+ LV-jEIvRt^RIt^RIHt^RIHt^RIt^RIH t Rt Rt Rt Rt R R ltR tR tRR ltR#)zn Routines for removing redundant (linearly dependent) equations from linear programming equality constraints. N)svd) interp_decompdtrsmcRp\P!\V4V8P^R74P 4#)a^ Counts the number of nonzeros in each row of input array A. Nonzeros are defined as any element with absolute value greater than tol = 1e-13. This value should probably be an input to the function. Parameters ---------- A : 2-D array An array representing a matrix Returns ------- rowcount : 1-D array Number of nonzeros in each row of A gvIh%<=axis)nparrayabssumflatten)Atols& r/Volumes/fast/ai/experiments/ui-tars-smoke/.venv/lib/python3.14/site-packages/scipy/optimize/_remove_redundancy.py _row_countrs7" C 88SVc\&&A&. / 7 7 99cP\V4p\P!W!,4#)a Returns the index of the densest row of A. Ignores rows that are not eligible for consideration. Parameters ---------- A : 2-D array An array representing a matrix eligibleRows : 1-D logical array Values indicate whether the corresponding row of A is eligible to be considered Returns ------- i_densest : int Index of the densest row in A eligible for consideration )rr argmax)r eligibleRows rowCountss&& r _get_densestr#s&1 I 99Y- ..rc^pRp\V4^8HpV\P!V4R3,p\P!W,^4'g^pRpV\P!V4,pWW#3#)a Eliminates trivial equations from system of equations defined by Ax = b and identifies trivial infeasibilities Parameters ---------- A : 2-D array An array representing the left-hand side of a system of equations b : 1-D array An array representing the right-hand side of a system of equations Returns ------- A : 2-D array An array representing the left-hand side of a system of equations b : 1-D array An array representing the right-hand side of a system of equations status: int An integer indicating the status of the removal operation 0: No infeasibility identified 2: Trivially infeasible message : str A string descriptor of the exit status of the optimization. NNNzbThere is a zero row in A_eq with a nonzero corresponding entry in b_eq. The problem is infeasible.)rr logical_notallclose)rbstatusmessagei_zeros&& r_remove_zero_rowsr!:sq4FG ]a F ".. ! #$A ;;qy! $ $> ".. !A   rcVwrEW!,p\^WF^^R7pVRV^,VRV^,1V3&Ws^,RpWCV3,p WC^,R1V3;;,W, , uu&WE3#))lowerdiagNr) pluperm_rvjLUpvpermulpivs &&&& rbg_update_denser0`sv EB IE a!!,ADQqS'Bt!tQwK A#$A T(CstQwKAEK 5Lrc RpRp^pRpRp\W4wrrVV^8wdWWV3#VPwr\\V44p \V 4p .p Rp Tp\P !WV ,3RR7p\P !V^4WRVR13&\P !V4p\P!WV ,\R7p\P!VP\R7p\P!VRR7\P!V43pV^,p V EFp^VV&V^8d ^VV^, &V V^, ,p\VWRV3,V^, 4p\PP%VV^R 7pVV,p^2p\^\'V4V4FpVV\)VV,\'V44p\+VRV3,P-4P/V44pVV8P14'gKnVV\P2!V4,,pVV V&R VVV, &EK4 VP4P/VP7R ^44p\PP9V4p \+V4^V ,, V8d ^pTpWWV3u#V P;V4VfEK\'V 4W, 8XgEKM \=\V44p!\V!\=V 4, 4p!VV!R3,VV!,WV3# \dt\PP!TRT 3,4pTwpp\\T44p \#T4FwppT T,T T,uT T&T T&K! ELTi;i) aw Eliminates redundant equations from system of equations defined by Ax = b and identifies infeasibilities. Parameters ---------- A : 2-D array An matrix representing the left-hand side of a system of equations rhs : 1-D array An array representing the right-hand side of a system of equations Returns ------- A : 2-D array A matrix representing the left-hand side of a system of equations rhs : 1-D array An array representing the right-hand side of a system of equations status: int An integer indicating the status of the system 0: No infeasibility identified 2: Trivially infeasible message : str A string descriptor of the exit status of the optimization. References ---------- .. [2] Andersen, Erling D. "Finding all linearly dependent rows in large-scale linear programming." Optimization Methods and Software 6.3 (1995): 219-227. :0yE>rThere is a linear combination of rows of A_eq that results in zero, suggesting a redundant constraint. However the same linear combination of b_eq is nonzero, suggesting that the constraints conflict and the problem is infeasible.NF)orderr)dtype)transF)r!shapelistranger zeros fill_diagonalarangeintonesbooleyer0 Exceptionscipylinalg lu_factor enumeratelu_solvelenminr transposedotanyrTreshapenormappendset)"rrhs true_ranktolapiv tolprimalrr inconsistentmnr(rdr'A_orige js_candidatesjs_maskluir)r*r+i1i2pijsbatchj_index j_indicescbibarbnormkeeps"&&& r_remove_redundancy_pivot_denserllsP@GI FG5L 07AF {v&& 77DA U1XA QA A F F !U3'AQaeH  AIIa1C0Mggm))6G  ryy| +B UF ! q5AacF @!A#A Vq!tWac:B\\ " "2q " 2 7 #QB/G7C s2w$?@IAalO--/33B78AG   ""w1-.!$! 0DDHHS[[Q/0EIINN3'E5z1U7#i/&F33 (SVq}-DUX uQx=D s1v D $'?CIv 66K @''!Q$0BEB%(^F#A,B)/VBZ&r F2J'  @s -MA:O  O cFRpRp^pRpRp\W4wrrEV^8wdWWE3#VPwrx\\V44p \V 4p \ \WwV,44p .p Tp \ P P\ P PV4V34P4p\P!V4pV EFpVRV 3,p^W&V^8d ^W^, &\ P PPVP4V4PR^4p\V \ V 4, 4p\P !VRV3,P4P#V44V8P%4^,p\'V4^8dVV^,,pVW&EKVP(P#VPR^44p\PP+V4p\!V4^V,, V8d ^pTpWWE3u#V P-V4EK \ \V44p\V\ V 4, 4pV VR3,VV,WE3#)a Eliminates redundant equations from system of equations defined by Ax = b and identifies infeasibilities. Parameters ---------- A : 2-D sparse array An matrix representing the left-hand side of a system of equations rhs : 1-D array An array representing the right-hand side of a system of equations Returns ------- A : 2-D sparse array A matrix representing the left-hand side of a system of equations rhs : 1-D array An array representing the right-hand side of a system of equations status: int An integer indicating the status of the system 0: No infeasibility identified 2: Trivially infeasible message : str A string descriptor of the exit status of the optimization. References ---------- .. [2] Andersen, Erling D. "Finding all linearly dependent rows in large-scale linear programming." Optimization Methods and Software 6.3 (1995): 219-227. r2rr3rr8)r!r9r:r;rRrDsparsehstack eye_arraytocscr r<rEspsolverKrOr rLnonzerorIrNrPrQ)rrSrUrVrrrWrXrYr(rkrZr[r\r`Brcrdrhr)rirjrks&& r_remove_redundancy_pivot_sparservs2BGI FG5L 07AF {v&& 77DA U1XA QA E!qSMA A F U\\33A6:;AACA  A, adG q5AcF \\ ( ( : B B2q I !CF(^VVAaeH&&(,,R0 1G ; D D Fq I q6A:1Q4AADDDHHS[[Q/0EIINN3'E5z1u9% 1&F33 QT uQx=D s1v D $'?CIv 66rc\W4wrr#V^8wdWW#3#\V4wrEp\P!\4P pVP 4\ VP4,V,pVPwrW8:d VR,M^p \V 4V8EdDVR,p \P!V 4VR,8p \P!V 4'dC\P!\P!V PV44V84'd^pRpM\P!\P!V PV44V^d,84'd^pRpMi\W 4p\P!W^R7p\P!W4p\V4wrEpVPwrW8:d VR,M^p EKTWW#3#)ar Eliminates redundant equations from system of equations defined by Ax = b and identifies infeasibilities. Parameters ---------- A : 2-D array An array representing the left-hand side of a system of equations b : 1-D array An array representing the right-hand side of a system of equations Returns ------- A : 2-D array An array representing the left-hand side of a system of equations b : 1-D array An array representing the right-hand side of a system of equations status: int An integer indicating the status of the system 0: No infeasibility identified 2: Trivially infeasible message : str A string descriptor of the exit status of the optimization. References ---------- .. [2] Andersen, Erling D. "Finding all linearly dependent rows in large-scale linear programming." Optimization Methods and Software 6.3 (1995): 219-227. gcAzDue to numerical issues, redundant equality constraints could not be removed automatically. Try providing your constraint matrices as sparse matrices to activate sparse presolve, try turning off redundancy removal, or try turning off presolve altogether.r3rr8)rr8) r!rr finfofloatepsmaxr9r rMrLrdelete)rrrrUsVhrzrrXrYs_minr(ri_removes&& r_remove_redundancy_svdrjsB.a3A& {V$$1vHA" ((5/  C %%'CL 3 &C 77DAVAbEE" e*s  eHvvay3:- vvl##rvvbffQUU1X.>.D'E'EF%G  66"&&q"S3Y. / /F8G 0 IIa * IIa "q6bww"Q   rc^pRpRp\W4wrrEV^8wdWWE3#VPwrxTp Vf \PP V4p \ VP WR7wr\P!WRV ,V ,WV R,4'g^pTp\V RV 4p W R3,p W,p WWE3#)agEliminates redundant equations from a system of equations. Eliminates redundant equations from system of equations defined by Ax = b and identifies infeasibilities. Parameters ---------- A : 2-D array An array representing the left-hand side of a system of equations rhs : 1-D array An array representing the right-hand side of a system of equations rank : int, optional The rank of A randomized: bool, optional True for randomized interpolative decomposition Returns ------- A : 2-D array An array representing the left-hand side of a system of equations rhs : 1-D array An array representing the right-hand side of a system of equations status: int An integer indicating the status of the system 0: No infeasibility identified 2: Trivially infeasible message : str A string descriptor of the exit status of the optimization. rr3N)randr) r!r9r rE matrix_rankrrNrsorted)rrSrank randomizedrrrWrXrYrtidxprojA2rhs2s&&&& r_remove_redundancy_idrs@FG5L 07AF {v&& 77DA A | II ! !! $acc16IC ;;sr7|d*CABL 9 9 Ra/C 6B 8D V $$r)N)NT)__doc__numpyr scipy.linalgrscipy.linalg.interpolativerrDscipy.linalg.blasrrrr!r0rlrvrrrrrsK 4 #:*/.#!L |7~|7~Y!xD%r