+ LV-jsNRt^RIt^RIt^RIt^RIHt^RIHtH t H t H t RR.t !RR4t !RR] 4t!R R ] 4t!R R ] 4tRR lt!RR] 4t!RR] 4t!RR] 4t!RR] 4t!RR] 4t!RR]4t!RR] 4tRtR#)aUAbstract linear algebra library. This module defines a class hierarchy that implements a kind of "lazy" matrix representation, called the ``LinearOperator``. It can be used to do linear algebra with extremely large sparse or structured matrices, without representing those explicitly in memory. Such matrices can be added, multiplied, transposed, etc. As a motivating example, suppose you want have a matrix where almost all of the elements have the value one. The standard sparse matrix representation skips the storage of zeros, but not ones. By contrast, a LinearOperator is able to represent such matrices efficiently. First, we need a compact way to represent an all-ones matrix:: >>> import numpy as np >>> from scipy.sparse.linalg._interface import LinearOperator >>> class Ones(LinearOperator): ... def __init__(self, shape): ... super().__init__(dtype=None, shape=shape) ... def _matvec(self, x): ... return np.repeat(x.sum(), self.shape[0]) Instances of this class emulate ``np.ones(shape)``, but using a constant amount of storage, independent of ``shape``. The ``_matvec`` method specifies how this linear operator multiplies with (operates on) a vector. We can now add this operator to a sparse matrix that stores only offsets from one:: >>> from scipy.sparse.linalg._interface import aslinearoperator >>> from scipy.sparse import csr_array >>> offsets = csr_array([[1, 0, 2], [0, -1, 0], [0, 0, 3]]) >>> A = aslinearoperator(offsets) + Ones(offsets.shape) >>> A.dot([1, 2, 3]) array([13, 4, 15]) The result is the same as that given by its dense, explicitly-stored counterpart:: >>> (np.ones(A.shape, A.dtype) + offsets.toarray()).dot([1, 2, 3]) array([13, 4, 15]) Several algorithms in the ``scipy.sparse`` library are able to operate on ``LinearOperator`` instances. N)issparse)isshape isintlikeasmatrixis_pydata_spmatrixLinearOperatoraslinearoperatorc$aa]tRt^8toRt^tRt]!]P4t V3Rlt Rt Rt RtRtRtR tR tR tR tR tRtRtRtRtRtRtRtRtRtRtRt Rt!Rt"Rt#]$!]#4t%Rt&]$!]&4t'Rt(Rt)Rt*Vt+V;t,#) ra Common interface for performing matrix vector products Many iterative methods (e.g. `cg`, `gmres`) do not need to know the individual entries of a matrix to solve a linear system ``A@x = b``. Such solvers only require the computation of matrix vector products, ``A@v`` where ``v`` is a dense vector. This class serves as an abstract interface between iterative solvers and matrix-like objects. To construct a concrete `LinearOperator`, either pass appropriate callables to the constructor of this class, or subclass it. A subclass must implement either one of the methods ``_matvec`` and ``_matmat``, and the attributes/properties ``shape`` (pair of integers) and ``dtype`` (may be None). It may call the ``__init__`` on this class to have these attributes validated. Implementing ``_matvec`` automatically implements ``_matmat`` (using a naive algorithm) and vice-versa. Optionally, a subclass may implement ``_rmatvec`` or ``_adjoint`` to implement the Hermitian adjoint (conjugate transpose). As with ``_matvec`` and ``_matmat``, implementing either ``_rmatvec`` or ``_adjoint`` implements the other automatically. Implementing ``_adjoint`` is preferable; ``_rmatvec`` is mostly there for backwards compatibility. Parameters ---------- shape : tuple Matrix dimensions ``(M, N)``. matvec : callable f(v) Returns returns ``A @ v``. rmatvec : callable f(v) Returns ``A^H @ v``, where ``A^H`` is the conjugate transpose of ``A``. matmat : callable f(V) Returns ``A @ V``, where ``V`` is a dense matrix with dimensions ``(N, K)``. dtype : dtype Data type of the matrix. rmatmat : callable f(V) Returns ``A^H @ V``, where ``V`` is a dense matrix with dimensions ``(M, K)``. Attributes ---------- args : tuple For linear operators describing products etc. of other linear operators, the operands of the binary operation. ndim : int Number of dimensions (this is always 2) See Also -------- aslinearoperator : Construct LinearOperators Notes ----- The user-defined `matvec` function must properly handle the case where ``v`` has shape ``(N,)`` as well as the ``(N,1)`` case. The shape of the return type is handled internally by `LinearOperator`. It is highly recommended to explicitly specify the `dtype`, otherwise it is determined automatically at the cost of a single matvec application on ``int8`` zero vector using the promoted `dtype` of the output. Python ``int`` could be difficult to automatically cast to numpy integers in the definition of the `matvec` so the determination may be inaccurate. It is assumed that `matmat`, `rmatvec`, and `rmatmat` would result in the same dtype of the output given an ``int8`` input as `matvec`. LinearOperator instances can also be multiplied, added with each other and exponentiated, all lazily: the result of these operations is always a new, composite LinearOperator, that defers linear operations to the original operators and combines the results. More details regarding how to subclass a LinearOperator and several examples of concrete LinearOperator instances can be found in the external project `PyLops `_. Examples -------- >>> import numpy as np >>> from scipy.sparse.linalg import LinearOperator >>> def mv(v): ... return np.array([2*v[0], 3*v[1]]) ... >>> A = LinearOperator((2,2), matvec=mv) >>> A <2x2 _CustomLinearOperator with dtype=int8> >>> A.matvec(np.ones(2)) array([ 2., 3.]) >>> A @ np.ones(2) array([ 2., 3.]) Nc:<V\Jd\SV` \4#\SV` V4p\ V4P \P 8XdF\ V4P \P 8Xd\P!R\^R7V#)zMLinearOperator subclass should implement at least one of _matvec and _matmat.)category stacklevel) rsuper__new___CustomLinearOperatortype_matvec_matmatwarningswarnRuntimeWarning)clsargskwargsobj __class__s&*, o/Volumes/fast/ai/experiments/ui-tars-smoke/.venv/lib/python3.14/site-packages/scipy/sparse/linalg/_interface.pyrLinearOperator.__new__sx . 7?#89 9'/#&CS !!^%;%;;S ))^-C-CC F'5!EJc Ve\P!V4p\V4p\V4'g\ RV: R24hWnW nR#)zInitialize this LinearOperator. To be called by subclasses. ``dtype`` may be None; ``shape`` should be convertible to a length-2 tuple. Nzinvalid shape z (must be 2-d))npdtypetupler ValueErrorshape)selfr r#s&&&r__init__LinearOperator.__init__sG  HHUOEe u~~~eYnEF F  rc dVPfq\P!VPR,\PR7p\P !VP V44pVPVnR#R# \d$\P!\4TnR#i;i)aDetermine the dtype by executing `matvec` on an `int8` test vector. In `np.promote_types` hierarchy, the type `int8` is the smallest, so we call `matvec` on `int8` and use the promoted dtype of the output to set the default `dtype` of the `LinearOperator`. We assume that `matmat`, `rmatvec`, and `rmatmat` would result in the same dtype of the output given an `int8` input as `matvec`. Called from subclasses at the end of the __init__ routine. N)r ) r rzerosr#int8asarraymatvec OverflowErrorint)r$vmatvec_vs& r _init_dtypeLinearOperator._init_dtypesw :: Brww7A ,::dkk!n5 &^^  ! +XXc]  +s%B*B/.B/c  \P!VPUu.uF#q PVP R^44NK% up4#uupi)zDefault matrix-matrix multiplication handler. Falls back on the user-defined _matvec method, so defining that will define matrix multiplication (though in a very suboptimal way). r()rhstackTr,reshaper$Xcols&& rrLinearOperator._matmats;yyACCHCS++ckk"Q&78CHIIHs)Ac DVPVPR^44#)aIDefault matrix-vector multiplication handler. If self is a linear operator of shape (M, N), then this method will be called on a shape (N,) or (N, 1) ndarray, and should return a shape (M,) or (M, 1) ndarray. This default implementation falls back on _matmat, so defining that will define matrix-vector multiplication as well. r()matmatr6r$xs&&rrLinearOperator._matvecs{{199R+,,rc \P!V4pVPwr#VPV38wdVPV^38wd \R4hVP V4p\ V\P 4'd \V4pM\P!V4pVP^8XdVPV4pV#VP^8XdVPV^4pV#\R4h)aMatrix-vector multiplication. Performs the operation y=A@x where A is an MxN linear operator and x is a column vector or 1-d array. Parameters ---------- x : {matrix, ndarray} An array with shape (N,) or (N,1). Returns ------- y : {matrix, ndarray} A matrix or ndarray with shape (M,) or (M,1) depending on the type and shape of the x argument. Notes ----- This matvec wraps the user-specified matvec routine or overridden _matvec method to ensure that y has the correct shape and type. dimension mismatchz/invalid shape returned by user-defined matvec()) r asanyarrayr#r"r isinstancematrixrr+ndimr6r$r>MNys&& rr,LinearOperator.matvecs0 MM! jj 77qd?qww1Q%/12 2 LLO a # # A 1 A 66Q; ! A  VVq[ !AANO Orc \P!V4pVPwr#VPV38wdVPV^38wd \R4hVP V4p\ V\P 4'd \V4pM\P!V4pVP^8XdVPV4pV#VP^8XdVPV^4pV#\R4h)a Adjoint matrix-vector multiplication. Performs the operation y = A^H @ x where A is an MxN linear operator and x is a column vector or 1-d array. Parameters ---------- x : {matrix, ndarray} An array with shape (M,) or (M,1). Returns ------- y : {matrix, ndarray} A matrix or ndarray with shape (N,) or (N,1) depending on the type and shape of the x argument. Notes ----- This rmatvec wraps the user-specified rmatvec routine or overridden _rmatvec method to ensure that y has the correct shape and type. rAz0invalid shape returned by user-defined rmatvec()) rrBr#r"_rmatvecrCrDrr+rEr6rFs&& rrmatvecLinearOperator.rmatvecs0 MM! jj 77qd?qww1Q%/12 2 MM!  a # # A 1 A 66Q; ! A  VVq[ !AAOP Prc h\V4P\P8Xdq\VR4'dY\V4P\P8wd1VP VP R^44P R4#\ hVPPV4#)z6Default implementation of _rmatvec; defers to adjoint._rmatmatr() r_adjointrhasattrrPr6NotImplementedErrorHr,r=s&&rrLLinearOperator._rmatvecEs} :  ."9"9 9j))T ++~/F/FF}}QYYr1%56>>rBB% %66==# #rc d\V4'g(\V4'g\P!V4pVP^8wd\ RVP R24hVP ^,VP ^,8wd&\ RVP RVP 24hVPV4p\T\P4'd \T4pT# \d5p\T4'g\T4'd \R4ThhRp?ii;i)aMatrix-matrix multiplication. Performs the operation y=A@X where A is an MxN linear operator and X dense N*K matrix or ndarray. Parameters ---------- X : {matrix, ndarray} An array with shape (N,K). Returns ------- Y : {matrix, ndarray} A matrix or ndarray with shape (M,K) depending on the type of the X argument. Notes ----- This matmat wraps any user-specified matmat routine or overridden _matmat method to ensure that y has the correct type. $expected 2-d ndarray or matrix, not -ddimension mismatch: , zdUnable to multiply a LinearOperator with a sparse matrix. Wrap the matrix in aslinearoperator first.N) rrrrBrEr"r#r Exception TypeErrorrCrDrr$r8Yes&& rr<LinearOperator.matmatQs. 1!44 a A 66Q;CAFF82NO O 771:A &3DJJ#NO O66==# #Os)BcW,#Nr=s&&r__call__LinearOperator.__call__s v rc$VPV4#rh)dotr=s&&r__mul__LinearOperator.__mul__sxx{rcv\P!V4'g \R4h\VRV, 4#)z.Can only divide a linear operator by a scalar.g?)risscalarr"_ScaledLinearOperatorr$others&&r __truediv__LinearOperator.__truediv__s.{{5!!MN N$T3u955rc \V\4'd \W4#\P!V4'd \ W4#\ V4'g(\V4'g\P!V4pVP^8Xg*VP^8Xd*VP^,^8XdVPV4#VP^8XdVPV4#\RV: 24h)a"Matrix-matrix or matrix-vector multiplication. Parameters ---------- x : array_like 1-d or 2-d array, representing a vector or matrix. Returns ------- Ax : array 1-d or 2-d array (depending on the shape of x) that represents the result of applying this linear operator on x. )expected 1-d or 2-d array or matrix, got )rCr_ProductLinearOperatorrrqrrrrr+rEr#r,r<r"r=s&&rrmLinearOperator.dots a ( ()$2 2 [[^^(1 1A;;'9!'<'<JJqMvv{affkaggajAo{{1~%1{{1~% #LQE!RSSrcr\P!V4'd \R4hVPV4#z0Scalar operands are not allowed, use '*' instead)rrqr"rnrss&&r __matmul__LinearOperator.__matmul__s2 ;;u  /0 0||E""rcr\P!V4'd \R4hVPV4#r|)rrqr"__rmul__rss&&r __rmatmul__LinearOperator.__rmatmul__s2 ;;u  /0 0}}U##rcr\P!V4'd \W4#VPV4#rh)rrqrr_rdotr=s&&rrLinearOperator.__rmul__s( ;;q>>(1 1::a= rc r\V\4'd \W4#\P!V4'd \ W4#\ V4'g(\V4'g\P!V4pVP^8Xg*VP^8XdHVP^,^8Xd0VPPVP4P#VP^8Xd0VPPVP4P#\RV: 24h)aMatrix-matrix or matrix-vector multiplication from the right. Parameters ---------- x : array_like 1-d or 2-d array, representing a vector or matrix. Returns ------- xA : array 1-d or 2-d array (depending on the shape of x) that represents the result of applying this linear operator on x from the right. Notes ----- This is copied from dot to implement right multiplication. rx)rCrryrrqrrrrr+rEr#r5r,r<r"r=s&&rrLinearOperator._rdots$ a ( ()!2 2 [[^^(1 1A;;'9!'<'<JJqMvv{affkaggajAovv}}QSS)+++1vv}}QSS)+++ #LQE!RSSrc\\P!V4'd \W4#\#rh)rrq_PowerLinearOperatorNotImplemented)r$ps&&r__pow__LinearOperator.__pow__s ;;q>>'0 0! !rcP\V\4'd \W4#\#rh)rCr_SumLinearOperatorrr=s&&r__add__LinearOperator.__add__s a ( (%d. .! !rc\VR4#)r()rrr$s&r__neg__LinearOperator.__neg__!s$T2..rc&VPV)4#rh)rr=s&&r__sub__LinearOperator.__sub__$s||QBrc VPwrVPfRpMR\VP4,pRV RV RVPP RV R2 #)Nzunspecified dtypezdtype= z with >)r#r strr__name__)r$rGrHdts& r__repr__LinearOperator.__repr__'sZjj :: $BC O+B1#Qqc4>>2236"Q??rc "VP4#)a;Hermitian adjoint. Returns the Hermitian adjoint of self, aka the Hermitian conjugate or Hermitian transpose. For a complex matrix, the Hermitian adjoint is equal to the conjugate transpose. Can be abbreviated self.H instead of self.adjoint(). Returns ------- A_H : LinearOperator Hermitian adjoint of self. )rQrs&radjointLinearOperator.adjoint0s}}rc "VP4#)zTranspose this linear operator. Returns a LinearOperator that represents the transpose of this one. Can be abbreviated self.T instead of self.transpose(). ) _transposers&r transposeLinearOperator.transposeBs   rc \V4#)z6Default implementation of _adjoint; defers to rmatvec.)_AdjointLinearOperatorrs&rrQLinearOperator._adjointLs %d++rc \V4#)z>Default implementation of _transpose; defers to rmatvec + conj)_TransposedLinearOperatorrs&rrLinearOperator._transposePs (..rr r#)-r __module__ __qualname____firstlineno____doc__rE__array_ufunc__ classmethodtypes GenericAlias__class_getitem__rr%r1rrr,rMrLr<rcrPrjrnrurmr}rrrrrrrrrpropertyrTrr5rQr__static_attributes____classdictcell__ __classcell__r __classdict__s@@rrr8s\| DO$E$6$67  ,*J --^-^ $-^+Z$6 T># $ ! "TH" " / @ A! A,//rcdaa]tRtRtoRtR V3RlltV3RltRtRtV3Rlt Rt R t Vt V;t #) riUz>Linear operator defined in terms of user-specified operations.c<\SV`WQ4RVnW nW0nW`nW@nVP4R#)Nri)r r%r"_CustomLinearOperator__matvec_impl#_CustomLinearOperator__rmatvec_impl#_CustomLinearOperator__rmatmat_impl"_CustomLinearOperator__matmat_implr1)r$r#r,rMr<r rcrs&&&&&&&rr%_CustomLinearOperator.__init__Xs; & #%%# rc`<VPeVPV4#\SV` V4#rh)rr rr$r8rs&&rr_CustomLinearOperator._matmates/    )%%a( (7?1% %rc$VPV4#rh)rr=s&&rr_CustomLinearOperator._matvecks!!!$$rcZVPpVf \R4hVPV4#)Nzrmatvec is not defined)rrS)r$r>funcs&& rrL_CustomLinearOperator._rmatvecns/"" <%&>? ?""1%%rc`<VPeVPV4#\SV` V4#rh)rr rPrs&&rrP_CustomLinearOperator._rmatmatts0    *&&q) )7#A& &rc \VP^,VP^,3VPVPVPVP VP R7#)r)r#r,rMr<rcr )rr#rrrrr rs&rrQ_CustomLinearOperator._adjointzsQ$DJJqM4::a=+I,0,?,?-1-?-?,0,?,?-1-?-?+/:: 7 7r) __matmat_impl __matvec_impl__rmatmat_impl__rmatvec_implr)NNNN)rrrrrr%rrrLrPrQrrrrs@@rrrUs+H & %& ' 77rrcNaa]tRtRtoRtV3RltRtRtRtRt Rt Vt V;t #) riz$Adjoint of arbitrary Linear Operatorc<VP^,VP^,3p\SV` VPVR7WnV3VnR#rrNr#r r%r Arr$rr#rs&& rr%_AdjointLinearOperator.__init__AQWWQZ( qwwe4D rc8VPPV4#rh)rrLr=s&&rr_AdjointLinearOperator._matvecvvq!!rc8VPPV4#rh)rrr=s&&rrL_AdjointLinearOperator._rmatvecvv~~a  rc8VPPV4#rh)rrPr=s&&rr_AdjointLinearOperator._matmatrrc8VPPV4#rh)rrr=s&&rrP_AdjointLinearOperator._rmatmatrrrr rrrrrr%rrLrrPrrrrs@@rrrs&. "!"!!rrcNaa]tRtRtoRtV3RltRtRtRtRt Rt Vt V;t #) riz*Transposition of arbitrary Linear Operatorc<VP^,VP^,3p\SV` VPVR7WnV3VnR#rrrs&& rr%"_TransposedLinearOperator.__init__rrc\P!VPP\P!V444#rh)rconjrrLr=s&&rr!_TransposedLinearOperator._matvec&wwtvvrwwqz233rc\P!VPP\P!V444#rh)rrrrr=s&&rrL"_TransposedLinearOperator._rmatvec&wwtvv~~bggaj122rc\P!VPP\P!V444#rh)rrrrPr=s&&rr!_TransposedLinearOperator._matmatrrc\P!VPP\P!V444#rh)rrrrr=s&&rrP"_TransposedLinearOperator._rmatmatrrrrrs@@rrrs&4 43433rrcVf.pVF8pVfK \VR4'gKVPVP4K: \P!V!#)Nr )rRappendr r result_type) operatorsdtypesrs&& r _get_dtypersH ~ ?wsG44 MM#)) $ >>6 ""rcPaa]tRtRtoV3RltRtRtRtRtRt Rt Vt V;t #) ric(<\V\4'd\V\4'g \R4hVPVP8wd\RV RV R24hW3Vn\ SV`\W.4VP4R#))both operands have to be a LinearOperatorz cannot add  and : shape mismatchN)rCrr"r#rr r%rr$rBrs&&&rr%_SumLinearOperator.__init__sw!^,,q.11HI I 77agg {1#U1#5EFG GF  QF+QWW5rcVP^,PV4VP^,PV4,#rr,r=s&&rr_SumLinearOperator._matvec3yy|""1% ! (;(;A(>>>rcVP^,PV4VP^,PV4,#rrrMr=s&&rrL_SumLinearOperator._rmatvec3yy|##A&1)=)=a)@@@rcVP^,PV4VP^,PV4,#rrrcr=s&&rrP_SumLinearOperator._rmatmatrrcVP^,PV4VP^,PV4,#rrr<r=s&&rr_SumLinearOperator._matmatr rcXVPwrVPVP,#rhrrTr$rrs& rrQ_SumLinearOperator._adjointyyssQSSyrr rrrrr%rrLrPrrQrrrrs@@rrrs*6?AA?rrcPaa]tRtRtoV3RltRtRtRtRtRt Rt Vt V;t #) ryicx<\V\4'd\V\4'g \R4hVP^,VP^,8wd\RV RV R24h\SV`\ W.4VP^,VP^,34W3VnR#)rzcannot multiply rrN)rCrr"r#r r%rrrs&&&rr%_ProductLinearOperator.__init__s!^,,q.11HI I 771: #/s%s:JKL L QF+67ggaj!''!*5M OF rcVP^,PVP^,PV44#rr r=s&&rr_ProductLinearOperator._matvec.yy|""499Q<#6#6q#9::rcVP^,PVP^,PV44#rrr=s&&rrL_ProductLinearOperator._rmatvec.yy|##DIIaL$8$8$;<>>rc\P!VP^,4VP^,PV4,#r%)rrrrcr=s&&rrP_ScaledLinearOperator._rmatmatr9rcvVP^,VP^,PV4,#r%rr=s&&rr_ScaledLinearOperator._matmat r6rclVPwrVP\P!V4,#rh)rrTrr)r$rr1s& rrQ_ScaledLinearOperator._adjoint s$99ssRWWU^##rrrrs@@rrrrrs(  5??5$$rrrcVaa]tRtRtoV3RltRtRtRtRtRt Rt R t Vt V;t #) ricX<\V\4'g \R4hVP^,VP^,8wd\RV: 24h\ V4'dV^8d \R4h\ SV`\V.4VP4W3VnR#)r0z$square LinearOperator expected, got z"non-negative integer expected as pN) rCrr"r#rr r%rr)r$rrrs&&&rr%_PowerLinearOperator.__init__s!^,,;< < 771: #CA5IJ J||q1uAB B QC!''2F rc\P!VRR7p\VP^,4F pV!V4pK V#)T)copy)rarrayranger)r$funr>resis&&& r_power_PowerLinearOperator._powers7hhqt$tyy|$Ac(C% rc\VPVP^,PV4#r)rJrr,r=s&&rr_PowerLinearOperator._matvec#!{{499Q<..22rc\VPVP^,PV4#r)rJrrMr=s&&rrL_PowerLinearOperator._rmatvec&!{{499Q<//33rc\VPVP^,PV4#r)rJrrcr=s&&rrP_PowerLinearOperator._rmatmat)rQrc\VPVP^,PV4#r)rJrr<r=s&&rr_PowerLinearOperator._matmat,rNrcDVPwrVPV,#rhr)r$rrs& rrQ_PowerLinearOperator._adjoint/syyssaxrr)rrrrr%rJrrLrPrrQrrrrs@@rrrs-  3443rrc>aa]tRtRtoV3RltRtRtRtVtV;t #)MatrixLinearOperatori4cz<\SV`VPVP4WnRVnV3VnR#rh)r r%r r#r_MatrixLinearOperator__adjr)r$rrs&&rr%MatrixLinearOperator.__init__5s/ !''* D rc8VPPV4#rh)rrm)r$r8s&&rrMatrixLinearOperator._matmat;svvzz!}rcjVPf\VP4VnVP#rh)r[_AdjointMatrixOperatorrrs&rrQMatrixLinearOperator._adjoint>s& :: /7DJzzr)r__adjr) rrrrr%rrQrrrrs@@rrYrY4s rrYc<a]tRtRtoRt]R4tRtRtVt R#)r`iDcVPP4VnV3VnVP^,VP^,3VnR#)rN)r5rrrr#)r$ adjoint_arrays&&rr%_AdjointMatrixOperator.__init__EsB%%'"$ "((+]-@-@-CC rc<VP^,P#r)rr rs&rr _AdjointMatrixOperator.dtypeJsyy|!!!rc:\VP^,4#r)rYrrs&rrQ_AdjointMatrixOperator._adjointNs#DIIaL11r)rrr#N) rrrrr%rr rQrr)rs@rr`r`Ds)D ""22rr`cTaa]tRtRtoR V3RlltRtRtRtRtRt Rt Vt V;t #) IdentityOperatoriRc&<\SV`W!4R#rh)r r%)r$r#r rs&&&rr%IdentityOperator.__init__Ss &rcV#rhrir=s&&rrIdentityOperator._matvecVrcV#rhrir=s&&rrLIdentityOperator._rmatvecYrqrcV#rhrir=s&&rrPIdentityOperator._rmatmat\rqrcV#rhrir=s&&rrIdentityOperator._matmat_rqrcV#rhrirs&rrQIdentityOperator._adjointbs rrirhrrs@@rrlrlRs('rrlc\V\4'dV#\V\P4'g!\V\P4'dRVP ^8d \ R4h\P!\P!V44p\V4#\V4'g\V4'd \V4#\VR4'd\VR4'dRpRpRp\VR4'd VPp\VR4'd VPp\VR4'd VPp\VP VP"VW#R7#\%R 4h) aReturn A as a LinearOperator. 'A' may be any of the following types: - ndarray - matrix - sparse array (e.g. csr_array, lil_array, etc.) - LinearOperator - An object with .shape and .matvec attributes See the LinearOperator documentation for additional information. Notes ----- If 'A' has no .dtype attribute, the data type is determined by calling :func:`LinearOperator.matvec()` - set the .dtype attribute to prevent this call upon the linear operator creation. Examples -------- >>> import numpy as np >>> from scipy.sparse.linalg import aslinearoperator >>> M = np.array([[1,2,3],[4,5,6]], dtype=np.int32) >>> aslinearoperator(M) <2x3 MatrixLinearOperator with dtype=int32> zarray must have ndim <= 2r#r,NrMrcr )rMrcr ztype not understood)rCrrndarrayrDrEr" atleast_2dr+rYrrrRrMrcr r#r,r\)rrMrcr s& rrrfs(4!^$$ Arzz " "jBII&>&> 66A:89 9 MM"**Q- (#A&& !*1--#A&& 1g  71h#7#7GGEq)$$))q)$$))q'""!!''188W*1@ @12 2rrh)rrrnumpyr scipy.sparserscipy.sparse._sputilsrrrr__all__rrrrrrryrrrrYr`rlrrirrrs*X !RR / 0Z/Z/z+7N+7\!^!*33.#6^8$N$D > F >  21 2~(63r