Inversion of a part of the numerator relationship matrix using pedigree information
Background In recent theoretical developments, the information available (e.g. genotypes) divides the original population into two groups: animals with this information (selected animals) and animals without this information (excluded animals). These developments require inversion of the part of the...
Ausführliche Beschreibung
Autor*in: |
Faux, Pierre [verfasserIn] |
---|
Format: |
E-Artikel |
---|---|
Sprache: |
Englisch |
Erschienen: |
2013 |
---|
Schlagwörter: |
---|
Anmerkung: |
© Faux and Gengler; licensee BioMed Central Ltd. 2013 |
---|
Übergeordnetes Werk: |
Enthalten in: Genetics, selection, evolution - London : BioMed Central, 1989, 45(2013), 1 vom: 06. Dez. |
---|---|
Übergeordnetes Werk: |
volume:45 ; year:2013 ; number:1 ; day:06 ; month:12 |
Links: |
---|
DOI / URN: |
10.1186/1297-9686-45-45 |
---|
Katalog-ID: |
SPR026807386 |
---|
LEADER | 01000caa a22002652 4500 | ||
---|---|---|---|
001 | SPR026807386 | ||
003 | DE-627 | ||
005 | 20230519182713.0 | ||
007 | cr uuu---uuuuu | ||
008 | 201007s2013 xx |||||o 00| ||eng c | ||
024 | 7 | |a 10.1186/1297-9686-45-45 |2 doi | |
035 | |a (DE-627)SPR026807386 | ||
035 | |a (SPR)1297-9686-45-45-e | ||
040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
041 | |a eng | ||
100 | 1 | |a Faux, Pierre |e verfasserin |4 aut | |
245 | 1 | 0 | |a Inversion of a part of the numerator relationship matrix using pedigree information |
264 | 1 | |c 2013 | |
336 | |a Text |b txt |2 rdacontent | ||
337 | |a Computermedien |b c |2 rdamedia | ||
338 | |a Online-Ressource |b cr |2 rdacarrier | ||
500 | |a © Faux and Gengler; licensee BioMed Central Ltd. 2013 | ||
520 | |a Background In recent theoretical developments, the information available (e.g. genotypes) divides the original population into two groups: animals with this information (selected animals) and animals without this information (excluded animals). These developments require inversion of the part of the pedigree-based numerator relationship matrix that describes the genetic covariance between selected animals (A22). Our main objective was to propose and evaluate methodology that takes advantage of any potential sparsity in the inverse of A22 in order to reduce the computing time required for its inversion. This potential sparsity is brought out by searching the pedigree for dependencies between the selected animals. Jointly, we expected distant ancestors to provide relationship ties that increase the density of matrix A22 but that their effect on might be minor. This hypothesis was also tested. Methods The inverse of A22 can be computed from the inverse of the triangular factor (T-1) obtained by Cholesky root-free decomposition of A22. We propose an algorithm that sets up the sparsity pattern of T-1 using pedigree information. This algorithm provides positions of the elements of T-1 worth to be computed (i.e. different from zero). A recursive computation of is then achieved with or without information on the sparsity pattern and time required for each computation was recorded. For three numbers of selected animals (4000; 8000 and 12 000), A22 was computed using different pedigree extractions and the closeness of the resulting to the inverse computed using the fully extracted pedigree was measured by an appropriate norm. Results The use of prior information on the sparsity of T-1 decreased the computing time for inversion by a factor of 1.73 on average. Computational issues and practical uses of the different algorithms were discussed. Cases involving more than 12 000 selected animals were considered. Inclusion of 10 generations was determined to be sufficient when computing A22. Conclusions Depending on the size and structure of the selected sub-population, gains in time to compute are possible and these gains may increase as the number of selected animals increases. Given the sequential nature of most computational steps, the proposed algorithm can benefit from optimization and may be convenient for genomic evaluations. | ||
650 | 4 | |a Genomic Prediction |7 (dpeaa)DE-He213 | |
650 | 4 | |a Inversion Algorithm |7 (dpeaa)DE-He213 | |
650 | 4 | |a Sparsity Pattern |7 (dpeaa)DE-He213 | |
650 | 4 | |a Sparse Vector |7 (dpeaa)DE-He213 | |
650 | 4 | |a Genomic Relationship Matrix |7 (dpeaa)DE-He213 | |
700 | 1 | |a Gengler, Nicolas |4 aut | |
773 | 0 | 8 | |i Enthalten in |t Genetics, selection, evolution |d London : BioMed Central, 1989 |g 45(2013), 1 vom: 06. Dez. |w (DE-627)312849052 |w (DE-600)2012369-3 |x 1297-9686 |7 nnns |
773 | 1 | 8 | |g volume:45 |g year:2013 |g number:1 |g day:06 |g month:12 |
856 | 4 | 0 | |u https://dx.doi.org/10.1186/1297-9686-45-45 |z kostenfrei |3 Volltext |
912 | |a GBV_USEFLAG_A | ||
912 | |a SYSFLAG_A | ||
912 | |a GBV_SPRINGER | ||
912 | |a SSG-OLC-PHA | ||
912 | |a GBV_ILN_11 | ||
912 | |a GBV_ILN_20 | ||
912 | |a GBV_ILN_22 | ||
912 | |a GBV_ILN_23 | ||
912 | |a GBV_ILN_24 | ||
912 | |a GBV_ILN_31 | ||
912 | |a GBV_ILN_39 | ||
912 | |a GBV_ILN_40 | ||
912 | |a GBV_ILN_60 | ||
912 | |a GBV_ILN_62 | ||
912 | |a GBV_ILN_63 | ||
912 | |a GBV_ILN_65 | ||
912 | |a GBV_ILN_69 | ||
912 | |a GBV_ILN_70 | ||
912 | |a GBV_ILN_73 | ||
912 | |a GBV_ILN_74 | ||
912 | |a GBV_ILN_95 | ||
912 | |a GBV_ILN_105 | ||
912 | |a GBV_ILN_110 | ||
912 | |a GBV_ILN_151 | ||
912 | |a GBV_ILN_161 | ||
912 | |a GBV_ILN_170 | ||
912 | |a GBV_ILN_213 | ||
912 | |a GBV_ILN_224 | ||
912 | |a GBV_ILN_230 | ||
912 | |a GBV_ILN_285 | ||
912 | |a GBV_ILN_293 | ||
912 | |a GBV_ILN_602 | ||
912 | |a GBV_ILN_2003 | ||
912 | |a GBV_ILN_2014 | ||
912 | |a GBV_ILN_4012 | ||
912 | |a GBV_ILN_4037 | ||
912 | |a GBV_ILN_4112 | ||
912 | |a GBV_ILN_4125 | ||
912 | |a GBV_ILN_4126 | ||
912 | |a GBV_ILN_4249 | ||
912 | |a GBV_ILN_4305 | ||
912 | |a GBV_ILN_4306 | ||
912 | |a GBV_ILN_4307 | ||
912 | |a GBV_ILN_4313 | ||
912 | |a GBV_ILN_4322 | ||
912 | |a GBV_ILN_4323 | ||
912 | |a GBV_ILN_4324 | ||
912 | |a GBV_ILN_4325 | ||
912 | |a GBV_ILN_4338 | ||
912 | |a GBV_ILN_4367 | ||
912 | |a GBV_ILN_4700 | ||
951 | |a AR | ||
952 | |d 45 |j 2013 |e 1 |b 06 |c 12 |
author_variant |
p f pf n g ng |
---|---|
matchkey_str |
article:12979686:2013----::nesooaatfhnmrtreainhparxsnp |
hierarchy_sort_str |
2013 |
publishDate |
2013 |
allfields |
10.1186/1297-9686-45-45 doi (DE-627)SPR026807386 (SPR)1297-9686-45-45-e DE-627 ger DE-627 rakwb eng Faux, Pierre verfasserin aut Inversion of a part of the numerator relationship matrix using pedigree information 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Faux and Gengler; licensee BioMed Central Ltd. 2013 Background In recent theoretical developments, the information available (e.g. genotypes) divides the original population into two groups: animals with this information (selected animals) and animals without this information (excluded animals). These developments require inversion of the part of the pedigree-based numerator relationship matrix that describes the genetic covariance between selected animals (A22). Our main objective was to propose and evaluate methodology that takes advantage of any potential sparsity in the inverse of A22 in order to reduce the computing time required for its inversion. This potential sparsity is brought out by searching the pedigree for dependencies between the selected animals. Jointly, we expected distant ancestors to provide relationship ties that increase the density of matrix A22 but that their effect on might be minor. This hypothesis was also tested. Methods The inverse of A22 can be computed from the inverse of the triangular factor (T-1) obtained by Cholesky root-free decomposition of A22. We propose an algorithm that sets up the sparsity pattern of T-1 using pedigree information. This algorithm provides positions of the elements of T-1 worth to be computed (i.e. different from zero). A recursive computation of is then achieved with or without information on the sparsity pattern and time required for each computation was recorded. For three numbers of selected animals (4000; 8000 and 12 000), A22 was computed using different pedigree extractions and the closeness of the resulting to the inverse computed using the fully extracted pedigree was measured by an appropriate norm. Results The use of prior information on the sparsity of T-1 decreased the computing time for inversion by a factor of 1.73 on average. Computational issues and practical uses of the different algorithms were discussed. Cases involving more than 12 000 selected animals were considered. Inclusion of 10 generations was determined to be sufficient when computing A22. Conclusions Depending on the size and structure of the selected sub-population, gains in time to compute are possible and these gains may increase as the number of selected animals increases. Given the sequential nature of most computational steps, the proposed algorithm can benefit from optimization and may be convenient for genomic evaluations. Genomic Prediction (dpeaa)DE-He213 Inversion Algorithm (dpeaa)DE-He213 Sparsity Pattern (dpeaa)DE-He213 Sparse Vector (dpeaa)DE-He213 Genomic Relationship Matrix (dpeaa)DE-He213 Gengler, Nicolas aut Enthalten in Genetics, selection, evolution London : BioMed Central, 1989 45(2013), 1 vom: 06. Dez. (DE-627)312849052 (DE-600)2012369-3 1297-9686 nnns volume:45 year:2013 number:1 day:06 month:12 https://dx.doi.org/10.1186/1297-9686-45-45 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 45 2013 1 06 12 |
spelling |
10.1186/1297-9686-45-45 doi (DE-627)SPR026807386 (SPR)1297-9686-45-45-e DE-627 ger DE-627 rakwb eng Faux, Pierre verfasserin aut Inversion of a part of the numerator relationship matrix using pedigree information 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Faux and Gengler; licensee BioMed Central Ltd. 2013 Background In recent theoretical developments, the information available (e.g. genotypes) divides the original population into two groups: animals with this information (selected animals) and animals without this information (excluded animals). These developments require inversion of the part of the pedigree-based numerator relationship matrix that describes the genetic covariance between selected animals (A22). Our main objective was to propose and evaluate methodology that takes advantage of any potential sparsity in the inverse of A22 in order to reduce the computing time required for its inversion. This potential sparsity is brought out by searching the pedigree for dependencies between the selected animals. Jointly, we expected distant ancestors to provide relationship ties that increase the density of matrix A22 but that their effect on might be minor. This hypothesis was also tested. Methods The inverse of A22 can be computed from the inverse of the triangular factor (T-1) obtained by Cholesky root-free decomposition of A22. We propose an algorithm that sets up the sparsity pattern of T-1 using pedigree information. This algorithm provides positions of the elements of T-1 worth to be computed (i.e. different from zero). A recursive computation of is then achieved with or without information on the sparsity pattern and time required for each computation was recorded. For three numbers of selected animals (4000; 8000 and 12 000), A22 was computed using different pedigree extractions and the closeness of the resulting to the inverse computed using the fully extracted pedigree was measured by an appropriate norm. Results The use of prior information on the sparsity of T-1 decreased the computing time for inversion by a factor of 1.73 on average. Computational issues and practical uses of the different algorithms were discussed. Cases involving more than 12 000 selected animals were considered. Inclusion of 10 generations was determined to be sufficient when computing A22. Conclusions Depending on the size and structure of the selected sub-population, gains in time to compute are possible and these gains may increase as the number of selected animals increases. Given the sequential nature of most computational steps, the proposed algorithm can benefit from optimization and may be convenient for genomic evaluations. Genomic Prediction (dpeaa)DE-He213 Inversion Algorithm (dpeaa)DE-He213 Sparsity Pattern (dpeaa)DE-He213 Sparse Vector (dpeaa)DE-He213 Genomic Relationship Matrix (dpeaa)DE-He213 Gengler, Nicolas aut Enthalten in Genetics, selection, evolution London : BioMed Central, 1989 45(2013), 1 vom: 06. Dez. (DE-627)312849052 (DE-600)2012369-3 1297-9686 nnns volume:45 year:2013 number:1 day:06 month:12 https://dx.doi.org/10.1186/1297-9686-45-45 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 45 2013 1 06 12 |
allfields_unstemmed |
10.1186/1297-9686-45-45 doi (DE-627)SPR026807386 (SPR)1297-9686-45-45-e DE-627 ger DE-627 rakwb eng Faux, Pierre verfasserin aut Inversion of a part of the numerator relationship matrix using pedigree information 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Faux and Gengler; licensee BioMed Central Ltd. 2013 Background In recent theoretical developments, the information available (e.g. genotypes) divides the original population into two groups: animals with this information (selected animals) and animals without this information (excluded animals). These developments require inversion of the part of the pedigree-based numerator relationship matrix that describes the genetic covariance between selected animals (A22). Our main objective was to propose and evaluate methodology that takes advantage of any potential sparsity in the inverse of A22 in order to reduce the computing time required for its inversion. This potential sparsity is brought out by searching the pedigree for dependencies between the selected animals. Jointly, we expected distant ancestors to provide relationship ties that increase the density of matrix A22 but that their effect on might be minor. This hypothesis was also tested. Methods The inverse of A22 can be computed from the inverse of the triangular factor (T-1) obtained by Cholesky root-free decomposition of A22. We propose an algorithm that sets up the sparsity pattern of T-1 using pedigree information. This algorithm provides positions of the elements of T-1 worth to be computed (i.e. different from zero). A recursive computation of is then achieved with or without information on the sparsity pattern and time required for each computation was recorded. For three numbers of selected animals (4000; 8000 and 12 000), A22 was computed using different pedigree extractions and the closeness of the resulting to the inverse computed using the fully extracted pedigree was measured by an appropriate norm. Results The use of prior information on the sparsity of T-1 decreased the computing time for inversion by a factor of 1.73 on average. Computational issues and practical uses of the different algorithms were discussed. Cases involving more than 12 000 selected animals were considered. Inclusion of 10 generations was determined to be sufficient when computing A22. Conclusions Depending on the size and structure of the selected sub-population, gains in time to compute are possible and these gains may increase as the number of selected animals increases. Given the sequential nature of most computational steps, the proposed algorithm can benefit from optimization and may be convenient for genomic evaluations. Genomic Prediction (dpeaa)DE-He213 Inversion Algorithm (dpeaa)DE-He213 Sparsity Pattern (dpeaa)DE-He213 Sparse Vector (dpeaa)DE-He213 Genomic Relationship Matrix (dpeaa)DE-He213 Gengler, Nicolas aut Enthalten in Genetics, selection, evolution London : BioMed Central, 1989 45(2013), 1 vom: 06. Dez. (DE-627)312849052 (DE-600)2012369-3 1297-9686 nnns volume:45 year:2013 number:1 day:06 month:12 https://dx.doi.org/10.1186/1297-9686-45-45 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 45 2013 1 06 12 |
allfieldsGer |
10.1186/1297-9686-45-45 doi (DE-627)SPR026807386 (SPR)1297-9686-45-45-e DE-627 ger DE-627 rakwb eng Faux, Pierre verfasserin aut Inversion of a part of the numerator relationship matrix using pedigree information 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Faux and Gengler; licensee BioMed Central Ltd. 2013 Background In recent theoretical developments, the information available (e.g. genotypes) divides the original population into two groups: animals with this information (selected animals) and animals without this information (excluded animals). These developments require inversion of the part of the pedigree-based numerator relationship matrix that describes the genetic covariance between selected animals (A22). Our main objective was to propose and evaluate methodology that takes advantage of any potential sparsity in the inverse of A22 in order to reduce the computing time required for its inversion. This potential sparsity is brought out by searching the pedigree for dependencies between the selected animals. Jointly, we expected distant ancestors to provide relationship ties that increase the density of matrix A22 but that their effect on might be minor. This hypothesis was also tested. Methods The inverse of A22 can be computed from the inverse of the triangular factor (T-1) obtained by Cholesky root-free decomposition of A22. We propose an algorithm that sets up the sparsity pattern of T-1 using pedigree information. This algorithm provides positions of the elements of T-1 worth to be computed (i.e. different from zero). A recursive computation of is then achieved with or without information on the sparsity pattern and time required for each computation was recorded. For three numbers of selected animals (4000; 8000 and 12 000), A22 was computed using different pedigree extractions and the closeness of the resulting to the inverse computed using the fully extracted pedigree was measured by an appropriate norm. Results The use of prior information on the sparsity of T-1 decreased the computing time for inversion by a factor of 1.73 on average. Computational issues and practical uses of the different algorithms were discussed. Cases involving more than 12 000 selected animals were considered. Inclusion of 10 generations was determined to be sufficient when computing A22. Conclusions Depending on the size and structure of the selected sub-population, gains in time to compute are possible and these gains may increase as the number of selected animals increases. Given the sequential nature of most computational steps, the proposed algorithm can benefit from optimization and may be convenient for genomic evaluations. Genomic Prediction (dpeaa)DE-He213 Inversion Algorithm (dpeaa)DE-He213 Sparsity Pattern (dpeaa)DE-He213 Sparse Vector (dpeaa)DE-He213 Genomic Relationship Matrix (dpeaa)DE-He213 Gengler, Nicolas aut Enthalten in Genetics, selection, evolution London : BioMed Central, 1989 45(2013), 1 vom: 06. Dez. (DE-627)312849052 (DE-600)2012369-3 1297-9686 nnns volume:45 year:2013 number:1 day:06 month:12 https://dx.doi.org/10.1186/1297-9686-45-45 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 45 2013 1 06 12 |
allfieldsSound |
10.1186/1297-9686-45-45 doi (DE-627)SPR026807386 (SPR)1297-9686-45-45-e DE-627 ger DE-627 rakwb eng Faux, Pierre verfasserin aut Inversion of a part of the numerator relationship matrix using pedigree information 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Faux and Gengler; licensee BioMed Central Ltd. 2013 Background In recent theoretical developments, the information available (e.g. genotypes) divides the original population into two groups: animals with this information (selected animals) and animals without this information (excluded animals). These developments require inversion of the part of the pedigree-based numerator relationship matrix that describes the genetic covariance between selected animals (A22). Our main objective was to propose and evaluate methodology that takes advantage of any potential sparsity in the inverse of A22 in order to reduce the computing time required for its inversion. This potential sparsity is brought out by searching the pedigree for dependencies between the selected animals. Jointly, we expected distant ancestors to provide relationship ties that increase the density of matrix A22 but that their effect on might be minor. This hypothesis was also tested. Methods The inverse of A22 can be computed from the inverse of the triangular factor (T-1) obtained by Cholesky root-free decomposition of A22. We propose an algorithm that sets up the sparsity pattern of T-1 using pedigree information. This algorithm provides positions of the elements of T-1 worth to be computed (i.e. different from zero). A recursive computation of is then achieved with or without information on the sparsity pattern and time required for each computation was recorded. For three numbers of selected animals (4000; 8000 and 12 000), A22 was computed using different pedigree extractions and the closeness of the resulting to the inverse computed using the fully extracted pedigree was measured by an appropriate norm. Results The use of prior information on the sparsity of T-1 decreased the computing time for inversion by a factor of 1.73 on average. Computational issues and practical uses of the different algorithms were discussed. Cases involving more than 12 000 selected animals were considered. Inclusion of 10 generations was determined to be sufficient when computing A22. Conclusions Depending on the size and structure of the selected sub-population, gains in time to compute are possible and these gains may increase as the number of selected animals increases. Given the sequential nature of most computational steps, the proposed algorithm can benefit from optimization and may be convenient for genomic evaluations. Genomic Prediction (dpeaa)DE-He213 Inversion Algorithm (dpeaa)DE-He213 Sparsity Pattern (dpeaa)DE-He213 Sparse Vector (dpeaa)DE-He213 Genomic Relationship Matrix (dpeaa)DE-He213 Gengler, Nicolas aut Enthalten in Genetics, selection, evolution London : BioMed Central, 1989 45(2013), 1 vom: 06. Dez. (DE-627)312849052 (DE-600)2012369-3 1297-9686 nnns volume:45 year:2013 number:1 day:06 month:12 https://dx.doi.org/10.1186/1297-9686-45-45 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 45 2013 1 06 12 |
language |
English |
source |
Enthalten in Genetics, selection, evolution 45(2013), 1 vom: 06. Dez. volume:45 year:2013 number:1 day:06 month:12 |
sourceStr |
Enthalten in Genetics, selection, evolution 45(2013), 1 vom: 06. Dez. volume:45 year:2013 number:1 day:06 month:12 |
format_phy_str_mv |
Article |
institution |
findex.gbv.de |
topic_facet |
Genomic Prediction Inversion Algorithm Sparsity Pattern Sparse Vector Genomic Relationship Matrix |
isfreeaccess_bool |
true |
container_title |
Genetics, selection, evolution |
authorswithroles_txt_mv |
Faux, Pierre @@aut@@ Gengler, Nicolas @@aut@@ |
publishDateDaySort_date |
2013-12-06T00:00:00Z |
hierarchy_top_id |
312849052 |
id |
SPR026807386 |
language_de |
englisch |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR026807386</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230519182713.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201007s2013 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1186/1297-9686-45-45</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR026807386</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)1297-9686-45-45-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Faux, Pierre</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Inversion of a part of the numerator relationship matrix using pedigree information</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2013</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Faux and Gengler; licensee BioMed Central Ltd. 2013</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Background In recent theoretical developments, the information available (e.g. genotypes) divides the original population into two groups: animals with this information (selected animals) and animals without this information (excluded animals). These developments require inversion of the part of the pedigree-based numerator relationship matrix that describes the genetic covariance between selected animals (A22). Our main objective was to propose and evaluate methodology that takes advantage of any potential sparsity in the inverse of A22 in order to reduce the computing time required for its inversion. This potential sparsity is brought out by searching the pedigree for dependencies between the selected animals. Jointly, we expected distant ancestors to provide relationship ties that increase the density of matrix A22 but that their effect on might be minor. This hypothesis was also tested. Methods The inverse of A22 can be computed from the inverse of the triangular factor (T-1) obtained by Cholesky root-free decomposition of A22. We propose an algorithm that sets up the sparsity pattern of T-1 using pedigree information. This algorithm provides positions of the elements of T-1 worth to be computed (i.e. different from zero). A recursive computation of is then achieved with or without information on the sparsity pattern and time required for each computation was recorded. For three numbers of selected animals (4000; 8000 and 12 000), A22 was computed using different pedigree extractions and the closeness of the resulting to the inverse computed using the fully extracted pedigree was measured by an appropriate norm. Results The use of prior information on the sparsity of T-1 decreased the computing time for inversion by a factor of 1.73 on average. Computational issues and practical uses of the different algorithms were discussed. Cases involving more than 12 000 selected animals were considered. Inclusion of 10 generations was determined to be sufficient when computing A22. Conclusions Depending on the size and structure of the selected sub-population, gains in time to compute are possible and these gains may increase as the number of selected animals increases. Given the sequential nature of most computational steps, the proposed algorithm can benefit from optimization and may be convenient for genomic evaluations.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Genomic Prediction</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Inversion Algorithm</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sparsity Pattern</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sparse Vector</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Genomic Relationship Matrix</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Gengler, Nicolas</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Genetics, selection, evolution</subfield><subfield code="d">London : BioMed Central, 1989</subfield><subfield code="g">45(2013), 1 vom: 06. Dez.</subfield><subfield code="w">(DE-627)312849052</subfield><subfield code="w">(DE-600)2012369-3</subfield><subfield code="x">1297-9686</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:45</subfield><subfield code="g">year:2013</subfield><subfield code="g">number:1</subfield><subfield code="g">day:06</subfield><subfield code="g">month:12</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1186/1297-9686-45-45</subfield><subfield code="z">kostenfrei</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_31</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_39</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_60</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_63</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_65</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_69</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_74</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_95</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_151</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_161</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_170</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_213</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_224</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_230</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_285</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_293</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_602</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2003</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4012</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4125</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4126</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4249</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4367</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">45</subfield><subfield code="j">2013</subfield><subfield code="e">1</subfield><subfield code="b">06</subfield><subfield code="c">12</subfield></datafield></record></collection>
|
author |
Faux, Pierre |
spellingShingle |
Faux, Pierre misc Genomic Prediction misc Inversion Algorithm misc Sparsity Pattern misc Sparse Vector misc Genomic Relationship Matrix Inversion of a part of the numerator relationship matrix using pedigree information |
authorStr |
Faux, Pierre |
ppnlink_with_tag_str_mv |
@@773@@(DE-627)312849052 |
format |
electronic Article |
delete_txt_mv |
keep |
author_role |
aut aut |
collection |
springer |
remote_str |
true |
illustrated |
Not Illustrated |
issn |
1297-9686 |
topic_title |
Inversion of a part of the numerator relationship matrix using pedigree information Genomic Prediction (dpeaa)DE-He213 Inversion Algorithm (dpeaa)DE-He213 Sparsity Pattern (dpeaa)DE-He213 Sparse Vector (dpeaa)DE-He213 Genomic Relationship Matrix (dpeaa)DE-He213 |
topic |
misc Genomic Prediction misc Inversion Algorithm misc Sparsity Pattern misc Sparse Vector misc Genomic Relationship Matrix |
topic_unstemmed |
misc Genomic Prediction misc Inversion Algorithm misc Sparsity Pattern misc Sparse Vector misc Genomic Relationship Matrix |
topic_browse |
misc Genomic Prediction misc Inversion Algorithm misc Sparsity Pattern misc Sparse Vector misc Genomic Relationship Matrix |
format_facet |
Elektronische Aufsätze Aufsätze Elektronische Ressource |
format_main_str_mv |
Text Zeitschrift/Artikel |
carriertype_str_mv |
cr |
hierarchy_parent_title |
Genetics, selection, evolution |
hierarchy_parent_id |
312849052 |
hierarchy_top_title |
Genetics, selection, evolution |
isfreeaccess_txt |
true |
familylinks_str_mv |
(DE-627)312849052 (DE-600)2012369-3 |
title |
Inversion of a part of the numerator relationship matrix using pedigree information |
ctrlnum |
(DE-627)SPR026807386 (SPR)1297-9686-45-45-e |
title_full |
Inversion of a part of the numerator relationship matrix using pedigree information |
author_sort |
Faux, Pierre |
journal |
Genetics, selection, evolution |
journalStr |
Genetics, selection, evolution |
lang_code |
eng |
isOA_bool |
true |
recordtype |
marc |
publishDateSort |
2013 |
contenttype_str_mv |
txt |
author_browse |
Faux, Pierre Gengler, Nicolas |
container_volume |
45 |
format_se |
Elektronische Aufsätze |
author-letter |
Faux, Pierre |
doi_str_mv |
10.1186/1297-9686-45-45 |
title_sort |
inversion of a part of the numerator relationship matrix using pedigree information |
title_auth |
Inversion of a part of the numerator relationship matrix using pedigree information |
abstract |
Background In recent theoretical developments, the information available (e.g. genotypes) divides the original population into two groups: animals with this information (selected animals) and animals without this information (excluded animals). These developments require inversion of the part of the pedigree-based numerator relationship matrix that describes the genetic covariance between selected animals (A22). Our main objective was to propose and evaluate methodology that takes advantage of any potential sparsity in the inverse of A22 in order to reduce the computing time required for its inversion. This potential sparsity is brought out by searching the pedigree for dependencies between the selected animals. Jointly, we expected distant ancestors to provide relationship ties that increase the density of matrix A22 but that their effect on might be minor. This hypothesis was also tested. Methods The inverse of A22 can be computed from the inverse of the triangular factor (T-1) obtained by Cholesky root-free decomposition of A22. We propose an algorithm that sets up the sparsity pattern of T-1 using pedigree information. This algorithm provides positions of the elements of T-1 worth to be computed (i.e. different from zero). A recursive computation of is then achieved with or without information on the sparsity pattern and time required for each computation was recorded. For three numbers of selected animals (4000; 8000 and 12 000), A22 was computed using different pedigree extractions and the closeness of the resulting to the inverse computed using the fully extracted pedigree was measured by an appropriate norm. Results The use of prior information on the sparsity of T-1 decreased the computing time for inversion by a factor of 1.73 on average. Computational issues and practical uses of the different algorithms were discussed. Cases involving more than 12 000 selected animals were considered. Inclusion of 10 generations was determined to be sufficient when computing A22. Conclusions Depending on the size and structure of the selected sub-population, gains in time to compute are possible and these gains may increase as the number of selected animals increases. Given the sequential nature of most computational steps, the proposed algorithm can benefit from optimization and may be convenient for genomic evaluations. © Faux and Gengler; licensee BioMed Central Ltd. 2013 |
abstractGer |
Background In recent theoretical developments, the information available (e.g. genotypes) divides the original population into two groups: animals with this information (selected animals) and animals without this information (excluded animals). These developments require inversion of the part of the pedigree-based numerator relationship matrix that describes the genetic covariance between selected animals (A22). Our main objective was to propose and evaluate methodology that takes advantage of any potential sparsity in the inverse of A22 in order to reduce the computing time required for its inversion. This potential sparsity is brought out by searching the pedigree for dependencies between the selected animals. Jointly, we expected distant ancestors to provide relationship ties that increase the density of matrix A22 but that their effect on might be minor. This hypothesis was also tested. Methods The inverse of A22 can be computed from the inverse of the triangular factor (T-1) obtained by Cholesky root-free decomposition of A22. We propose an algorithm that sets up the sparsity pattern of T-1 using pedigree information. This algorithm provides positions of the elements of T-1 worth to be computed (i.e. different from zero). A recursive computation of is then achieved with or without information on the sparsity pattern and time required for each computation was recorded. For three numbers of selected animals (4000; 8000 and 12 000), A22 was computed using different pedigree extractions and the closeness of the resulting to the inverse computed using the fully extracted pedigree was measured by an appropriate norm. Results The use of prior information on the sparsity of T-1 decreased the computing time for inversion by a factor of 1.73 on average. Computational issues and practical uses of the different algorithms were discussed. Cases involving more than 12 000 selected animals were considered. Inclusion of 10 generations was determined to be sufficient when computing A22. Conclusions Depending on the size and structure of the selected sub-population, gains in time to compute are possible and these gains may increase as the number of selected animals increases. Given the sequential nature of most computational steps, the proposed algorithm can benefit from optimization and may be convenient for genomic evaluations. © Faux and Gengler; licensee BioMed Central Ltd. 2013 |
abstract_unstemmed |
Background In recent theoretical developments, the information available (e.g. genotypes) divides the original population into two groups: animals with this information (selected animals) and animals without this information (excluded animals). These developments require inversion of the part of the pedigree-based numerator relationship matrix that describes the genetic covariance between selected animals (A22). Our main objective was to propose and evaluate methodology that takes advantage of any potential sparsity in the inverse of A22 in order to reduce the computing time required for its inversion. This potential sparsity is brought out by searching the pedigree for dependencies between the selected animals. Jointly, we expected distant ancestors to provide relationship ties that increase the density of matrix A22 but that their effect on might be minor. This hypothesis was also tested. Methods The inverse of A22 can be computed from the inverse of the triangular factor (T-1) obtained by Cholesky root-free decomposition of A22. We propose an algorithm that sets up the sparsity pattern of T-1 using pedigree information. This algorithm provides positions of the elements of T-1 worth to be computed (i.e. different from zero). A recursive computation of is then achieved with or without information on the sparsity pattern and time required for each computation was recorded. For three numbers of selected animals (4000; 8000 and 12 000), A22 was computed using different pedigree extractions and the closeness of the resulting to the inverse computed using the fully extracted pedigree was measured by an appropriate norm. Results The use of prior information on the sparsity of T-1 decreased the computing time for inversion by a factor of 1.73 on average. Computational issues and practical uses of the different algorithms were discussed. Cases involving more than 12 000 selected animals were considered. Inclusion of 10 generations was determined to be sufficient when computing A22. Conclusions Depending on the size and structure of the selected sub-population, gains in time to compute are possible and these gains may increase as the number of selected animals increases. Given the sequential nature of most computational steps, the proposed algorithm can benefit from optimization and may be convenient for genomic evaluations. © Faux and Gengler; licensee BioMed Central Ltd. 2013 |
collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 |
container_issue |
1 |
title_short |
Inversion of a part of the numerator relationship matrix using pedigree information |
url |
https://dx.doi.org/10.1186/1297-9686-45-45 |
remote_bool |
true |
author2 |
Gengler, Nicolas |
author2Str |
Gengler, Nicolas |
ppnlink |
312849052 |
mediatype_str_mv |
c |
isOA_txt |
true |
hochschulschrift_bool |
false |
doi_str |
10.1186/1297-9686-45-45 |
up_date |
2024-07-03T22:50:24.011Z |
_version_ |
1803600028253552640 |
fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR026807386</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230519182713.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201007s2013 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1186/1297-9686-45-45</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR026807386</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)1297-9686-45-45-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Faux, Pierre</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Inversion of a part of the numerator relationship matrix using pedigree information</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2013</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Faux and Gengler; licensee BioMed Central Ltd. 2013</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Background In recent theoretical developments, the information available (e.g. genotypes) divides the original population into two groups: animals with this information (selected animals) and animals without this information (excluded animals). These developments require inversion of the part of the pedigree-based numerator relationship matrix that describes the genetic covariance between selected animals (A22). Our main objective was to propose and evaluate methodology that takes advantage of any potential sparsity in the inverse of A22 in order to reduce the computing time required for its inversion. This potential sparsity is brought out by searching the pedigree for dependencies between the selected animals. Jointly, we expected distant ancestors to provide relationship ties that increase the density of matrix A22 but that their effect on might be minor. This hypothesis was also tested. Methods The inverse of A22 can be computed from the inverse of the triangular factor (T-1) obtained by Cholesky root-free decomposition of A22. We propose an algorithm that sets up the sparsity pattern of T-1 using pedigree information. This algorithm provides positions of the elements of T-1 worth to be computed (i.e. different from zero). A recursive computation of is then achieved with or without information on the sparsity pattern and time required for each computation was recorded. For three numbers of selected animals (4000; 8000 and 12 000), A22 was computed using different pedigree extractions and the closeness of the resulting to the inverse computed using the fully extracted pedigree was measured by an appropriate norm. Results The use of prior information on the sparsity of T-1 decreased the computing time for inversion by a factor of 1.73 on average. Computational issues and practical uses of the different algorithms were discussed. Cases involving more than 12 000 selected animals were considered. Inclusion of 10 generations was determined to be sufficient when computing A22. Conclusions Depending on the size and structure of the selected sub-population, gains in time to compute are possible and these gains may increase as the number of selected animals increases. Given the sequential nature of most computational steps, the proposed algorithm can benefit from optimization and may be convenient for genomic evaluations.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Genomic Prediction</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Inversion Algorithm</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sparsity Pattern</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sparse Vector</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Genomic Relationship Matrix</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Gengler, Nicolas</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Genetics, selection, evolution</subfield><subfield code="d">London : BioMed Central, 1989</subfield><subfield code="g">45(2013), 1 vom: 06. Dez.</subfield><subfield code="w">(DE-627)312849052</subfield><subfield code="w">(DE-600)2012369-3</subfield><subfield code="x">1297-9686</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:45</subfield><subfield code="g">year:2013</subfield><subfield code="g">number:1</subfield><subfield code="g">day:06</subfield><subfield code="g">month:12</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1186/1297-9686-45-45</subfield><subfield code="z">kostenfrei</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_31</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_39</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_60</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_63</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_65</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_69</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_74</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_95</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_151</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_161</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_170</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_213</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_224</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_230</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_285</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_293</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_602</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2003</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4012</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4125</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4126</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4249</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4367</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">45</subfield><subfield code="j">2013</subfield><subfield code="e">1</subfield><subfield code="b">06</subfield><subfield code="c">12</subfield></datafield></record></collection>
|
score |
7.3988447 |