parallel_num = 3  # the number of parallels
        with open(prefix + ".merge", 'w') as fout:
            with open(prefix + '.1') as fin:
                head_line = fin.readline()
                fout.write(head_line)
            for i in range(1, parallel_num+1):
                with open(prefix + '.' + str(i)) as fin:
                    head_line = fin.readline()
                    for line in fin:
                        fout.write(line)
                os.remove(prefix + '.' + str(i))
        
        # Step 5: Select top SNPs and add the SNP position
        from gmat.remma import annotation_snp_pos
        res_file = 'epiAA_parallel_a_d_axa.merge'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        ```
        
        #### (3) approximate test (recommended for big data)
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        import pandas as pd
        from gmat.gmatrix import agmat, dgmat_as
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        from gmat.remma.remma_epiAA import remma_epiAA_approx
        from gmat.remma import annotation_snp_pos
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file)  # additive genomic relationship matrix
        dgmat_as(bed_file)  # dominance genomic relationship matrix
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        dg = np.loadtxt(bed_file + '.dgrm_as0')  # load the dominance genomic relationship matrix
        gmat_lst = [ag, dg, ag*ag]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var_a_d_axa.txt')
        
        # Step 3: Approximate test
        var_com = np.loadtxt('var_a_d_axa.txt')  # numpy array： [0] addtive variance; [1] dominance variance; [2] additive by additive variance; [3] residual variance
        remma_epiAA_approx(pheno_file, bed_file, gmat_lst, var_com, p_cut=1.0e-5, num_random_pair=100000, out_file='epiAA_approx_a_d_axa')
        
        # Step 4: Select top SNPs and add the SNP position
        res_file = 'epiAA_approx_a_d_axa'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        ```
        
        #### (4) Parallel approximate test (recommended for big data)
        Analysis can be subdivided with remma_epiAA_approx_parallel and run parallelly on different machines.
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        import pandas as pd
        from gmat.gmatrix import agmat, dgmat_as
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file) 
        dgmat_as(bed_file)  # dominance genomic relationship matrix
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        dg = np.loadtxt(bed_file + '.dgrm_as0')  # load the dominance genomic relationship matrix
        gmat_lst = [ag, dg, ag*ag]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var_a_d_axa.txt')
        
        # Step 3: parallel approximate test. Write codes of thist step in separate scripts and run parallelly
        
        ## parallel 1
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAA import remma_epiAA_approx_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var_a_d_axa.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag]
        # parallel=[3, 1] means divide total tests into three parts and run part 1
        remma_epiAA_approx_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 1], p_cut=1.0e-5, out_file='epiAA_approx_parallel_a_d_axa')
        
        ## parallel 2
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAA import remma_epiAA_approx_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var_a_d_axa.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag]
        # parallel=[3, 2] means divide total tests into three parts and run part 2
        remma_epiAA_approx_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 2], p_cut=1.0e-5, out_file='epiAA_approx_parallel_a_d_axa')
        
        ## parallel 3
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAA import remma_epiAA_approx_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var_a_d_axa.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag]
        # parallel=[3, 3] means divide total tests into three parts and run part 3
        remma_epiAA_approx_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 3], p_cut=1.0e-5, out_file='epiAA_approx_parallel_a_d_axa')
        
        # Step 4: Merge files 'epiAA_approx_parallel_a_d_axa.*' 
        # with the following codes.
        import os
        prefix = 'epiAA_approx_parallel_a_d_axa'
        parallel_num = 3  # the number of parallels
        with open(prefix + '.merge', 'w') as fout:
            with open(prefix + '.1') as fin:
                head_line = fin.readline()
                fout.write(head_line)
            for i in range(1, parallel_num+1):
                with open(prefix + '.' + str(i)) as fin:
                    head_line = fin.readline()
                    for line in fin:
                        fout.write(line)
                os.remove(prefix + '.' + str(i))
        
        # Step 5: Select top SNPs and add the SNP position
        from gmat.remma import annotation_snp_pos                   
        res_file = 'epiAA_approx_parallel_a_d_axa.merge'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        ```
        
        ### 3.2.3 Include additive, dominance and three kinds of epistatic genomic relationship matrix
        additive, dominance, additive by additive, additive by dominance and dominance by dominance genomic relationship matrix   
        #### (1) Exact test (for small data)
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.gmatrix import agmat, dgmat_as
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        from gmat.remma.remma_epiAA import remma_epiAA
        from gmat.remma import annotation_snp_pos
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file)  # additive genomic relationship matrix
        dgmat_as(bed_file)  # dominance genomic relationship matrix
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        dg = np.loadtxt(bed_file + '.dgrm_as0')  # load the dominance genomic relationship matrix
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var.txt')
        
        # Step 3: Test
        var_com = np.loadtxt('var.txt') # numpy array： [0] addtive variance; [1] dominance variance; [2] additive by additive variance; 
                                        #               [3] additive by dominance variance; [4] dominance by dominance variance; [5] residual variance
        remma_epiAA(pheno_file, bed_file, gmat_lst, var_com, p_cut=1.0e-5, out_file='epiAA')
        
        # Step 4: Select top SNPs and add the SNP position
        res_file = 'epiAA'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        ```
        
        #### (2) Parallel exact test (for small data)
        Analysis can be subdivided with remma_epiAA_parallel and run parallelly on different machines.
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.gmatrix import agmat, dgmat_as
        from gmat.uvlmm.design_matrix import design_matrix_wemai_multi_gmat
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file)  # additive genomic relationship matrix
        dgmat_as(bed_file)  # dominance genomic relationship matrix
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        dg = np.loadtxt(bed_file + '.dgrm_as0')  # load the dominance genomic relationship matrix
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var.txt')
        
        # Step 3: parallel test. Write codes of thist step in separate scripts and run parallelly
        
        ## parallel 1
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAA import remma_epiAA_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg] 
        # parallel=[3, 1] means divide total tests into three parts and run part 1
        remma_epiAA_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 1], p_cut=1.0e-5, out_file='epiAA_parallel')
        
        ## parallel 2
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAA import remma_epiAA_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg] 
        # parallel=[3, 2] means divide total tests into three parts and run part 2
        remma_epiAA_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 2], p_cut=1.0e-5, out_file='epiAA_parallel')
        
        ## parallel 3
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAA import remma_epiAA_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg] 
        # parallel=[3, 3] means divide total tests into three parts and run part 3
        remma_epiAA_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 3], p_cut=1.0e-5, out_file='epiAA_parallel')
        
        # Step 4: Merge files 'epiAA_parallel_a_d_axa.*' with the following codes.
        import os
        prefix = 'epiAA_parallel'
        parallel_num = 3  # the number of parallels
        with open(prefix + ".merge", 'w') as fout:
            with open(prefix + '.1') as fin:
                head_line = fin.readline()
                fout.write(head_line)
            for i in range(1, parallel_num+1):
                with open(prefix + '.' + str(i)) as fin:
                    head_line = fin.readline()
                    for line in fin:
                        fout.write(line)
                os.remove(prefix + '.' + str(i))
        
        # Step 5: Select top SNPs and add the SNP position
        from gmat.remma import annotation_snp_pos
        res_file = 'epiAA_parallel.merge'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        ```
        
        #### (3) approximate test (recommended for big data)
        
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        import pandas as pd
        from gmat.gmatrix import agmat, dgmat_as
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        from gmat.remma.remma_epiAA import remma_epiAA_approx
        from gmat.remma import annotation_snp_pos
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file)  # additive genomic relationship matrix
        dgmat_as(bed_file)  # dominance genomic relationship matrix
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        dg = np.loadtxt(bed_file + '.dgrm_as0')  # load the dominance genomic relationship matrix
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var.txt')
        
        # Step 3: Approximate test
        var_com = np.loadtxt('var.txt')  # numpy array： [0] addtive variance; [1] dominance variance; [2] additive by additive variance; [3] residual variance
        remma_epiAA_approx(pheno_file, bed_file, gmat_lst, var_com, p_cut=1.0e-5, num_random_pair=100000, out_file='epiAA_approx')
        
        # Step 4: Select top SNPs and add the SNP position
        res_file = 'epiAA_approx'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        
        ```
        
        #### (4) Parallel approximate test (recommended for big data)
        Analysis can be subdivided with remma_epiAA_approx_parallel and run parallelly on different machines.
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        import pandas as pd
        from gmat.gmatrix import agmat, dgmat_as
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file) 
        dgmat_as(bed_file)  # dominance genomic relationship matrix
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        dg = np.loadtxt(bed_file + '.dgrm_as0')  # load the dominance genomic relationship matrix
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var.txt')
        
        # Step 3: parallel approximate test. Write codes of thist step in separate scripts and run parallelly
        
        ## parallel 1
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAA import remma_epiAA_approx_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]
        # parallel=[3, 1] means divide total tests into three parts and run part 1
        remma_epiAA_approx_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 1], p_cut=1.0e-5, out_file='epiAA_approx_parallel')
        
        ## parallel 2
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAA import remma_epiAA_approx_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]
        # parallel=[3, 2] means divide total tests into three parts and run part 2
        remma_epiAA_approx_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 2], p_cut=1.0e-5, out_file='epiAA_approx_parallel')
        
        ## parallel 3
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAA import remma_epiAA_approx_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]
        # parallel=[3, 3] means divide total tests into three parts and run part 3
        remma_epiAA_approx_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 3], p_cut=1.0e-5, out_file='epiAA_approx_parallel')
        
        # Step 4: Merge files 'epiAA_approx_parallel_a_d_axa.*' 
        # with the following codes.
        import os
        prefix = 'epiAA_approx_parallel'
        parallel_num = 3  # the number of parallels
        with open(prefix + '.merge', 'w') as fout:
            with open(prefix + '.1') as fin:
                head_line = fin.readline()
                fout.write(head_line)
            for i in range(1, parallel_num+1):
                with open(prefix + '.' + str(i)) as fin:
                    head_line = fin.readline()
                    for line in fin:
                        fout.write(line)
                os.remove(prefix + '.' + str(i))
        
        # Step 5: Select top SNPs and add the SNP position
        from gmat.remma import annotation_snp_pos                   
        res_file = 'epiAA_approx_parallel.merge'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        ```
        
        ## 3.3 Exhaustive additive by dominance epistatis  
        Include additive, dominance, additive by additive, additive by dominance and dominance by dominance genomic relationship matrix  
        #### (1) Exact test (for small data)
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.gmatrix import agmat, dgmat_as
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        from gmat.remma.remma_epiAD import remma_epiAD
        from gmat.remma import annotation_snp_pos
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file)  # additive genomic relationship matrix
        dgmat_as(bed_file)  # dominance genomic relationship matrix
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        dg = np.loadtxt(bed_file + '.dgrm_as0')  # load the dominance genomic relationship matrix
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var.txt')
        
        # Step 3: Test
        var_com = np.loadtxt('var.txt') # numpy array： [0] addtive variance; [1] dominance variance; [2] additive by additive variance; 
                                        #               [3] additive by dominance variance; [4] dominance by dominance variance; [5] residual variance
        remma_epiAD(pheno_file, bed_file, gmat_lst, var_com, p_cut=1.0e-5, out_file='epiAD')
        
        # Step 4: Select top SNPs and add the SNP position
        res_file = 'epiAD'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        
        ```
        
        #### (2) Parallel exact test (for small data)
        Analysis can be subdivided with remma_epiAD_parallel and run parallelly on different machines.
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.gmatrix import agmat, dgmat_as
        from gmat.uvlmm.design_matrix import design_matrix_wemai_multi_gmat
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file)  # additive genomic relationship matrix
        dgmat_as(bed_file)  # dominance genomic relationship matrix
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        dg = np.loadtxt(bed_file + '.dgrm_as0')  # load the dominance genomic relationship matrix
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var.txt')
        
        # Step 3: parallel test. Write codes of thist step in separate scripts and run parallelly
        
        ## parallel 1
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAD import remma_epiAD_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg] 
        # parallel=[3, 1] means divide total tests into three parts and run part 1
        remma_epiAD_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 1], p_cut=1.0e-5, out_file='epiAD_parallel')
        
        ## parallel 2
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAD import remma_epiAD_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg] 
        # parallel=[3, 2] means divide total tests into three parts and run part 2
        remma_epiAD_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 2], p_cut=1.0e-5, out_file='epiAD_parallel')
        
        ## parallel 3
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAD import remma_epiAD_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg] 
        # parallel=[3, 3] means divide total tests into three parts and run part 3
        remma_epiAD_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 3], p_cut=1.0e-5, out_file='epiAD_parallel')
        
        # Step 4: Merge files 'epiAD_parallel.*' with the following codes.
        import os
        prefix = 'epiAD_parallel'
        parallel_num = 3  # the number of parallels
        with open(prefix + ".merge", 'w') as fout:
            with open(prefix + '.1') as fin:
                head_line = fin.readline()
                fout.write(head_line)
            for i in range(1, parallel_num+1):
                with open(prefix + '.' + str(i)) as fin:
                    head_line = fin.readline()
                    for line in fin:
                        fout.write(line)
                os.remove(prefix + '.' + str(i))
        
        # Step 5: Select top SNPs and add the SNP position
        from gmat.remma import annotation_snp_pos
        res_file = 'epiAD_parallel.merge'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        ```
        
        #### (3) approximate test (recommended for big data)
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        import pandas as pd
        from gmat.gmatrix import agmat, dgmat_as
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        from gmat.remma.remma_epiAD import remma_epiAD_approx
        from gmat.remma import annotation_snp_pos
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file)  # additive genomic relationship matrix
        dgmat_as(bed_file)  # dominance genomic relationship matrix
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        dg = np.loadtxt(bed_file + '.dgrm_as0')  # load the dominance genomic relationship matrix
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var.txt')
        
        # Step 3: Approximate test
        var_com = np.loadtxt('var.txt')  # numpy array： [0] addtive variance; [1] dominance variance; [2] additive by additive variance; [3] residual variance
        remma_epiAD_approx(pheno_file, bed_file, gmat_lst, var_com, p_cut=1.0e-5, num_random_pair=100000, out_file='epiAD_approx')
        
        # Step 4: Select top SNPs and add the SNP position
        res_file = 'epiAD_approx'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        ```
        
        #### (4) Parallel approximate test (recommended for big data)
        Analysis can be subdivided with remma_epiAD_approx_parallel and run parallelly on different machines.
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        import pandas as pd
        from gmat.gmatrix import agmat, dgmat_as
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file) 
        dgmat_as(bed_file)  # dominance genomic relationship matrix
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        dg = np.loadtxt(bed_file + '.dgrm_as0')  # load the dominance genomic relationship matrix
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var.txt')
        
        # Step 3: parallel approximate test. Write codes of thist step in separate scripts and run parallelly
        
        ## parallel 1
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAD import remma_epiAD_approx_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]
        # parallel=[3, 1] means divide total tests into three parts and run part 1
        remma_epiAD_approx_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 1], p_cut=1.0e-5, out_file='epiAD_approx_parallel')
        
        ## parallel 2
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAD import remma_epiAD_approx_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]
        # parallel=[3, 2] means divide total tests into three parts and run part 2
        remma_epiAD_approx_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 2], p_cut=1.0e-5, out_file='epiAD_approx_parallel')
        
        ## parallel 3
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiAD import remma_epiAD_approx_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]
        # parallel=[3, 3] means divide total tests into three parts and run part 3
        remma_epiAD_approx_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 3], p_cut=1.0e-5, out_file='epiAD_approx_parallel')
        
        # Step 4: Merge files 'epiAA_approx_parallel.*' 
        # with the following codes.
        import os
        prefix = 'epiAD_approx_parallel'
        parallel_num = 3  # the number of parallels
        with open(prefix + '.merge', 'w') as fout:
            with open(prefix + '.1') as fin:
                head_line = fin.readline()
                fout.write(head_line)
            for i in range(1, parallel_num+1):
                with open(prefix + '.' + str(i)) as fin:
                    head_line = fin.readline()
                    for line in fin:
                        fout.write(line)
                os.remove(prefix + '.' + str(i))
        
        # Step 5: Select top SNPs and add the SNP position
        from gmat.remma import annotation_snp_pos                   
        res_file = 'epiAD_approx_parallel.merge'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        ```
        
        ## 3.4 Exhaustive dominance by dominance epistatis  
        Include additive, dominance, additive by additive, additive by dominance and dominance by dominance genomic relationship matrix  
        #### (1) Exact test (for small data)
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.gmatrix import agmat, dgmat_as
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        from gmat.remma.remma_epiDD import remma_epiDD
        from gmat.remma import annotation_snp_pos
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file)  # additive genomic relationship matrix
        dgmat_as(bed_file)  # dominance genomic relationship matrix
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        dg = np.loadtxt(bed_file + '.dgrm_as0')  # load the dominance genomic relationship matrix
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var.txt')
        
        # Step 3: Test
        var_com = np.loadtxt('var.txt') # numpy array： [0] addtive variance; [1] dominance variance; [2] additive by additive variance; 
                                        #               [3] additive by dominance variance; [4] dominance by dominance variance; [5] residual variance
        remma_epiDD(pheno_file, bed_file, gmat_lst, var_com, p_cut=1.0e-5, out_file='epiDD')
        
        # Step 4: Select top SNPs and add the SNP position
        res_file = 'epiDD'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        ```
        
        #### (2) Parallel exact test (for small data)
        Analysis can be subdivided with remma_epiDD_parallel and run parallelly on different machines.
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.gmatrix import agmat, dgmat_as
        from gmat.uvlmm.design_matrix import design_matrix_wemai_multi_gmat
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file)  # additive genomic relationship matrix
        dgmat_as(bed_file)  # dominance genomic relationship matrix
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        dg = np.loadtxt(bed_file + '.dgrm_as0')  # load the dominance genomic relationship matrix
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var.txt')
        
        # Step 3: parallel test. Write codes of thist step in separate scripts and run parallelly
        
        ## parallel 1
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiDD import remma_epiDD_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg] 
        # parallel=[3, 1] means divide total tests into three parts and run part 1
        remma_epiDD_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 1], p_cut=1.0e-5, out_file='epiDD_parallel')
        
        ## parallel 2
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiDD import remma_epiDD_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg] 
        # parallel=[3, 2] means divide total tests into three parts and run part 2
        remma_epiDD_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 2], p_cut=1.0e-5, out_file='epiDD_parallel')
        
        ## parallel 3
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiDD import remma_epiDD_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg] 
        # parallel=[3, 3] means divide total tests into three parts and run part 3
        remma_epiDD_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 3], p_cut=1.0e-5, out_file='epiDD_parallel')
        
        # Step 4: Merge files 'epiDD_parallel.*' with the following codes.
        import os
        prefix = 'epiDD_parallel'
        parallel_num = 3  # the number of parallels
        with open(prefix + ".merge", 'w') as fout:
            with open(prefix + '.1') as fin:
                head_line = fin.readline()
                fout.write(head_line)
            for i in range(1, parallel_num+1):
                with open(prefix + '.' + str(i)) as fin:
                    head_line = fin.readline()
                    for line in fin:
                        fout.write(line)
                os.remove(prefix + '.' + str(i))
        
        # Step 5: Select top SNPs and add the SNP position
        from gmat.remma import annotation_snp_pos
        res_file = 'epiDD_parallel.merge'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        ```
        
        #### (3) approximate test (recommended for big data)
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        import pandas as pd
        from gmat.gmatrix import agmat, dgmat_as
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        from gmat.remma.remma_epiDD import remma_epiDD_approx
        from gmat.remma import annotation_snp_pos
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file)  # additive genomic relationship matrix
        dgmat_as(bed_file)  # dominance genomic relationship matrix
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        dg = np.loadtxt(bed_file + '.dgrm_as0')  # load the dominance genomic relationship matrix
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var.txt')
        
        # Step 3: Approximate test
        var_com = np.loadtxt('var.txt')  # numpy array： [0] addtive variance; [1] dominance variance; [2] additive by additive variance; [3] residual variance
        remma_epiDD_approx(pheno_file, bed_file, gmat_lst, var_com, p_cut=1.0e-5, num_random_pair=100000, out_file='epiDD_approx')
        
        # Step 4: Select top SNPs and add the SNP position
        res_file = 'epiDD_approx'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        ```
        
        #### (4) Parallel approximate test (recommended for big data)
        Analysis can be subdivided with remma_epiDD_approx_parallel and run parallelly on different machines.
        
        
        ```python
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        import pandas as pd
        from gmat.gmatrix import agmat, dgmat_as
        from gmat.uvlmm.uvlmm_varcom import wemai_multi_gmat
        
        # Step 1: Calculate the genomic relationship matrix
        bed_file = 'plink'  # the prefix for the plink binary file
        agmat(bed_file) 
        dgmat_as(bed_file)  # dominance genomic relationship matrix
        
        # Step 2: Estimate the variances
        pheno_file = 'pheno'  # phenotypic file
        ag = np.loadtxt(bed_file + '.agrm0')  # load the additive genomic relationship matrix
        dg = np.loadtxt(bed_file + '.dgrm_as0')  # load the dominance genomic relationship matrix
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]  # ag*ag is the additive by additive genomic relationship matrix
        wemai_multi_gmat(pheno_file, bed_file, gmat_lst, out_file='var.txt')
        
        # Step 3: parallel approximate test. Write codes of thist step in separate scripts and run parallelly
        
        ## parallel 1
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiDD import remma_epiDD_approx_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]
        # parallel=[3, 1] means divide total tests into three parts and run part 1
        remma_epiDD_approx_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 1], p_cut=1.0e-5, out_file='epiDD_approx_parallel')
        
        ## parallel 2
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiDD import remma_epiDD_approx_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]
        # parallel=[3, 2] means divide total tests into three parts and run part 2
        remma_epiDD_approx_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 2], p_cut=1.0e-5, out_file='epiDD_approx_parallel')
        
        ## parallel 3
        import logging
        logging.basicConfig(level=logging.INFO)
        import numpy as np
        from gmat.remma.remma_epiDD import remma_epiDD_approx_parallel
        bed_file = 'plink'
        pheno_file = 'pheno'
        var_com = np.loadtxt('var.txt')
        ag = np.loadtxt(bed_file + '.agrm0')
        dg = np.loadtxt(bed_file + '.dgrm_as0')
        gmat_lst = [ag, dg, ag*ag, ag*dg, dg*dg]
        # parallel=[3, 3] means divide total tests into three parts and run part 3
        remma_epiDD_approx_parallel(pheno_file, bed_file, gmat_lst, var_com, parallel=[3, 3], p_cut=1.0e-5, out_file='epiDD_approx_parallel')
        
        # Step 4: Merge files 'epiDD_approx_parallel.*' 
        # with the following codes.
        import os
        prefix = 'epiDD_approx_parallel'
        parallel_num = 3  # the number of parallels
        with open(prefix + '.merge', 'w') as fout:
            with open(prefix + '.1') as fin:
                head_line = fin.readline()
                fout.write(head_line)
            for i in range(1, parallel_num+1):
                with open(prefix + '.' + str(i)) as fin:
                    head_line = fin.readline()
                    for line in fin:
                        fout.write(line)
                os.remove(prefix + '.' + str(i))
        
        # Step 5: Select top SNPs and add the SNP position
        from gmat.remma import annotation_snp_pos                   
        res_file = 'epiDD_approx_parallel.merge'  # result file
        annotation_snp_pos(res_file, bed_file, p_cut=1.0e-5, dis=0)  # p values < 1.0e-5 and the distance between SNP pairs > 0
        ```
        
Platform: all
Description-Content-Type: text/markdown
