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< a href = "lu__factorization_8h.html" > Go to the documentation of this file.< / a > < div class = "fragment" > < div class = "line" > < a name = "l00001" > < / a > < span class = "lineno" > 1< / span >   < span class = "comment" > // Copyright 2010-2021 Google LLC< / span > < / div >
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< div class = "line" > < a name = "l00002" > < / a > < span class = "lineno" > 2< / span >   < span class = "comment" > // Licensed under the Apache License, Version 2.0 (the " License" );< / span > < / div >
< div class = "line" > < a name = "l00003" > < / a > < span class = "lineno" > 3< / span >   < span class = "comment" > // you may not use this file except in compliance with the License.< / span > < / div >
< div class = "line" > < a name = "l00004" > < / a > < span class = "lineno" > 4< / span >   < span class = "comment" > // You may obtain a copy of the License at< / span > < / div >
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< div class = "line" > < a name = "l00007" > < / a > < span class = "lineno" > 7< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00008" > < / a > < span class = "lineno" > 8< / span >   < span class = "comment" > // Unless required by applicable law or agreed to in writing, software< / span > < / div >
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< div class = "line" > < a name = "l00014" > < / a > < span class = "lineno" > 14< / span >   < span class = "preprocessor" > #ifndef OR_TOOLS_GLOP_LU_FACTORIZATION_H_< / span > < / div >
< div class = "line" > < a name = "l00015" > < / a > < span class = "lineno" > 15< / span >   < span class = "preprocessor" > #define OR_TOOLS_GLOP_LU_FACTORIZATION_H_< / span > < / div >
< div class = "line" > < a name = "l00016" > < / a > < span class = "lineno" > 16< / span >   < / div >
< div class = "line" > < a name = "l00017" > < / a > < span class = "lineno" > 17< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "markowitz_8h.html" > ortools/glop/markowitz.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00018" > < / a > < span class = "lineno" > 18< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "parameters_8pb_8h.html" > ortools/glop/parameters.pb.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00019" > < / a > < span class = "lineno" > 19< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "status_8h.html" > ortools/glop/status.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00020" > < / a > < span class = "lineno" > 20< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "lp__types_8h.html" > ortools/lp_data/lp_types.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00021" > < / a > < span class = "lineno" > 21< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "lp__data_2permutation_8h.html" > ortools/lp_data/permutation.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00022" > < / a > < span class = "lineno" > 22< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "scattered__vector_8h.html" > ortools/lp_data/scattered_vector.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00023" > < / a > < span class = "lineno" > 23< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "sparse_8h.html" > ortools/lp_data/sparse.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00024" > < / a > < span class = "lineno" > 24< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "sparse__column_8h.html" > ortools/lp_data/sparse_column.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00025" > < / a > < span class = "lineno" > 25< / span >   < span class = "preprocessor" > #include " < a class = "code" href = "stats_8h.html" > ortools/util/stats.h< / a > " < / span > < / div >
< div class = "line" > < a name = "l00026" > < / a > < span class = "lineno" > 26< / span >   < / div >
< div class = "line" > < a name = "l00027" > < / a > < span class = "lineno" > 27< / span >   < span class = "keyword" > namespace < / span > < a class = "code" href = "namespaceoperations__research.html" > operations_research< / a > {< / div >
< div class = "line" > < a name = "l00028" > < / a > < span class = "lineno" > 28< / span >   < span class = "keyword" > namespace < / span > glop {< / div >
< div class = "line" > < a name = "l00029" > < / a > < span class = "lineno" > 29< / span >   < / div >
< div class = "line" > < a name = "l00030" > < / a > < span class = "lineno" > 30< / span >   < span class = "comment" > // An LU-Factorization class encapsulating the LU factorization data and< / span > < / div >
< div class = "line" > < a name = "l00031" > < / a > < span class = "lineno" > 31< / span >   < span class = "comment" > // algorithms. The actual algorithm is in markowitz.h and .cc. This class holds< / span > < / div >
< div class = "line" > < a name = "l00032" > < / a > < span class = "lineno" > 32< / span >   < span class = "comment" > // all the Solve() functions that deal with the permutations and the L and U< / span > < / div >
< div class = "line" > < a name = "l00033" > < / a > < span class = "lineno" > 33< / span >   < span class = "comment" > // factors once they are computed.< / span > < / div >
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< div class = "line" > < a name = "l00034" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1glop_1_1_lu_factorization.html" > 34< / a > < / span >   < span class = "keyword" > class < / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html" > LuFactorization< / a > {< / div >
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< div class = "line" > < a name = "l00035" > < / a > < span class = "lineno" > 35< / span >   < span class = "keyword" > public< / span > :< / div >
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< div class = "line" > < a name = "l00036" > < / a > < span class = "lineno" > 36< / span >   < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#af0b37b89dc1909384e822287c1091aa0" > LuFactorization< / a > ();< / div >
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< div class = "line" > < a name = "l00037" > < / a > < span class = "lineno" > 37< / span >   < / div >
< div class = "line" > < a name = "l00038" > < / a > < span class = "lineno" > 38< / span >   < span class = "comment" > // Returns true if the LuFactorization is a factorization of the identity< / span > < / div >
< div class = "line" > < a name = "l00039" > < / a > < span class = "lineno" > 39< / span >   < span class = "comment" > // matrix. In this state, all the Solve() functions will work for any< / span > < / div >
< div class = "line" > < a name = "l00040" > < / a > < span class = "lineno" > 40< / span >   < span class = "comment" > // vector dimension.< / span > < / div >
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< div class = "line" > < a name = "l00041" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#adbf20cf678d328e6b36c8bb43dc499cf" > 41< / a > < / span >   < span class = "keywordtype" > bool< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#adbf20cf678d328e6b36c8bb43dc499cf" > IsIdentityFactorization< / a > () { < span class = "keywordflow" > return< / span > is_identity_factorization_; }< / div >
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< div class = "line" > < a name = "l00042" > < / a > < span class = "lineno" > 42< / span >   < / div >
< div class = "line" > < a name = "l00043" > < / a > < span class = "lineno" > 43< / span >   < span class = "comment" > // Clears internal data structure and reset this class to the factorization< / span > < / div >
< div class = "line" > < a name = "l00044" > < / a > < span class = "lineno" > 44< / span >   < span class = "comment" > // of an identity matrix.< / span > < / div >
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< div class = "line" > < a name = "l00045" > < / a > < span class = "lineno" > 45< / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#aa71d36872f416feaa853788a7a7a7ef8" > Clear< / a > ();< / div >
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< div class = "line" > < a name = "l00046" > < / a > < span class = "lineno" > 46< / span >   < / div >
< div class = "line" > < a name = "l00047" > < / a > < span class = "lineno" > 47< / span >   < span class = "comment" > // Computes an LU-decomposition for a given matrix B. If for some reason,< / span > < / div >
< div class = "line" > < a name = "l00048" > < / a > < span class = "lineno" > 48< / span >   < span class = "comment" > // there was an error, then the factorization is reset to the one of the< / span > < / div >
< div class = "line" > < a name = "l00049" > < / a > < span class = "lineno" > 49< / span >   < span class = "comment" > // identity matrix, and an error is reported.< / span > < / div >
< div class = "line" > < a name = "l00050" > < / a > < span class = "lineno" > 50< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00051" > < / a > < span class = "lineno" > 51< / span >   < span class = "comment" > // Note(user): Since a client must use the result, there is little chance of< / span > < / div >
< div class = "line" > < a name = "l00052" > < / a > < span class = "lineno" > 52< / span >   < span class = "comment" > // it being confused by this revert to identity factorization behavior. The< / span > < / div >
< div class = "line" > < a name = "l00053" > < / a > < span class = "lineno" > 53< / span >   < span class = "comment" > // reason behind it is that this way, calling any public function of this< / span > < / div >
< div class = "line" > < a name = "l00054" > < / a > < span class = "lineno" > 54< / span >   < span class = "comment" > // class will never cause a crash of the program.< / span > < / div >
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< div class = "line" > < a name = "l00055" > < / a > < span class = "lineno" > 55< / span >   ABSL_MUST_USE_RESULT < a class = "code" href = "classoperations__research_1_1glop_1_1_status.html" > Status< / a > < / div >
< div class = "line" > < a name = "l00056" > < / a > < span class = "lineno" > 56< / span >   < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#ace58a4f9d6a147c3455ff8dc029537c4" > ComputeFactorization< / a > (< span class = "keyword" > const< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html" > CompactSparseMatrixView< / a > & compact_matrix);< / div >
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< div class = "line" > < a name = "l00057" > < / a > < span class = "lineno" > 57< / span >   < / div >
< div class = "line" > < a name = "l00058" > < / a > < span class = "lineno" > 58< / span >   < span class = "comment" > // Returns the column permutation used by the LU factorization.< / span > < / div >
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< div class = "line" > < a name = "l00059" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a56d08f5289eea3f018dca5b93b6fca6b" > 59< / a > < / span >   < span class = "keyword" > const< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_permutation.html" > ColumnPermutation< / a > & < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a56d08f5289eea3f018dca5b93b6fca6b" > GetColumnPermutation< / a > ()< span class = "keyword" > const < / span > { < span class = "keywordflow" > return< / span > col_perm_; }< / div >
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< div class = "line" > < a name = "l00060" > < / a > < span class = "lineno" > 60< / span >   < / div >
< div class = "line" > < a name = "l00061" > < / a > < span class = "lineno" > 61< / span >   < span class = "comment" > // Sets the column permutation to the identity permutation. The idea is that< / span > < / div >
< div class = "line" > < a name = "l00062" > < / a > < span class = "lineno" > 62< / span >   < span class = "comment" > // the column permutation can be incorporated in the basis RowToColMapping,< / span > < / div >
< div class = "line" > < a name = "l00063" > < / a > < span class = "lineno" > 63< / span >   < span class = "comment" > // and once this is done, then a client can call this and effectively remove< / span > < / div >
< div class = "line" > < a name = "l00064" > < / a > < span class = "lineno" > 64< / span >   < span class = "comment" > // the need for a column permutation on each solve.< / span > < / div >
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< div class = "line" > < a name = "l00065" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#ad91a397910de30b87b9fb45298fa5c58" > 65< / a > < / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#ad91a397910de30b87b9fb45298fa5c58" > SetColumnPermutationToIdentity< / a > () {< / div >
< div class = "line" > < a name = "l00066" > < / a > < span class = "lineno" > 66< / span >   col_perm_.< a class = "code" href = "classoperations__research_1_1glop_1_1_permutation.html#ac8bb3912a3ce86b15842e79d0b421204" > clear< / a > ();< / div >
< div class = "line" > < a name = "l00067" > < / a > < span class = "lineno" > 67< / span >   inverse_col_perm_.< a class = "code" href = "classoperations__research_1_1glop_1_1_permutation.html#ac8bb3912a3ce86b15842e79d0b421204" > clear< / a > ();< / div >
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< div class = "line" > < a name = "l00068" > < / a > < span class = "lineno" > 68< / span >   }< / div >
< div class = "line" > < a name = "l00069" > < / a > < span class = "lineno" > 69< / span >   < / div >
< div class = "line" > < a name = "l00070" > < / a > < span class = "lineno" > 70< / span >   < span class = "comment" > // Solves ' B.x = b' , x initially contains b, and is replaced by ' B^{-1}.b' .< / span > < / div >
< div class = "line" > < a name = "l00071" > < / a > < span class = "lineno" > 71< / span >   < span class = "comment" > // Since P.B.Q^{-1} = L.U, we have B = P^{-1}.L.U.Q.< / span > < / div >
< div class = "line" > < a name = "l00072" > < / a > < span class = "lineno" > 72< / span >   < span class = "comment" > // 1/ Solve P^{-1}.y = b for y by computing y = P.b,< / span > < / div >
< div class = "line" > < a name = "l00073" > < / a > < span class = "lineno" > 73< / span >   < span class = "comment" > // 2/ solve L.z = y for z,< / span > < / div >
< div class = "line" > < a name = "l00074" > < / a > < span class = "lineno" > 74< / span >   < span class = "comment" > // 3/ solve U.t = z for t,< / span > < / div >
< div class = "line" > < a name = "l00075" > < / a > < span class = "lineno" > 75< / span >   < span class = "comment" > // 4/ finally solve Q.x = t, by computing x = Q^{-1}.t.< / span > < / div >
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< div class = "line" > < a name = "l00076" > < / a > < span class = "lineno" > 76< / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a6ec53ed3afa3d8affb6941568dcfec76" > RightSolve< / a > (< a class = "code" href = "classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html" > DenseColumn< / a > * x) < span class = "keyword" > const< / span > ;< / div >
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< div class = "line" > < a name = "l00077" > < / a > < span class = "lineno" > 77< / span >   < / div >
< div class = "line" > < a name = "l00078" > < / a > < span class = "lineno" > 78< / span >   < span class = "comment" > // Solves ' y.B = r' , y initially contains r, and is replaced by r.B^{-1}.< / span > < / div >
< div class = "line" > < a name = "l00079" > < / a > < span class = "lineno" > 79< / span >   < span class = "comment" > // Internally, it takes x = y^T, b = r^T and solves B^T.x = b.< / span > < / div >
< div class = "line" > < a name = "l00080" > < / a > < span class = "lineno" > 80< / span >   < span class = "comment" > // We have P.B.Q^{-1} = P.B.Q^T = L.U, thus (L.U)^T = Q.B^T.P^T.< / span > < / div >
< div class = "line" > < a name = "l00081" > < / a > < span class = "lineno" > 81< / span >   < span class = "comment" > // Therefore B^T = Q^{-1}.U^T.L^T.P^T.P^{-1} = Q^{-1}.U^T.L^T.P< / span > < / div >
< div class = "line" > < a name = "l00082" > < / a > < span class = "lineno" > 82< / span >   < span class = "comment" > // The procedure is thus:< / span > < / div >
< div class = "line" > < a name = "l00083" > < / a > < span class = "lineno" > 83< / span >   < span class = "comment" > // 1/ Solve Q^{-1}.y = b for y, by computing y = Q.b,< / span > < / div >
< div class = "line" > < a name = "l00084" > < / a > < span class = "lineno" > 84< / span >   < span class = "comment" > // 2/ solve U^T.z = y for z,< / span > < / div >
< div class = "line" > < a name = "l00085" > < / a > < span class = "lineno" > 85< / span >   < span class = "comment" > // 3/ solve L^T.t = z for t,< / span > < / div >
< div class = "line" > < a name = "l00086" > < / a > < span class = "lineno" > 86< / span >   < span class = "comment" > // 4/ finally, solve P.x = t for x by computing x = P^{-1}.t.< / span > < / div >
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< div class = "line" > < a name = "l00087" > < / a > < span class = "lineno" > 87< / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a6b5f31c4068711b8e6823f4888f410ce" > LeftSolve< / a > (< a class = "code" href = "classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html" > DenseRow< / a > * y) < span class = "keyword" > const< / span > ;< / div >
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< div class = "line" > < a name = "l00088" > < / a > < span class = "lineno" > 88< / span >   < / div >
< div class = "line" > < a name = "l00089" > < / a > < span class = "lineno" > 89< / span >   < span class = "comment" > // More fine-grained right/left solve functions that may exploit the initial< / span > < / div >
< div class = "line" > < a name = "l00090" > < / a > < span class = "lineno" > 90< / span >   < span class = "comment" > // non-zeros of the input vector if non-empty. Note that a solve involving L< / span > < / div >
< div class = "line" > < a name = "l00091" > < / a > < span class = "lineno" > 91< / span >   < span class = "comment" > // actually solves P^{-1}.L and a solve involving U actually solves U.Q. To< / span > < / div >
< div class = "line" > < a name = "l00092" > < / a > < span class = "lineno" > 92< / span >   < span class = "comment" > // solve a system with the initial matrix B, one needs to call:< / span > < / div >
< div class = "line" > < a name = "l00093" > < / a > < span class = "lineno" > 93< / span >   < span class = "comment" > // - RightSolveL() and then RightSolveU() for a right solve (B.x = initial x).< / span > < / div >
< div class = "line" > < a name = "l00094" > < / a > < span class = "lineno" > 94< / span >   < span class = "comment" > // - LeftSolveU() and then LeftSolveL() for a left solve (y.B = initial y).< / span > < / div >
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< div class = "line" > < a name = "l00095" > < / a > < span class = "lineno" > 95< / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#aa35c31899babb961a8100bc605136424" > RightSolveLWithNonZeros< / a > (< a class = "code" href = "structoperations__research_1_1glop_1_1_scattered_column.html" > ScatteredColumn< / a > * x) < span class = "keyword" > const< / span > ;< / div >
< div class = "line" > < a name = "l00096" > < / a > < span class = "lineno" > 96< / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a577c37faff9567f86849dd74c3fcf4ac" > RightSolveUWithNonZeros< / a > (< a class = "code" href = "structoperations__research_1_1glop_1_1_scattered_column.html" > ScatteredColumn< / a > * x) < span class = "keyword" > const< / span > ;< / div >
< div class = "line" > < a name = "l00097" > < / a > < span class = "lineno" > 97< / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a1ea8d0a49dad57416810ab7b1a2e2108" > LeftSolveUWithNonZeros< / a > (< a class = "code" href = "structoperations__research_1_1glop_1_1_scattered_row.html" > ScatteredRow< / a > * y) < span class = "keyword" > const< / span > ;< / div >
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< div class = "line" > < a name = "l00098" > < / a > < span class = "lineno" > 98< / span >   < / div >
< div class = "line" > < a name = "l00099" > < / a > < span class = "lineno" > 99< / span >   < span class = "comment" > // Specialized version of LeftSolveL() that may exploit the initial non_zeros< / span > < / div >
< div class = "line" > < a name = "l00100" > < / a > < span class = "lineno" > 100< / span >   < span class = "comment" > // of y if it is non empty. Moreover, if result_before_permutation is not< / span > < / div >
< div class = "line" > < a name = "l00101" > < / a > < span class = "lineno" > 101< / span >   < span class = "comment" > // NULL, it might be filled with the result just before row_perm_ is applied< / span > < / div >
< div class = "line" > < a name = "l00102" > < / a > < span class = "lineno" > 102< / span >   < span class = "comment" > // to it and true is returned. If result_before_permutation is not filled,< / span > < / div >
< div class = "line" > < a name = "l00103" > < / a > < span class = "lineno" > 103< / span >   < span class = "comment" > // then false is returned.< / span > < / div >
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< div class = "line" > < a name = "l00104" > < / a > < span class = "lineno" > 104< / span >   < span class = "keywordtype" > bool< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a6c5735e4c25655dd4533504d22b1d66c" > LeftSolveLWithNonZeros< / a > (< a class = "code" href = "structoperations__research_1_1glop_1_1_scattered_row.html" > ScatteredRow< / a > * y,< / div >
< div class = "line" > < a name = "l00105" > < / a > < span class = "lineno" > 105< / span >   < a class = "code" href = "structoperations__research_1_1glop_1_1_scattered_column.html" > ScatteredColumn< / a > * result_before_permutation) < span class = "keyword" > const< / span > ;< / div >
< div class = "line" > < a name = "l00106" > < / a > < span class = "lineno" > 106< / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a6c5735e4c25655dd4533504d22b1d66c" > LeftSolveLWithNonZeros< / a > (< a class = "code" href = "structoperations__research_1_1glop_1_1_scattered_row.html" > ScatteredRow< / a > * y) < span class = "keyword" > const< / span > ;< / div >
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< div class = "line" > < a name = "l00107" > < / a > < span class = "lineno" > 107< / span >   < / div >
< div class = "line" > < a name = "l00108" > < / a > < span class = "lineno" > 108< / span >   < span class = "comment" > // Specialized version of RightSolveLWithNonZeros() that takes a SparseColumn< / span > < / div >
< div class = "line" > < a name = "l00109" > < / a > < span class = "lineno" > 109< / span >   < span class = "comment" > // or a ScatteredColumn as input. non_zeros will either be cleared or set to< / span > < / div >
< div class = "line" > < a name = "l00110" > < / a > < span class = "lineno" > 110< / span >   < span class = "comment" > // the non zeros of the result. Important: the output x must be of the correct< / span > < / div >
< div class = "line" > < a name = "l00111" > < / a > < span class = "lineno" > 111< / span >   < span class = "comment" > // size and all zero.< / span > < / div >
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< div class = "line" > < a name = "l00112" > < / a > < span class = "lineno" > 112< / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a40757145002c85d47ad8df1b53707661" > RightSolveLForColumnView< / a > (< span class = "keyword" > const< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_column_view.html" > ColumnView< / a > & < a class = "code" href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > , < a class = "code" href = "structoperations__research_1_1glop_1_1_scattered_column.html" > ScatteredColumn< / a > * x) < span class = "keyword" > const< / span > ;< / div >
< div class = "line" > < a name = "l00113" > < / a > < span class = "lineno" > 113< / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#aa1222207079d0d679ef52f8b465cd00a" > RightSolveLForScatteredColumn< / a > (< span class = "keyword" > const< / span > < a class = "code" href = "structoperations__research_1_1glop_1_1_scattered_column.html" > ScatteredColumn< / a > & < a class = "code" href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > ,< / div >
2020-10-09 12:00:09 +02:00
< div class = "line" > < a name = "l00114" > < / a > < span class = "lineno" > 114< / span >   < a class = "code" href = "structoperations__research_1_1glop_1_1_scattered_column.html" > ScatteredColumn< / a > * x) < span class = "keyword" > const< / span > ;< / div >
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< div class = "line" > < a name = "l00115" > < / a > < span class = "lineno" > 115< / span >   < / div >
< div class = "line" > < a name = "l00116" > < / a > < span class = "lineno" > 116< / span >   < span class = "comment" > // Specialized version of RightSolveLWithNonZeros() where x is originaly equal< / span > < / div >
< div class = "line" > < a name = "l00117" > < / a > < span class = "lineno" > 117< / span >   < span class = "comment" > // to ' a' permuted by row_perm_. Note that ' a' is only used for DCHECK.< / span > < / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00118" > < / a > < span class = "lineno" > 118< / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a43e095088501053427e317e905d5fc83" > RightSolveLWithPermutedInput< / a > (< span class = "keyword" > const< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html" > DenseColumn< / a > & < a class = "code" href = "constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6" > a< / a > ,< / div >
2020-10-09 12:00:09 +02:00
< div class = "line" > < a name = "l00119" > < / a > < span class = "lineno" > 119< / span >   < a class = "code" href = "structoperations__research_1_1glop_1_1_scattered_column.html" > ScatteredColumn< / a > * x) < span class = "keyword" > const< / span > ;< / div >
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< div class = "line" > < a name = "l00120" > < / a > < span class = "lineno" > 120< / span >   < / div >
< div class = "line" > < a name = "l00121" > < / a > < span class = "lineno" > 121< / span >   < span class = "comment" > // Specialized version of LeftSolveU() for an unit right-hand side.< / span > < / div >
< div class = "line" > < a name = "l00122" > < / a > < span class = "lineno" > 122< / span >   < span class = "comment" > // non_zeros will either be cleared or set to the non zeros of the results.< / span > < / div >
< div class = "line" > < a name = "l00123" > < / a > < span class = "lineno" > 123< / span >   < span class = "comment" > // It also returns the value of col permuted by Q (which is the position< / span > < / div >
< div class = "line" > < a name = "l00124" > < / a > < span class = "lineno" > 124< / span >   < span class = "comment" > // of the unit-vector rhs in the solve system: y.U = rhs).< / span > < / div >
< div class = "line" > < a name = "l00125" > < / a > < span class = "lineno" > 125< / span >   < span class = "comment" > // Important: the output y must be of the correct size and all zero.< / span > < / div >
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< div class = "line" > < a name = "l00126" > < / a > < span class = "lineno" > 126< / span >   ColIndex < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a9438a3ceb0327c1bd75ff3b4fa58d3b0" > LeftSolveUForUnitRow< / a > (ColIndex < a class = "code" href = "markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c" > col< / a > , < a class = "code" href = "structoperations__research_1_1glop_1_1_scattered_row.html" > ScatteredRow< / a > * y) < span class = "keyword" > const< / span > ;< / div >
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< div class = "line" > < a name = "l00127" > < / a > < span class = "lineno" > 127< / span >   < / div >
< div class = "line" > < a name = "l00128" > < / a > < span class = "lineno" > 128< / span >   < span class = "comment" > // Returns the given column of U.< / span > < / div >
< div class = "line" > < a name = "l00129" > < / a > < span class = "lineno" > 129< / span >   < span class = "comment" > // It will only be valid until the next call to GetColumnOfU().< / span > < / div >
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< div class = "line" > < a name = "l00130" > < / a > < span class = "lineno" > 130< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_sparse_column.html" > SparseColumn< / a > & < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a3042b0778d3d901556345438e482d88a" > GetColumnOfU< / a > (ColIndex < a class = "code" href = "markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c" > col< / a > ) < span class = "keyword" > const< / span > ;< / div >
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< div class = "line" > < a name = "l00131" > < / a > < span class = "lineno" > 131< / span >   < / div >
< div class = "line" > < a name = "l00132" > < / a > < span class = "lineno" > 132< / span >   < span class = "comment" > // Returns the norm of B^{-1}.a< / span > < / div >
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< div class = "line" > < a name = "l00133" > < / a > < span class = "lineno" > 133< / span >   < a class = "code" href = "namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7" > Fractional< / a > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a4bf241af6b1844669171d6e170ef991d" > RightSolveSquaredNorm< / a > (< span class = "keyword" > const< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_column_view.html" > ColumnView< / a > & < a class = "code" href = "constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6" > a< / a > ) < span class = "keyword" > const< / span > ;< / div >
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< div class = "line" > < a name = "l00134" > < / a > < span class = "lineno" > 134< / span >   < / div >
< div class = "line" > < a name = "l00135" > < / a > < span class = "lineno" > 135< / span >   < span class = "comment" > // Returns the norm of (B^T)^{-1}.e_row where e is an unit vector.< / span > < / div >
2020-10-09 12:00:09 +02:00
< div class = "line" > < a name = "l00136" > < / a > < span class = "lineno" > 136< / span >   < a class = "code" href = "namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7" > Fractional< / a > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a9b738f6b485a4d4ef866b8d82ac07876" > DualEdgeSquaredNorm< / a > (RowIndex < a class = "code" href = "markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52" > row< / a > ) < span class = "keyword" > const< / span > ;< / div >
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< div class = "line" > < a name = "l00137" > < / a > < span class = "lineno" > 137< / span >   < / div >
< div class = "line" > < a name = "l00138" > < / a > < span class = "lineno" > 138< / span >   < span class = "comment" > // The fill-in of the LU-factorization is defined as the sum of the number< / span > < / div >
< div class = "line" > < a name = "l00139" > < / a > < span class = "lineno" > 139< / span >   < span class = "comment" > // of entries of both the lower- and upper-triangular matrices L and U minus< / span > < / div >
< div class = "line" > < a name = "l00140" > < / a > < span class = "lineno" > 140< / span >   < span class = "comment" > // the number of entries in the initial matrix B.< / span > < / div >
< div class = "line" > < a name = "l00141" > < / a > < span class = "lineno" > 141< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00142" > < / a > < span class = "lineno" > 142< / span >   < span class = "comment" > // This returns the number of entries in lower + upper as the percentage of< / span > < / div >
< div class = "line" > < a name = "l00143" > < / a > < span class = "lineno" > 143< / span >   < span class = "comment" > // the number of entries in B.< / span > < / div >
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< div class = "line" > < a name = "l00144" > < / a > < span class = "lineno" > 144< / span >   < span class = "keywordtype" > double< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a4523b56a271bfeb588757e64e4bf1425" > GetFillInPercentage< / a > (< span class = "keyword" > const< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html" > CompactSparseMatrixView< / a > & matrix) < span class = "keyword" > const< / span > ;< / div >
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< div class = "line" > < a name = "l00145" > < / a > < span class = "lineno" > 145< / span >   < / div >
< div class = "line" > < a name = "l00146" > < / a > < span class = "lineno" > 146< / span >   < span class = "comment" > // Returns the number of entries in L + U.< / span > < / div >
< div class = "line" > < a name = "l00147" > < / a > < span class = "lineno" > 147< / span >   < span class = "comment" > // If the factorization is the identity, this returns 0.< / span > < / div >
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< div class = "line" > < a name = "l00148" > < / a > < span class = "lineno" > 148< / span >   EntryIndex < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#ad9e11229fed5416bf22fb3b4fa65f4c1" > NumberOfEntries< / a > () < span class = "keyword" > const< / span > ;< / div >
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< div class = "line" > < a name = "l00149" > < / a > < span class = "lineno" > 149< / span >   < / div >
< div class = "line" > < a name = "l00150" > < / a > < span class = "lineno" > 150< / span >   < span class = "comment" > // Computes the determinant of the input matrix B.< / span > < / div >
< div class = "line" > < a name = "l00151" > < / a > < span class = "lineno" > 151< / span >   < span class = "comment" > // Since P.B.Q^{-1} = L.U, det(P) * det(B) * det(Q^{-1}) = det(L) * det(U).< / span > < / div >
< div class = "line" > < a name = "l00152" > < / a > < span class = "lineno" > 152< / span >   < span class = "comment" > // det(L) = 1 since L is a lower-triangular matrix with 1 on the diagonal.< / span > < / div >
< div class = "line" > < a name = "l00153" > < / a > < span class = "lineno" > 153< / span >   < span class = "comment" > // det(P) = +1 or -1 (by definition it is the sign of the permutation P)< / span > < / div >
< div class = "line" > < a name = "l00154" > < / a > < span class = "lineno" > 154< / span >   < span class = "comment" > // det(Q^{-1}) = +1 or -1 (the sign of the permutation Q^{-1})< / span > < / div >
< div class = "line" > < a name = "l00155" > < / a > < span class = "lineno" > 155< / span >   < span class = "comment" > // Finally det(U) = product of the diagonal elements of U, since U is an< / span > < / div >
< div class = "line" > < a name = "l00156" > < / a > < span class = "lineno" > 156< / span >   < span class = "comment" > // upper-triangular matrix.< / span > < / div >
< div class = "line" > < a name = "l00157" > < / a > < span class = "lineno" > 157< / span >   < span class = "comment" > // Taking all this into account:< / span > < / div >
< div class = "line" > < a name = "l00158" > < / a > < span class = "lineno" > 158< / span >   < span class = "comment" > // det(B) = sign(P) * sign(Q^{-1}) * prod_i u_ii .< / span > < / div >
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< div class = "line" > < a name = "l00159" > < / a > < span class = "lineno" > 159< / span >   < a class = "code" href = "namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7" > Fractional< / a > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#aa40655f0310c3616632354ffeb7d466e" > ComputeDeterminant< / a > () < span class = "keyword" > const< / span > ;< / div >
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< div class = "line" > < a name = "l00160" > < / a > < span class = "lineno" > 160< / span >   < / div >
< div class = "line" > < a name = "l00161" > < / a > < span class = "lineno" > 161< / span >   < span class = "comment" > // Computes the 1-norm of the inverse of the input matrix B.< / span > < / div >
< div class = "line" > < a name = "l00162" > < / a > < span class = "lineno" > 162< / span >   < span class = "comment" > // For this we iteratively solve B.x = e_j, where e_j is the jth unit vector.< / span > < / div >
< div class = "line" > < a name = "l00163" > < / a > < span class = "lineno" > 163< / span >   < span class = "comment" > // The result of this computation is the jth column of B^-1.< / span > < / div >
< div class = "line" > < a name = "l00164" > < / a > < span class = "lineno" > 164< / span >   < span class = "comment" > // The 1-norm |B| is defined as max_j sum_i |a_ij|< / span > < / div >
< div class = "line" > < a name = "l00165" > < / a > < span class = "lineno" > 165< / span >   < span class = "comment" > // http://en.wikipedia.org/wiki/Matrix_norm< / span > < / div >
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< div class = "line" > < a name = "l00166" > < / a > < span class = "lineno" > 166< / span >   < a class = "code" href = "namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7" > Fractional< / a > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a05d6979828b99ac719553f75335a1937" > ComputeInverseOneNorm< / a > () < span class = "keyword" > const< / span > ;< / div >
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< div class = "line" > < a name = "l00167" > < / a > < span class = "lineno" > 167< / span >   < / div >
< div class = "line" > < a name = "l00168" > < / a > < span class = "lineno" > 168< / span >   < span class = "comment" > // Computes the infinity-norm of the inverse of the input matrix B.< / span > < / div >
< div class = "line" > < a name = "l00169" > < / a > < span class = "lineno" > 169< / span >   < span class = "comment" > // The infinity-norm |B| is defined as max_i sum_j |a_ij|< / span > < / div >
< div class = "line" > < a name = "l00170" > < / a > < span class = "lineno" > 170< / span >   < span class = "comment" > // http://en.wikipedia.org/wiki/Matrix_norm< / span > < / div >
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< div class = "line" > < a name = "l00171" > < / a > < span class = "lineno" > 171< / span >   < a class = "code" href = "namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7" > Fractional< / a > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a3a6bb95b9009b1c578a27e6139d52696" > ComputeInverseInfinityNorm< / a > () < span class = "keyword" > const< / span > ;< / div >
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< div class = "line" > < a name = "l00172" > < / a > < span class = "lineno" > 172< / span >   < / div >
< div class = "line" > < a name = "l00173" > < / a > < span class = "lineno" > 173< / span >   < span class = "comment" > // Computes the condition number of the input matrix B.< / span > < / div >
< div class = "line" > < a name = "l00174" > < / a > < span class = "lineno" > 174< / span >   < span class = "comment" > // For a given norm, this is the matrix norm times the norm of its inverse.< / span > < / div >
< div class = "line" > < a name = "l00175" > < / a > < span class = "lineno" > 175< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00176" > < / a > < span class = "lineno" > 176< / span >   < span class = "comment" > // Note that because the LuFactorization class does not keep the< / span > < / div >
< div class = "line" > < a name = "l00177" > < / a > < span class = "lineno" > 177< / span >   < span class = "comment" > // non-factorized matrix in memory, it needs to be passed to these functions.< / span > < / div >
< div class = "line" > < a name = "l00178" > < / a > < span class = "lineno" > 178< / span >   < span class = "comment" > // It is up to the client to pass exactly the same matrix as the one used< / span > < / div >
< div class = "line" > < a name = "l00179" > < / a > < span class = "lineno" > 179< / span >   < span class = "comment" > // for ComputeFactorization().< / span > < / div >
< div class = "line" > < a name = "l00180" > < / a > < span class = "lineno" > 180< / span >   < span class = "comment" > //< / span > < / div >
< div class = "line" > < a name = "l00181" > < / a > < span class = "lineno" > 181< / span >   < span class = "comment" > // TODO(user): separate this from LuFactorization.< / span > < / div >
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< div class = "line" > < a name = "l00182" > < / a > < span class = "lineno" > 182< / span >   < a class = "code" href = "namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7" > Fractional< / a > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#af03b66d5eb557d6d95ad01d446c2cba8" > ComputeOneNormConditionNumber< / a > (< / div >
< div class = "line" > < a name = "l00183" > < / a > < span class = "lineno" > 183< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html" > CompactSparseMatrixView< / a > & matrix) < span class = "keyword" > const< / span > ;< / div >
< div class = "line" > < a name = "l00184" > < / a > < span class = "lineno" > 184< / span >   < a class = "code" href = "namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7" > Fractional< / a > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#ac22943ff00ae631c58ad2c42932d4657" > ComputeInfinityNormConditionNumber< / a > (< / div >
< div class = "line" > < a name = "l00185" > < / a > < span class = "lineno" > 185< / span >   < span class = "keyword" > const< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html" > CompactSparseMatrixView< / a > & matrix) < span class = "keyword" > const< / span > ;< / div >
< div class = "line" > < a name = "l00186" > < / a > < span class = "lineno" > 186< / span >   < a class = "code" href = "namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7" > Fractional< / a > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#ada69c9026d5d933471bf27c9ad2d1b38" > ComputeInverseInfinityNormUpperBound< / a > () < span class = "keyword" > const< / span > ;< / div >
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< div class = "line" > < a name = "l00187" > < / a > < span class = "lineno" > 187< / span >   < / div >
< div class = "line" > < a name = "l00188" > < / a > < span class = "lineno" > 188< / span >   < span class = "comment" > // Sets the current parameters.< / span > < / div >
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< div class = "line" > < a name = "l00189" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#ae7202d055b6b172a8a1da4f5b136f9ea" > 189< / a > < / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#ae7202d055b6b172a8a1da4f5b136f9ea" > SetParameters< / a > (< span class = "keyword" > const< / span > GlopParameters& < a class = "code" href = "cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219" > parameters< / a > ) {< / div >
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< div class = "line" > < a name = "l00190" > < / a > < span class = "lineno" > 190< / span >   parameters_ = < a class = "code" href = "cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219" > parameters< / a > ;< / div >
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< div class = "line" > < a name = "l00191" > < / a > < span class = "lineno" > 191< / span >   markowitz_.< a class = "code" href = "classoperations__research_1_1glop_1_1_markowitz.html#ae7202d055b6b172a8a1da4f5b136f9ea" > SetParameters< / a > (< a class = "code" href = "cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219" > parameters< / a > );< / div >
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< div class = "line" > < a name = "l00192" > < / a > < span class = "lineno" > 192< / span >   }< / div >
< div class = "line" > < a name = "l00193" > < / a > < span class = "lineno" > 193< / span >   < / div >
< div class = "line" > < a name = "l00194" > < / a > < span class = "lineno" > 194< / span >   < span class = "comment" > // Returns a string containing the statistics for this class.< / span > < / div >
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< div class = "line" > < a name = "l00195" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#af9bc435481ae9e6e60d66a65d5394a7f" > 195< / a > < / span >   std::string < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#af9bc435481ae9e6e60d66a65d5394a7f" > StatString< / a > ()< span class = "keyword" > const < / span > {< / div >
< div class = "line" > < a name = "l00196" > < / a > < span class = "lineno" > 196< / span >   < span class = "keywordflow" > return< / span > stats_.StatString() + markowitz_.< a class = "code" href = "classoperations__research_1_1glop_1_1_markowitz.html#af9bc435481ae9e6e60d66a65d5394a7f" > StatString< / a > ();< / div >
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< div class = "line" > < a name = "l00197" > < / a > < span class = "lineno" > 197< / span >   }< / div >
< div class = "line" > < a name = "l00198" > < / a > < span class = "lineno" > 198< / span >   < / div >
< div class = "line" > < a name = "l00199" > < / a > < span class = "lineno" > 199< / span >   < span class = "comment" > // This is only used for testing and in debug mode.< / span > < / div >
< div class = "line" > < a name = "l00200" > < / a > < span class = "lineno" > 200< / span >   < span class = "comment" > // TODO(user): avoid the matrix conversion by multiplying TriangularMatrix< / span > < / div >
< div class = "line" > < a name = "l00201" > < / a > < span class = "lineno" > 201< / span >   < span class = "comment" > // directly.< / span > < / div >
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< div class = "line" > < a name = "l00202" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#acd3d874c6fe9195587688508b6cd0305" > 202< / a > < / span >   < span class = "keywordtype" > void< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#acd3d874c6fe9195587688508b6cd0305" > ComputeLowerTimesUpper< / a > (< a class = "code" href = "classoperations__research_1_1glop_1_1_sparse_matrix.html" > SparseMatrix< / a > * product)< span class = "keyword" > const < / span > {< / div >
< div class = "line" > < a name = "l00203" > < / a > < span class = "lineno" > 203< / span >   < a class = "code" href = "classoperations__research_1_1glop_1_1_sparse_matrix.html" > SparseMatrix< / a > temp_lower, temp_upper;< / div >
< div class = "line" > < a name = "l00204" > < / a > < span class = "lineno" > 204< / span >   lower_.< a class = "code" href = "classoperations__research_1_1glop_1_1_triangular_matrix.html#a138580a401252ec46ad8e08925e4e92e" > CopyToSparseMatrix< / a > (& temp_lower);< / div >
< div class = "line" > < a name = "l00205" > < / a > < span class = "lineno" > 205< / span >   upper_.< a class = "code" href = "classoperations__research_1_1glop_1_1_triangular_matrix.html#a138580a401252ec46ad8e08925e4e92e" > CopyToSparseMatrix< / a > (& temp_upper);< / div >
< div class = "line" > < a name = "l00206" > < / a > < span class = "lineno" > 206< / span >   product-> < a class = "code" href = "classoperations__research_1_1glop_1_1_sparse_matrix.html#aa1c2872fa7d491d4c093c8b2124a53b9" > PopulateFromProduct< / a > (temp_lower, temp_upper);< / div >
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< div class = "line" > < a name = "l00207" > < / a > < span class = "lineno" > 207< / span >   }< / div >
< div class = "line" > < a name = "l00208" > < / a > < span class = "lineno" > 208< / span >   < / div >
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< div class = "line" > < a name = "l00209" > < / a > < span class = "lineno" > 209< / span >   < span class = "comment" > // Returns the deterministic time of the last factorization.< / span > < / div >
< div class = "line" > < a name = "l00210" > < / a > < span class = "lineno" > 210< / span >   < span class = "keywordtype" > double< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a627511bf305a6af5d7e114817c1792c2" > DeterministicTimeOfLastFactorization< / a > () < span class = "keyword" > const< / span > ;< / div >
< div class = "line" > < a name = "l00211" > < / a > < span class = "lineno" > 211< / span >   < / div >
< div class = "line" > < a name = "l00212" > < / a > < span class = "lineno" > 212< / span >   < span class = "comment" > // Visible for testing.< / span > < / div >
< div class = "line" > < a name = "l00213" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a5a3f1ad730713e296dcbbed8b1123130" > 213< / a > < / span >   < span class = "keyword" > const< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_permutation.html" > RowPermutation< / a > & < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a5a3f1ad730713e296dcbbed8b1123130" > row_perm< / a > ()< span class = "keyword" > const < / span > { < span class = "keywordflow" > return< / span > row_perm_; }< / div >
< div class = "line" > < a name = "l00214" > < / a > < span class = "lineno" > < a class = "line" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a864ad5596d017729a4ca349fed8949a8" > 214< / a > < / span >   < span class = "keyword" > const< / span > < a class = "code" href = "classoperations__research_1_1glop_1_1_permutation.html" > ColumnPermutation< / a > & < a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a864ad5596d017729a4ca349fed8949a8" > inverse_col_perm< / a > ()< span class = "keyword" > const < / span > {< / div >
< div class = "line" > < a name = "l00215" > < / a > < span class = "lineno" > 215< / span >   < span class = "keywordflow" > return< / span > inverse_col_perm_;< / div >
< div class = "line" > < a name = "l00216" > < / a > < span class = "lineno" > 216< / span >   }< / div >
< div class = "line" > < a name = "l00217" > < / a > < span class = "lineno" > 217< / span >   < / div >
< div class = "line" > < a name = "l00218" > < / a > < span class = "lineno" > 218< / span >   < span class = "keyword" > private< / span > :< / div >
< div class = "line" > < a name = "l00219" > < / a > < span class = "lineno" > 219< / span >   < span class = "comment" > // Statistics about this class.< / span > < / div >
< div class = "line" > < a name = "l00220" > < / a > < span class = "lineno" > 220< / span >   < span class = "keyword" > struct < / span > Stats : < span class = "keyword" > public< / span > < a class = "code" href = "classoperations__research_1_1_stats_group.html" > StatsGroup< / a > {< / div >
< div class = "line" > < a name = "l00221" > < / a > < span class = "lineno" > 221< / span >   Stats()< / div >
< div class = "line" > < a name = "l00222" > < / a > < span class = "lineno" > 222< / span >   : < a class = "code" href = "classoperations__research_1_1_stats_group.html" > StatsGroup< / a > (< span class = "stringliteral" > " LuFactorization" < / span > ),< / div >
< div class = "line" > < a name = "l00223" > < / a > < span class = "lineno" > 223< / span >   basis_num_entries(< span class = "stringliteral" > " basis_num_entries" < / span > , this),< / div >
< div class = "line" > < a name = "l00224" > < / a > < span class = "lineno" > 224< / span >   lu_fill_in(< span class = "stringliteral" > " lu_fill_in" < / span > , this) {}< / div >
< div class = "line" > < a name = "l00225" > < / a > < span class = "lineno" > 225< / span >   < a class = "code" href = "classoperations__research_1_1_integer_distribution.html" > IntegerDistribution< / a > basis_num_entries;< / div >
< div class = "line" > < a name = "l00226" > < / a > < span class = "lineno" > 226< / span >   < a class = "code" href = "classoperations__research_1_1_ratio_distribution.html" > RatioDistribution< / a > lu_fill_in;< / div >
< div class = "line" > < a name = "l00227" > < / a > < span class = "lineno" > 227< / span >   };< / div >
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< div class = "line" > < a name = "l00228" > < / a > < span class = "lineno" > 228< / span >   < / div >
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< div class = "line" > < a name = "l00229" > < / a > < span class = "lineno" > 229< / span >   < span class = "comment" > // Internal function used in the left solve functions.< / span > < / div >
< div class = "line" > < a name = "l00230" > < / a > < span class = "lineno" > 230< / span >   < span class = "keywordtype" > void< / span > LeftSolveScratchpad() < span class = "keyword" > const< / span > ;< / div >
< div class = "line" > < a name = "l00231" > < / a > < span class = "lineno" > 231< / span >   < / div >
< div class = "line" > < a name = "l00232" > < / a > < span class = "lineno" > 232< / span >   < span class = "comment" > // Internal function used in the right solve functions< / span > < / div >
< div class = "line" > < a name = "l00233" > < / a > < span class = "lineno" > 233< / span >   < span class = "keyword" > template< / span > < < span class = "keyword" > typename< / span > Column> < / div >
< div class = "line" > < a name = "l00234" > < / a > < span class = "lineno" > 234< / span >   < span class = "keywordtype" > void< / span > RightSolveLInternal(< span class = "keyword" > const< / span > Column& < a class = "code" href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > , ScatteredColumn* x) < span class = "keyword" > const< / span > ;< / div >
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< div class = "line" > < a name = "l00235" > < / a > < span class = "lineno" > 235< / span >   < / div >
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< div class = "line" > < a name = "l00236" > < / a > < span class = "lineno" > 236< / span >   < span class = "comment" > // Fills transpose_upper_ from upper_.< / span > < / div >
< div class = "line" > < a name = "l00237" > < / a > < span class = "lineno" > 237< / span >   < span class = "keywordtype" > void< / span > ComputeTransposeUpper();< / div >
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< div class = "line" > < a name = "l00238" > < / a > < span class = "lineno" > 238< / span >   < / div >
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< div class = "line" > < a name = "l00239" > < / a > < span class = "lineno" > 239< / span >   < span class = "comment" > // transpose_lower_ is only needed when we compute dual norms.< / span > < / div >
< div class = "line" > < a name = "l00240" > < / a > < span class = "lineno" > 240< / span >   < span class = "keywordtype" > void< / span > ComputeTransposeLower() < span class = "keyword" > const< / span > ;< / div >
< div class = "line" > < a name = "l00241" > < / a > < span class = "lineno" > 241< / span >   < / div >
< div class = "line" > < a name = "l00242" > < / a > < span class = "lineno" > 242< / span >   < span class = "comment" > // Computes R = P.B.Q^{-1} - L.U and returns false if the largest magnitude of< / span > < / div >
< div class = "line" > < a name = "l00243" > < / a > < span class = "lineno" > 243< / span >   < span class = "comment" > // the coefficients of P.B.Q^{-1} - L.U is greater than tolerance.< / span > < / div >
< div class = "line" > < a name = "l00244" > < / a > < span class = "lineno" > 244< / span >   < span class = "keywordtype" > bool< / span > CheckFactorization(< span class = "keyword" > const< / span > CompactSparseMatrixView& matrix,< / div >
< div class = "line" > < a name = "l00245" > < / a > < span class = "lineno" > 245< / span >   < a class = "code" href = "namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7" > Fractional< / a > tolerance) < span class = "keyword" > const< / span > ;< / div >
< div class = "line" > < a name = "l00246" > < / a > < span class = "lineno" > 246< / span >   < / div >
< div class = "line" > < a name = "l00247" > < / a > < span class = "lineno" > 247< / span >   < span class = "comment" > // Special case where we have nothing to do. This happens at the beginning< / span > < / div >
< div class = "line" > < a name = "l00248" > < / a > < span class = "lineno" > 248< / span >   < span class = "comment" > // when we start the problem with an all-slack basis and gives a good speedup< / span > < / div >
< div class = "line" > < a name = "l00249" > < / a > < span class = "lineno" > 249< / span >   < span class = "comment" > // on really easy problems. It is initially true and set to true each time we< / span > < / div >
< div class = "line" > < a name = "l00250" > < / a > < span class = "lineno" > 250< / span >   < span class = "comment" > // call Clear(). We set it to false if a call to ComputeFactorization()< / span > < / div >
< div class = "line" > < a name = "l00251" > < / a > < span class = "lineno" > 251< / span >   < span class = "comment" > // succeeds.< / span > < / div >
< div class = "line" > < a name = "l00252" > < / a > < span class = "lineno" > 252< / span >   < span class = "keywordtype" > bool< / span > is_identity_factorization_;< / div >
< div class = "line" > < a name = "l00253" > < / a > < span class = "lineno" > 253< / span >   < / div >
< div class = "line" > < a name = "l00254" > < / a > < span class = "lineno" > 254< / span >   < span class = "comment" > // The triangular factor L and U (and its transpose).< / span > < / div >
< div class = "line" > < a name = "l00255" > < / a > < span class = "lineno" > 255< / span >   TriangularMatrix lower_;< / div >
< div class = "line" > < a name = "l00256" > < / a > < span class = "lineno" > 256< / span >   TriangularMatrix upper_;< / div >
< div class = "line" > < a name = "l00257" > < / a > < span class = "lineno" > 257< / span >   TriangularMatrix transpose_upper_;< / div >
< div class = "line" > < a name = "l00258" > < / a > < span class = "lineno" > 258< / span >   < / div >
< div class = "line" > < a name = "l00259" > < / a > < span class = "lineno" > 259< / span >   < span class = "comment" > // The transpose of lower_. It is just used by DualEdgeSquaredNorm()< / span > < / div >
< div class = "line" > < a name = "l00260" > < / a > < span class = "lineno" > 260< / span >   < span class = "comment" > // and mutable so it can be lazily initialized.< / span > < / div >
< div class = "line" > < a name = "l00261" > < / a > < span class = "lineno" > 261< / span >   < span class = "keyword" > mutable< / span > TriangularMatrix transpose_lower_;< / div >
< div class = "line" > < a name = "l00262" > < / a > < span class = "lineno" > 262< / span >   < / div >
< div class = "line" > < a name = "l00263" > < / a > < span class = "lineno" > 263< / span >   < span class = "comment" > // The column permutation Q and its inverse Q^{-1} in P.B.Q^{-1} = L.U.< / span > < / div >
< div class = "line" > < a name = "l00264" > < / a > < span class = "lineno" > 264< / span >   < a class = "code" href = "namespaceoperations__research_1_1glop.html#a6b1b56ad0cb77edbd314f2bec33b467a" > ColumnPermutation< / a > col_perm_;< / div >
< div class = "line" > < a name = "l00265" > < / a > < span class = "lineno" > 265< / span >   < a class = "code" href = "namespaceoperations__research_1_1glop.html#a6b1b56ad0cb77edbd314f2bec33b467a" > ColumnPermutation< / a > inverse_col_perm_;< / div >
< div class = "line" > < a name = "l00266" > < / a > < span class = "lineno" > 266< / span >   < / div >
< div class = "line" > < a name = "l00267" > < / a > < span class = "lineno" > 267< / span >   < span class = "comment" > // The row permutation P and its inverse P^{-1} in P.B.Q^{-1} = L.U.< / span > < / div >
< div class = "line" > < a name = "l00268" > < / a > < span class = "lineno" > 268< / span >   < a class = "code" href = "namespaceoperations__research_1_1glop.html#ae69267cf0653a77925ee13121b9857ec" > RowPermutation< / a > row_perm_;< / div >
< div class = "line" > < a name = "l00269" > < / a > < span class = "lineno" > 269< / span >   < a class = "code" href = "namespaceoperations__research_1_1glop.html#ae69267cf0653a77925ee13121b9857ec" > RowPermutation< / a > inverse_row_perm_;< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00270" > < / a > < span class = "lineno" > 270< / span >   < / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00271" > < / a > < span class = "lineno" > 271< / span >   < span class = "comment" > // Temporary storage used by LeftSolve()/RightSolve().< / span > < / div >
< div class = "line" > < a name = "l00272" > < / a > < span class = "lineno" > 272< / span >   < span class = "keyword" > mutable< / span > < a class = "code" href = "namespaceoperations__research_1_1glop.html#ae5fa9e57c2d31b294195ed8a9e17bfac" > DenseColumn< / a > dense_column_scratchpad_;< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00273" > < / a > < span class = "lineno" > 273< / span >   < / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00274" > < / a > < span class = "lineno" > 274< / span >   < span class = "comment" > // Temporary storage used by GetColumnOfU().< / span > < / div >
< div class = "line" > < a name = "l00275" > < / a > < span class = "lineno" > 275< / span >   < span class = "keyword" > mutable< / span > SparseColumn column_of_upper_;< / div >
< div class = "line" > < a name = "l00276" > < / a > < span class = "lineno" > 276< / span >   < / div >
< div class = "line" > < a name = "l00277" > < / a > < span class = "lineno" > 277< / span >   < span class = "comment" > // Same as dense_column_scratchpad_ but this vector is always reset to zero by< / span > < / div >
< div class = "line" > < a name = "l00278" > < / a > < span class = "lineno" > 278< / span >   < span class = "comment" > // the functions that use it. non_zero_rows_ is used to track the< / span > < / div >
< div class = "line" > < a name = "l00279" > < / a > < span class = "lineno" > 279< / span >   < span class = "comment" > // non_zero_rows_ position of dense_column_scratchpad_.< / span > < / div >
< div class = "line" > < a name = "l00280" > < / a > < span class = "lineno" > 280< / span >   < span class = "keyword" > mutable< / span > < a class = "code" href = "namespaceoperations__research_1_1glop.html#ae5fa9e57c2d31b294195ed8a9e17bfac" > DenseColumn< / a > dense_zero_scratchpad_;< / div >
< div class = "line" > < a name = "l00281" > < / a > < span class = "lineno" > 281< / span >   < span class = "keyword" > mutable< / span > std::vector< RowIndex> non_zero_rows_;< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00282" > < / a > < span class = "lineno" > 282< / span >   < / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00283" > < / a > < span class = "lineno" > 283< / span >   < span class = "comment" > // Statistics, mutable so const functions can still update it.< / span > < / div >
< div class = "line" > < a name = "l00284" > < / a > < span class = "lineno" > 284< / span >   < span class = "keyword" > mutable< / span > Stats stats_;< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00285" > < / a > < span class = "lineno" > 285< / span >   < / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00286" > < / a > < span class = "lineno" > 286< / span >   < span class = "comment" > // Proto holding all the parameters of this algorithm.< / span > < / div >
< div class = "line" > < a name = "l00287" > < / a > < span class = "lineno" > 287< / span >   GlopParameters parameters_;< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00288" > < / a > < span class = "lineno" > 288< / span >   < / div >
2021-04-27 23:00:03 +02:00
< div class = "line" > < a name = "l00289" > < / a > < span class = "lineno" > 289< / span >   < span class = "comment" > // The class doing the Markowitz LU factorization.< / span > < / div >
< div class = "line" > < a name = "l00290" > < / a > < span class = "lineno" > 290< / span >   Markowitz markowitz_;< / div >
2020-09-02 09:42:51 +02:00
< div class = "line" > < a name = "l00291" > < / a > < span class = "lineno" > 291< / span >   < / div >
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< div class = "line" > < a name = "l00292" > < / a > < span class = "lineno" > 292< / span >   DISALLOW_COPY_AND_ASSIGN(< a class = "code" href = "classoperations__research_1_1glop_1_1_lu_factorization.html#af0b37b89dc1909384e822287c1091aa0" > LuFactorization< / a > );< / div >
< div class = "line" > < a name = "l00293" > < / a > < span class = "lineno" > 293< / span >   };< / div >
< div class = "line" > < a name = "l00294" > < / a > < span class = "lineno" > 294< / span >   < / div >
< div class = "line" > < a name = "l00295" > < / a > < span class = "lineno" > 295< / span >   } < span class = "comment" > // namespace glop< / span > < / div >
< div class = "line" > < a name = "l00296" > < / a > < span class = "lineno" > 296< / span >   } < span class = "comment" > // namespace operations_research< / span > < / div >
< div class = "line" > < a name = "l00297" > < / a > < span class = "lineno" > 297< / span >   < span class = "preprocessor" > #endif < / span > < span class = "comment" > // OR_TOOLS_GLOP_LU_FACTORIZATION_H_< / span > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1_integer_distribution_html" > < div class = "ttname" > < a href = "classoperations__research_1_1_integer_distribution.html" > operations_research::IntegerDistribution< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "stats_8h_source.html#l00287" > stats.h:287< / a > < / div > < / div >
2020-10-09 12:00:09 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1_ratio_distribution_html" > < div class = "ttname" > < a href = "classoperations__research_1_1_ratio_distribution.html" > operations_research::RatioDistribution< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "stats_8h_source.html#l00263" > stats.h:263< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1_stats_group_html" > < div class = "ttname" > < a href = "classoperations__research_1_1_stats_group.html" > operations_research::StatsGroup< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "stats_8h_source.html#l00131" > stats.h:131< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_column_view_html" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_column_view.html" > operations_research::glop::ColumnView< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "sparse__column_8h_source.html#l00065" > sparse_column.h:65< / a > < / div > < / div >
2020-10-09 12:00:09 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html" > operations_research::glop::CompactSparseMatrixView< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "sparse_8h_source.html#l00471" > sparse.h:471< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html" > operations_research::glop::LuFactorization< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8h_source.html#l00034" > lu_factorization.h:34< / a > < / div > < / div >
2021-04-27 23:00:03 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_a05d6979828b99ac719553f75335a1937" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a05d6979828b99ac719553f75335a1937" > operations_research::glop::LuFactorization::ComputeInverseOneNorm< / a > < / div > < div class = "ttdeci" > Fractional ComputeInverseOneNorm() const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00464" > lu_factorization.cc:464< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_a1ea8d0a49dad57416810ab7b1a2e2108" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a1ea8d0a49dad57416810ab7b1a2e2108" > operations_research::glop::LuFactorization::LeftSolveUWithNonZeros< / a > < / div > < div class = "ttdeci" > void LeftSolveUWithNonZeros(ScatteredRow *y) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00290" > lu_factorization.cc:290< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_a3042b0778d3d901556345438e482d88a" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a3042b0778d3d901556345438e482d88a" > operations_research::glop::LuFactorization::GetColumnOfU< / a > < / div > < div class = "ttdeci" > const SparseColumn & GetColumnOfU(ColIndex col) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00426" > lu_factorization.cc:426< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_a3a6bb95b9009b1c578a27e6139d52696" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a3a6bb95b9009b1c578a27e6139d52696" > operations_research::glop::LuFactorization::ComputeInverseInfinityNorm< / a > < / div > < div class = "ttdeci" > Fractional ComputeInverseInfinityNorm() const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00485" > lu_factorization.cc:485< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_a40757145002c85d47ad8df1b53707661" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a40757145002c85d47ad8df1b53707661" > operations_research::glop::LuFactorization::RightSolveLForColumnView< / a > < / div > < div class = "ttdeci" > void RightSolveLForColumnView(const ColumnView & b, ScatteredColumn *x) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00236" > lu_factorization.cc:236< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_a43e095088501053427e317e905d5fc83" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a43e095088501053427e317e905d5fc83" > operations_research::glop::LuFactorization::RightSolveLWithPermutedInput< / a > < / div > < div class = "ttdeci" > void RightSolveLWithPermutedInput(const DenseColumn & a, ScatteredColumn *x) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00188" > lu_factorization.cc:188< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_a4523b56a271bfeb588757e64e4bf1425" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a4523b56a271bfeb588757e64e4bf1425" > operations_research::glop::LuFactorization::GetFillInPercentage< / a > < / div > < div class = "ttdeci" > double GetFillInPercentage(const CompactSparseMatrixView & matrix) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00437" > lu_factorization.cc:437< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_a4bf241af6b1844669171d6e170ef991d" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a4bf241af6b1844669171d6e170ef991d" > operations_research::glop::LuFactorization::RightSolveSquaredNorm< / a > < / div > < div class = "ttdeci" > Fractional RightSolveSquaredNorm(const ColumnView & a) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00114" > lu_factorization.cc:114< / a > < / div > < / div >
2020-10-09 12:00:09 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_a56d08f5289eea3f018dca5b93b6fca6b" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a56d08f5289eea3f018dca5b93b6fca6b" > operations_research::glop::LuFactorization::GetColumnPermutation< / a > < / div > < div class = "ttdeci" > const ColumnPermutation & GetColumnPermutation() const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8h_source.html#l00059" > lu_factorization.h:59< / a > < / div > < / div >
2021-04-27 23:00:03 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_a577c37faff9567f86849dd74c3fcf4ac" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a577c37faff9567f86849dd74c3fcf4ac" > operations_research::glop::LuFactorization::RightSolveUWithNonZeros< / a > < / div > < div class = "ttdeci" > void RightSolveUWithNonZeros(ScatteredColumn *x) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00306" > lu_factorization.cc:306< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_a5a3f1ad730713e296dcbbed8b1123130" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a5a3f1ad730713e296dcbbed8b1123130" > operations_research::glop::LuFactorization::row_perm< / a > < / div > < div class = "ttdeci" > const RowPermutation & row_perm() const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8h_source.html#l00213" > lu_factorization.h:213< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_a627511bf305a6af5d7e114817c1792c2" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a627511bf305a6af5d7e114817c1792c2" > operations_research::glop::LuFactorization::DeterministicTimeOfLastFactorization< / a > < / div > < div class = "ttdeci" > double DeterministicTimeOfLastFactorization() const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00068" > lu_factorization.cc:68< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_a6b5f31c4068711b8e6823f4888f410ce" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a6b5f31c4068711b8e6823f4888f410ce" > operations_research::glop::LuFactorization::LeftSolve< / a > < / div > < div class = "ttdeci" > void LeftSolve(DenseRow *y) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00082" > lu_factorization.cc:82< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_a6c5735e4c25655dd4533504d22b1d66c" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a6c5735e4c25655dd4533504d22b1d66c" > operations_research::glop::LuFactorization::LeftSolveLWithNonZeros< / a > < / div > < div class = "ttdeci" > bool LeftSolveLWithNonZeros(ScatteredRow *y, ScatteredColumn *result_before_permutation) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00324" > lu_factorization.cc:324< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_a6ec53ed3afa3d8affb6941568dcfec76" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a6ec53ed3afa3d8affb6941568dcfec76" > operations_research::glop::LuFactorization::RightSolve< / a > < / div > < div class = "ttdeci" > void RightSolve(DenseColumn *x) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00072" > lu_factorization.cc:72< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_a864ad5596d017729a4ca349fed8949a8" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a864ad5596d017729a4ca349fed8949a8" > operations_research::glop::LuFactorization::inverse_col_perm< / a > < / div > < div class = "ttdeci" > const ColumnPermutation & inverse_col_perm() const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8h_source.html#l00214" > lu_factorization.h:214< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_a9438a3ceb0327c1bd75ff3b4fa58d3b0" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a9438a3ceb0327c1bd75ff3b4fa58d3b0" > operations_research::glop::LuFactorization::LeftSolveUForUnitRow< / a > < / div > < div class = "ttdeci" > ColIndex LeftSolveUForUnitRow(ColIndex col, ScatteredRow *y) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00393" > lu_factorization.cc:393< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_a9b738f6b485a4d4ef866b8d82ac07876" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#a9b738f6b485a4d4ef866b8d82ac07876" > operations_research::glop::LuFactorization::DualEdgeSquaredNorm< / a > < / div > < div class = "ttdeci" > Fractional DualEdgeSquaredNorm(RowIndex row) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00145" > lu_factorization.cc:145< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_aa1222207079d0d679ef52f8b465cd00a" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#aa1222207079d0d679ef52f8b465cd00a" > operations_research::glop::LuFactorization::RightSolveLForScatteredColumn< / a > < / div > < div class = "ttdeci" > void RightSolveLForScatteredColumn(const ScatteredColumn & b, ScatteredColumn *x) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00271" > lu_factorization.cc:271< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_aa35c31899babb961a8100bc605136424" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#aa35c31899babb961a8100bc605136424" > operations_research::glop::LuFactorization::RightSolveLWithNonZeros< / a > < / div > < div class = "ttdeci" > void RightSolveLWithNonZeros(ScatteredColumn *x) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00252" > lu_factorization.cc:252< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_aa40655f0310c3616632354ffeb7d466e" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#aa40655f0310c3616632354ffeb7d466e" > operations_research::glop::LuFactorization::ComputeDeterminant< / a > < / div > < div class = "ttdeci" > Fractional ComputeDeterminant() const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00453" > lu_factorization.cc:453< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_aa71d36872f416feaa853788a7a7a7ef8" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#aa71d36872f416feaa853788a7a7a7ef8" > operations_research::glop::LuFactorization::Clear< / a > < / div > < div class = "ttdeci" > void Clear()< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00031" > lu_factorization.cc:31< / a > < / div > < / div >
2021-04-27 23:00:03 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_ac22943ff00ae631c58ad2c42932d4657" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#ac22943ff00ae631c58ad2c42932d4657" > operations_research::glop::LuFactorization::ComputeInfinityNormConditionNumber< / a > < / div > < div class = "ttdeci" > Fractional ComputeInfinityNormConditionNumber(const CompactSparseMatrixView & matrix) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00514" > lu_factorization.cc:514< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_acd3d874c6fe9195587688508b6cd0305" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#acd3d874c6fe9195587688508b6cd0305" > operations_research::glop::LuFactorization::ComputeLowerTimesUpper< / a > < / div > < div class = "ttdeci" > void ComputeLowerTimesUpper(SparseMatrix *product) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8h_source.html#l00202" > lu_factorization.h:202< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_ace58a4f9d6a147c3455ff8dc029537c4" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#ace58a4f9d6a147c3455ff8dc029537c4" > operations_research::glop::LuFactorization::ComputeFactorization< / a > < / div > < div class = "ttdeci" > ABSL_MUST_USE_RESULT Status ComputeFactorization(const CompactSparseMatrixView & compact_matrix)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00044" > lu_factorization.cc:44< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_ad91a397910de30b87b9fb45298fa5c58" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#ad91a397910de30b87b9fb45298fa5c58" > operations_research::glop::LuFactorization::SetColumnPermutationToIdentity< / a > < / div > < div class = "ttdeci" > void SetColumnPermutationToIdentity()< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8h_source.html#l00065" > lu_factorization.h:65< / a > < / div > < / div >
2021-04-27 23:00:03 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_ad9e11229fed5416bf22fb3b4fa65f4c1" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#ad9e11229fed5416bf22fb3b4fa65f4c1" > operations_research::glop::LuFactorization::NumberOfEntries< / a > < / div > < div class = "ttdeci" > EntryIndex NumberOfEntries() const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00447" > lu_factorization.cc:447< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_ada69c9026d5d933471bf27c9ad2d1b38" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#ada69c9026d5d933471bf27c9ad2d1b38" > operations_research::glop::LuFactorization::ComputeInverseInfinityNormUpperBound< / a > < / div > < div class = "ttdeci" > Fractional ComputeInverseInfinityNormUpperBound() const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00520" > lu_factorization.cc:520< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_adbf20cf678d328e6b36c8bb43dc499cf" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#adbf20cf678d328e6b36c8bb43dc499cf" > operations_research::glop::LuFactorization::IsIdentityFactorization< / a > < / div > < div class = "ttdeci" > bool IsIdentityFactorization()< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8h_source.html#l00041" > lu_factorization.h:41< / a > < / div > < / div >
2020-10-09 12:00:09 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_ae7202d055b6b172a8a1da4f5b136f9ea" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#ae7202d055b6b172a8a1da4f5b136f9ea" > operations_research::glop::LuFactorization::SetParameters< / a > < / div > < div class = "ttdeci" > void SetParameters(const GlopParameters & parameters)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8h_source.html#l00189" > lu_factorization.h:189< / a > < / div > < / div >
2021-04-27 23:00:03 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_af03b66d5eb557d6d95ad01d446c2cba8" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#af03b66d5eb557d6d95ad01d446c2cba8" > operations_research::glop::LuFactorization::ComputeOneNormConditionNumber< / a > < / div > < div class = "ttdeci" > Fractional ComputeOneNormConditionNumber(const CompactSparseMatrixView & matrix) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00508" > lu_factorization.cc:508< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_af0b37b89dc1909384e822287c1091aa0" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#af0b37b89dc1909384e822287c1091aa0" > operations_research::glop::LuFactorization::LuFactorization< / a > < / div > < div class = "ttdeci" > LuFactorization()< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8cc_source.html#l00024" > lu_factorization.cc:24< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_lu_factorization_html_af9bc435481ae9e6e60d66a65d5394a7f" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_lu_factorization.html#af9bc435481ae9e6e60d66a65d5394a7f" > operations_research::glop::LuFactorization::StatString< / a > < / div > < div class = "ttdeci" > std::string StatString() const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lu__factorization_8h_source.html#l00195" > lu_factorization.h:195< / a > < / div > < / div >
2021-04-27 23:00:03 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_markowitz_html_ae7202d055b6b172a8a1da4f5b136f9ea" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_markowitz.html#ae7202d055b6b172a8a1da4f5b136f9ea" > operations_research::glop::Markowitz::SetParameters< / a > < / div > < div class = "ttdeci" > void SetParameters(const GlopParameters & parameters)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "markowitz_8h_source.html#l00313" > markowitz.h:313< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_markowitz_html_af9bc435481ae9e6e60d66a65d5394a7f" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_markowitz.html#af9bc435481ae9e6e60d66a65d5394a7f" > operations_research::glop::Markowitz::StatString< / a > < / div > < div class = "ttdeci" > std::string StatString() const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "markowitz_8h_source.html#l00310" > markowitz.h:310< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_permutation_html" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_permutation.html" > operations_research::glop::Permutation< ColIndex > < / a > < / div > < / div >
2020-12-29 22:27:47 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_permutation_html_ac8bb3912a3ce86b15842e79d0b421204" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_permutation.html#ac8bb3912a3ce86b15842e79d0b421204" > operations_research::glop::Permutation::clear< / a > < / div > < div class = "ttdeci" > void clear()< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lp__data_2permutation_8h_source.html#l00053" > lp_data/permutation.h:53< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_sparse_column_html" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_sparse_column.html" > operations_research::glop::SparseColumn< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "sparse__column_8h_source.html#l00044" > sparse_column.h:44< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_sparse_matrix_html" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_sparse_matrix.html" > operations_research::glop::SparseMatrix< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "sparse_8h_source.html#l00061" > sparse.h:61< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_sparse_matrix_html_aa1c2872fa7d491d4c093c8b2124a53b9" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_sparse_matrix.html#aa1c2872fa7d491d4c093c8b2124a53b9" > operations_research::glop::SparseMatrix::PopulateFromProduct< / a > < / div > < div class = "ttdeci" > void PopulateFromProduct(const SparseMatrix & a, const SparseMatrix & b)< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "sparse_8cc_source.html#l00250" > sparse.cc:250< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_status_html" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_status.html" > operations_research::glop::Status< / a > < / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "status_8h_source.html#l00024" > status.h:24< / a > < / div > < / div >
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_strict_i_t_i_vector_html" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html" > operations_research::glop::StrictITIVector< RowIndex, Fractional > < / a > < / div > < / div >
2020-10-09 12:00:09 +02:00
< div class = "ttc" id = "aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a138580a401252ec46ad8e08925e4e92e" > < div class = "ttname" > < a href = "classoperations__research_1_1glop_1_1_triangular_matrix.html#a138580a401252ec46ad8e08925e4e92e" > operations_research::glop::TriangularMatrix::CopyToSparseMatrix< / a > < / div > < div class = "ttdeci" > void CopyToSparseMatrix(SparseMatrix *output) const< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "sparse_8cc_source.html#l00730" > sparse.cc:730< / a > < / div > < / div >
2021-04-27 23:00:03 +02:00
< div class = "ttc" id = "aconstraint__solver_2table_8cc_html_a9293e4d29cac928301645070dd307683" > < div class = "ttname" > < a href = "constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683" > b< / a > < / div > < div class = "ttdeci" > int64_t b< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "constraint__solver_2table_8cc_source.html#l00047" > constraint_solver/table.cc:47< / a > < / div > < / div >
< div class = "ttc" id = "aconstraint__solver_2table_8cc_html_acb18315d548212835cd8ed4287e6c0b6" > < div class = "ttname" > < a href = "constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6" > a< / a > < / div > < div class = "ttdeci" > int64_t a< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "constraint__solver_2table_8cc_source.html#l00046" > constraint_solver/table.cc:46< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "acp__model__fz__solver_8cc_html_a10a1eab179b472c030bdc2a2efef7219" > < div class = "ttname" > < a href = "cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219" > parameters< / a > < / div > < div class = "ttdeci" > SatParameters parameters< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "cp__model__fz__solver_8cc_source.html#l00108" > cp_model_fz_solver.cc:108< / a > < / div > < / div >
2020-09-02 09:42:51 +02:00
< div class = "ttc" id = "alp__data_2permutation_8h_html" > < div class = "ttname" > < a href = "lp__data_2permutation_8h.html" > permutation.h< / a > < / div > < / div >
< div class = "ttc" id = "alp__types_8h_html" > < div class = "ttname" > < a href = "lp__types_8h.html" > lp_types.h< / a > < / div > < / div >
2021-04-27 23:00:03 +02:00
< div class = "ttc" id = "amarkowitz_8cc_html_aa9d6c98fdf8d89b0e2321fda02adc82c" > < div class = "ttname" > < a href = "markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c" > col< / a > < / div > < div class = "ttdeci" > ColIndex col< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "markowitz_8cc_source.html#l00183" > markowitz.cc:183< / a > < / div > < / div >
< div class = "ttc" id = "amarkowitz_8cc_html_aea35f36ba98d5bbd8d033382f50c9e52" > < div class = "ttname" > < a href = "markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52" > row< / a > < / div > < div class = "ttdeci" > RowIndex row< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "markowitz_8cc_source.html#l00182" > markowitz.cc:182< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
< div class = "ttc" id = "amarkowitz_8h_html" > < div class = "ttname" > < a href = "markowitz_8h.html" > markowitz.h< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_1_1glop_html_a6b1b56ad0cb77edbd314f2bec33b467a" > < div class = "ttname" > < a href = "namespaceoperations__research_1_1glop.html#a6b1b56ad0cb77edbd314f2bec33b467a" > operations_research::glop::ColumnPermutation< / a > < / div > < div class = "ttdeci" > Permutation< ColIndex > ColumnPermutation< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lp__data_2permutation_8h_source.html#l00095" > lp_data/permutation.h:95< / a > < / div > < / div >
2021-04-27 23:00:03 +02:00
< div class = "ttc" id = "anamespaceoperations__research_1_1glop_html_a733947145e3e1631165b618b05c9ccb7" > < div class = "ttname" > < a href = "namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7" > operations_research::glop::Fractional< / a > < / div > < div class = "ttdeci" > double Fractional< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lp__types_8h_source.html#l00078" > lp_types.h:78< / a > < / div > < / div >
< div class = "ttc" id = "anamespaceoperations__research_1_1glop_html_ae5fa9e57c2d31b294195ed8a9e17bfac" > < div class = "ttname" > < a href = "namespaceoperations__research_1_1glop.html#ae5fa9e57c2d31b294195ed8a9e17bfac" > operations_research::glop::DenseColumn< / a > < / div > < div class = "ttdeci" > StrictITIVector< RowIndex, Fractional > DenseColumn< / div > < div class = "ttdef" > < b > Definition:< / b > < a href = "lp__types_8h_source.html#l00329" > lp_types.h:329< / a > < / div > < / div >
2021-01-26 11:28:50 +01:00
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