From 0345245e860375a32c9a437c4a9d9cae807134e9 Mon Sep 17 00:00:00 2001 From: Shashank Date: Mon, 29 May 2017 12:40:26 +0530 Subject: CMSCOPE changed --- modules/sparse/help/en_US/addchapter.sce | 11 + modules/sparse/help/en_US/chfact.xml | 82 ++++ modules/sparse/help/en_US/chsolve.xml | 81 ++++ modules/sparse/help/en_US/decomposition/CHAPTER | 1 + modules/sparse/help/en_US/decomposition/ludel.xml | 71 +++ modules/sparse/help/en_US/decomposition/lufact.xml | 106 +++++ modules/sparse/help/en_US/decomposition/luget.xml | 106 +++++ .../sparse/help/en_US/decomposition/lusolve.xml | 102 +++++ modules/sparse/help/en_US/decomposition/spchol.xml | 108 +++++ modules/sparse/help/en_US/iterativesolvers/CHAPTER | 1 + .../help/en_US/iterativesolvers/conjgrad.xml | 406 +++++++++++++++++ .../sparse/help/en_US/iterativesolvers/gmres.xml | 252 +++++++++++ modules/sparse/help/en_US/iterativesolvers/qmr.xml | 374 ++++++++++++++++ modules/sparse/help/en_US/matrixmanip/CHAPTER | 1 + 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modules/sparse/help/ja_JP/decomposition/ludel.xml | 126 ++++++ modules/sparse/help/ja_JP/decomposition/lufact.xml | 271 ++++++++++++ modules/sparse/help/ja_JP/decomposition/luget.xml | 202 +++++++++ .../sparse/help/ja_JP/decomposition/lusolve.xml | 175 ++++++++ modules/sparse/help/ja_JP/decomposition/spchol.xml | 173 ++++++++ modules/sparse/help/ja_JP/iterativesolvers/CHAPTER | 1 + .../help/ja_JP/iterativesolvers/conjgrad.xml | 402 +++++++++++++++++ .../sparse/help/ja_JP/iterativesolvers/gmres.xml | 406 +++++++++++++++++ modules/sparse/help/ja_JP/iterativesolvers/qmr.xml | 490 +++++++++++++++++++++ modules/sparse/help/ja_JP/matrixmanip/CHAPTER | 1 + modules/sparse/help/ja_JP/matrixmanip/issparse.xml | 69 +++ modules/sparse/help/ja_JP/matrixmanip/nnz.xml | 111 +++++ modules/sparse/help/ja_JP/matrixmanip/speye.xml | 182 ++++++++ modules/sparse/help/ja_JP/matrixmanip/spones.xml | 137 ++++++ modules/sparse/help/ja_JP/matrixmanip/sprand.xml | 332 ++++++++++++++ modules/sparse/help/ja_JP/matrixmanip/spzeros.xml | 100 +++++ modules/sparse/help/ja_JP/ordmmd.xml | 388 ++++++++++++++++ modules/sparse/help/ja_JP/sparseconvert/CHAPTER | 1 + modules/sparse/help/ja_JP/sparseconvert/adj2sp.xml | 384 ++++++++++++++++ modules/sparse/help/ja_JP/sparseconvert/full.xml | 125 ++++++ .../help/ja_JP/sparseconvert/mtlb_sparse.xml | 145 ++++++ modules/sparse/help/ja_JP/sparseconvert/sp2adj.xml | 369 ++++++++++++++++ modules/sparse/help/ja_JP/sparseconvert/sparse.xml | 277 ++++++++++++ .../sparse/help/ja_JP/sparseconvert/spcompack.xml | 165 +++++++ modules/sparse/help/ja_JP/sparseconvert/spget.xml | 87 ++++ modules/sparse/help/pt_BR/addchapter.sce | 11 + modules/sparse/help/pt_BR/chfact.xml | 72 +++ modules/sparse/help/pt_BR/chsolve.xml | 82 ++++ modules/sparse/help/pt_BR/decomposition/CHAPTER | 1 + modules/sparse/help/pt_BR/decomposition/ludel.xml | 60 +++ modules/sparse/help/pt_BR/decomposition/lufact.xml | 136 ++++++ modules/sparse/help/pt_BR/decomposition/luget.xml | 110 +++++ .../sparse/help/pt_BR/decomposition/lusolve.xml | 100 +++++ modules/sparse/help/pt_BR/decomposition/spchol.xml | 91 ++++ modules/sparse/help/pt_BR/matrixmanip/CHAPTER | 1 + modules/sparse/help/pt_BR/matrixmanip/nnz.xml | 63 +++ modules/sparse/help/pt_BR/matrixmanip/speye.xml | 97 ++++ modules/sparse/help/pt_BR/matrixmanip/spones.xml | 76 ++++ modules/sparse/help/pt_BR/matrixmanip/sprand.xml | 98 +++++ modules/sparse/help/pt_BR/matrixmanip/spzeros.xml | 99 +++++ modules/sparse/help/pt_BR/sparseconvert/CHAPTER | 1 + modules/sparse/help/pt_BR/sparseconvert/adj2sp.xml | 101 +++++ modules/sparse/help/pt_BR/sparseconvert/full.xml | 69 +++ .../help/pt_BR/sparseconvert/mtlb_sparse.xml | 75 ++++ modules/sparse/help/pt_BR/sparseconvert/sp2adj.xml | 100 +++++ modules/sparse/help/pt_BR/sparseconvert/sparse.xml | 122 +++++ .../sparse/help/pt_BR/sparseconvert/spcompack.xml | 109 +++++ modules/sparse/help/pt_BR/sparseconvert/spget.xml | 93 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+// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab +// Copyright (C) 2009 - DIGITEO +// +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + +add_help_chapter("Sparse Matrix",SCI+"/modules/sparse/help/en_US",%T); + diff --git a/modules/sparse/help/en_US/chfact.xml b/modules/sparse/help/en_US/chfact.xml new file mode 100755 index 000000000..d8b43a5d2 --- /dev/null +++ b/modules/sparse/help/en_US/chfact.xml @@ -0,0 +1,82 @@ + + + + + chfact + sparse Cholesky factorization + + + Calling Sequence + spcho=chfact(A) + + + Arguments + + + A + + square symmetric positive sparse matrix + + + + spcho + + list containing the Cholesky factors in coded form + + + + + + Description + + spcho=chfact(A) computes the sparse Cholesky factors of sparse + matrix A, assumed symmetric positive definite. + This function is based on the Ng-Peyton programs (ORNL). See the + Fortran programs for a complete description of the variables in + spcho. This function is to be used with chsolve. + + + + Examples + + + + + See Also + + + chsolve + + + sparse + + + lufact + + + luget + + + spchol + + + + diff --git a/modules/sparse/help/en_US/chsolve.xml b/modules/sparse/help/en_US/chsolve.xml new file mode 100755 index 000000000..eac01c73c --- /dev/null +++ b/modules/sparse/help/en_US/chsolve.xml @@ -0,0 +1,81 @@ + + + + + chsolve + sparse Cholesky solver + + + Calling Sequence + sol=chsolve(spcho,rhs) + + + Arguments + + + spcho + + list containing the Cholesky factors in coded form returned by chfact + + + + rhs, sol + + full column vectors + + + + + + Description + + sol=chsolve(spcho,rhs) computes the solution of + rhs=A*sol, with A a symmetric sparse positive definite + matrix. This function is based on the Ng-Peyton programs (ORNL). See the + Fortran programs for a complete description of the variables in + spcho. + + + + Examples + + + + See Also + + + chfact + + + sparse + + + lufact + + + luget + + + spchol + + + + diff --git a/modules/sparse/help/en_US/decomposition/CHAPTER b/modules/sparse/help/en_US/decomposition/CHAPTER new file mode 100755 index 000000000..ccebc80d8 --- /dev/null +++ b/modules/sparse/help/en_US/decomposition/CHAPTER @@ -0,0 +1 @@ +title = Sparse Decompositions diff --git a/modules/sparse/help/en_US/decomposition/ludel.xml b/modules/sparse/help/en_US/decomposition/ludel.xml new file mode 100755 index 000000000..2efca3fb0 --- /dev/null +++ b/modules/sparse/help/en_US/decomposition/ludel.xml @@ -0,0 +1,71 @@ + + + + + ludel + utility function used with lufact + + + Calling Sequence + ludel(hand) + + + Arguments + + + hand + + handle to sparse lu factors (output of lufact) + + + + + + Description + + This function is used in conjunction with lufact. It clears + the internal memory space used to store the result of lufact. + + + The sequence of commands [p,r]=lufact(A);x=lusolve(p,b);ludel(p); + solves the sparse linear system A*x = b and clears p. + + + + Examples + + + + + See Also + + + sparse + + + lufact + + + luget + + + + diff --git a/modules/sparse/help/en_US/decomposition/lufact.xml b/modules/sparse/help/en_US/decomposition/lufact.xml new file mode 100755 index 000000000..eba959262 --- /dev/null +++ b/modules/sparse/help/en_US/decomposition/lufact.xml @@ -0,0 +1,106 @@ + + + + + lufact + sparse lu factorization + + + Calling Sequence + [hand,rk]=lufact(A,prec) + + + Arguments + + + A + + square sparse real matrix + + + + hand + + handle to sparse lu factors + + + + rk + + integer (rank of A) + + + + prec + + + a vector of size two prec=[eps,reps] giving the absolute and relative thresolds. + + + + + + + Description + + [hand,rk]=lufact(A) performs the lu factorization of sparse matrix A. + hand (no display) is used by lusolve (for solving linear + system) and luget (for retrieving the factors). + hand should be cleared by the command: ludel(hand); + + + The A matrix needs not be full rank but must be square + (since A is assumed sparse one may add zeros if necessary to squaring + down A). + + + + eps : + + + The absolute magnitude an element must have to be considered as a pivot candidate, except as a last resort. This number should be set significantly smaller than the smallest diagonal element that is is expected to be placed in the matrix. the default value is %eps. + + + + + reps : + + This number determines what the pivot relative threshold will be. It should be between zero and one. If it is one then the pivoting method becomes complete pivoting, which is very slow and tends to fill up the matrix. If it is set close to zero the pivoting method becomes strict Markowitz with no threshold. The pivot threshold is used to eliminate pivot candidates that would cause excessive element growth if they were used. Element growth is the cause of roundoff error. Element growth occurs even in well-conditioned matrices. Setting the reps large will reduce element growth and roundoff error, but setting it too large will cause execution time to be excessive and will result in a large number of fill-ins. If this occurs, accuracy can actually be degraded because of the large number of operations required on the matrix due to the large number of fill-ins. A good value seems to be 0.001 which is the default value. The default is chosen by giving a value larger than one or less than or equal to zero. This value should be increased and the matrix resolved if growth is found to be excessive. Changing the pivot threshold does not improve performance on matrices where growth is low, as is often the case with ill-conditioned matrices. reps was chosen for use with nearly diagonally dominant matrices such as node- and modified-node admittance matrices. For these matrices it is usually best to use diagonal pivoting. For matrices without a strong diagonal, it is usually best to use a larger threshold, such as 0.01 or 0.1. + + + + + + Examples + + + + See Also + + + sparse + + + lusolve + + + luget + + + + diff --git a/modules/sparse/help/en_US/decomposition/luget.xml b/modules/sparse/help/en_US/decomposition/luget.xml new file mode 100755 index 000000000..f05f01dcf --- /dev/null +++ b/modules/sparse/help/en_US/decomposition/luget.xml @@ -0,0 +1,106 @@ + + + + + luget + extraction of sparse LU factors + + + Calling Sequence + [P,L,U,Q]=luget(hand) + + + Arguments + + + hand + + + handle, output of lufact + + + + + P + + sparse permutation matrix + + + + L + + + sparse matrix, lower triangular if hand is obtained from a non singular matrix + + + + + U + + square non singular upper triangular sparse matrix with ones along the main diagonal + + + + Q + + sparse permutation matrix + + + + + + Description + + [P,L,U,Q]=luget(hand) with hand obtained by + the command [hand,rk]=lufact(A) with A a sparse matrix + returns four sparse matrices such that P*L*U*Q=A. + + + The A matrix needs not be full rank but must be square + (since A is assumed sparse one may add zeros if necessary to squaring + down A). + + + If A is singular, the L matrix is column compressed (with + rk independent nonzero columns): the nonsingular sparse + matrix Q'*inv(U) column compresses A. + + + + Examples + + + + See Also + + + sparse + + + lusolve + + + luget + + + clean + + + + diff --git a/modules/sparse/help/en_US/decomposition/lusolve.xml b/modules/sparse/help/en_US/decomposition/lusolve.xml new file mode 100755 index 000000000..9063c4bda --- /dev/null +++ b/modules/sparse/help/en_US/decomposition/lusolve.xml @@ -0,0 +1,102 @@ + + + + + lusolve + sparse linear system solver + + + Calling Sequence + x=lusolve(hand,b) + x=lusolve(A,b) + + + + Arguments + + + b + + full real matrix + + + + A + + real square sparse invertible matrix + + + + hand + + handle to a previously computed sparse lu factors (output of lufact) + + + + x + + full real matrix + + + + + + Description + + x=lusolve(hand,b) solves the sparse linear system + A*x = b. + + + [hand,rk]=lufact(A) is the output of lufact. + + + x=lusolve(A,b) solves the sparse linear system + A*x = b + + + + Examples + + + + See Also + + + sparse + + + lufact + + + slash + + + backslash + + + + diff --git a/modules/sparse/help/en_US/decomposition/spchol.xml b/modules/sparse/help/en_US/decomposition/spchol.xml new file mode 100755 index 000000000..dafaf0dde --- /dev/null +++ b/modules/sparse/help/en_US/decomposition/spchol.xml @@ -0,0 +1,108 @@ + + + + + spchol + sparse cholesky factorization + + + Calling Sequence + [R,P] = spchol(X) + + + Arguments + + + X + + symmetric positive definite real sparse matrix + + + + P + + permutation matrix + + + + R + + cholesky factor + + + + + + Description + + [R,P] = spchol(X) produces a + lower triangular matrix R such that P*R*R'*P' = X. + + + + Examples + + + + See Also + + + sparse + + + lusolve + + + luget + + + chol + + + + diff --git a/modules/sparse/help/en_US/iterativesolvers/CHAPTER b/modules/sparse/help/en_US/iterativesolvers/CHAPTER new file mode 100755 index 000000000..c59edd550 --- /dev/null +++ b/modules/sparse/help/en_US/iterativesolvers/CHAPTER @@ -0,0 +1 @@ +title = Linear Equations (Iterative Solvers) diff --git a/modules/sparse/help/en_US/iterativesolvers/conjgrad.xml b/modules/sparse/help/en_US/iterativesolvers/conjgrad.xml new file mode 100755 index 000000000..e011282e4 --- /dev/null +++ b/modules/sparse/help/en_US/iterativesolvers/conjgrad.xml @@ -0,0 +1,406 @@ + + + + + conjgrad + conjugate gradient solvers + + + Calling Sequence + + [x, flag, err, iter, res] = conjgrad(A, b [, method [, tol [, maxIter [, M [, M2 [, x0 [, verbose]]]]]]]) + [x, flag, err, iter, res] = conjgrad(A, b [, method [, key=value,...]]) + + + + Arguments + + + A + + + a matrix, or a function, or a list computing + A*x for each given x. The + following is a description of the computation of A*x depending on + the type of A. + + + + + matrix.If A is a matrix, it can be + dense or sparse + + + + + function.If A is a function, it must + have the following header : + + + + + + list.If A is a list, the first element + of the list is expected to be a function and the other elements + in the list are the arguments of the function, from index 2 to + the end. When the function is called, the current value of x is + passed to the function as the first argument. The other + arguments passed are the one given in the list. + + + + + + + b + + right hand side vector (size: nx1) + + + + mehtod + + scalar string, "pcg", "cgs", "bicg" or "bicgstab" (default "bicgstab") + + + + tol + + error relative tolerance (default: 1e-8). + The termination criteria is based on the 2-norm of the + residual r=b-Ax, divided by the 2-norm of the right hand side b. + + + + + maxIter + + maximum number of iterations (default: n) + + + + M + + preconditioner: full or sparse matrix or function returning + M\x (default: none) + + + + + M2 + + preconditioner: full or sparse matrix or function returning + M2\x for each x (default: + none) + + + + + x0 + + initial guess vector (default: zeros(n,1)) + + + + verbose + + set to 1 to enable verbose logging (default 0) + + + + x + + solution vector + + + + flag + + + 0 if conjgrad converged to the desired tolerance + within maxi iterations, 1 else + + + + + err + + final relative norm of the residual (the 2-norm of the right-hand side b is used) + + + + iter + + number of iterations performed + + + + res + + vector of the residual relative norms + + + + + + Description + + Solves the linear system Ax=b using the conjugate + gradient method with or without preconditioning. The preconditionning + should be defined by a symmetric positive definite matrix + M, or two matrices M1 and + M2 such that M=M1*M2. in the case + the function solves inv(M)*A*x = inv(M)*b for + x. M, M1 and + M2 can be Scilab functions with calling sequence + y=Milx(x) which computes the corresponding left + division y=Mi\x. + + + The method input argument selects the solver to be used: + + + "pcg" Preconditioned Conjugate Gradient + + + "cgs" preconditioned Conjugate Gradient Squared + + + "bicg" preconditioned BiConjugate Gradient + + + "bicgstab" preconditioned BiConjugate Gradient Stabilized (default) + + + + + If method="pcg", then the A matrix + must be a symmetric positive definite matrix (full or sparse) + or a function with calling sequence y=Ax(x) which computes + y=A*x. + Otherwise (method="cgs", "bicg" or "bicgstab"), + A just needs to be square. + + + + Example with well-conditionned and ill-conditionned + problems + + In the following example, two linear systems are solved. The first + maxtrix has a condition number equals to ~0.02, which makes the algorithm + converge in exactly 10 iterations. Since this is the size of the matrix, + it is an expected behaviour for a gradient conjugate method. The second + one has a low condition number equals to 1.d-6, which makes the algorithm + converge in a larger 22 iterations. This is why the parameter maxIter is + set to 30. See below for other examples of the "key=value" syntax. + + + + + Examples with A given as a sparse matrix, or function, or + list + + The following example shows that the method can handle sparse + matrices as well. It also shows the case where a function, computing the + right-hand side, is given to the "conjgrad" primitive. The final case shown by + this example, is when a list is passed to the primitive. + + + + + Examples with key=value syntax + The following example shows how to pass arguments with the + "key=value" syntax. This allows to set non-positionnal arguments, that is, + to set arguments which are not depending on their order in the list of + arguments. The available keys are the names of the optional arguments, + that is : tol, maxIter, %M, %M2, x0, verbose. Notice that, in the + following example, the verbose option is given before the maxIter option. + Without the "key=value" syntax, the positionnal arguments would require + that maxIter come first and verbose after. + + + + + See Also + + + backslash + + + qmr + + + gmres + + + + + References + + PCG + + "Templates for the Solution of Linear Systems: Building Blocks for + Iterative Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra, + Eijkhout, Pozo, Romine, and Van der Vorst, SIAM Publications, 1993, ftp + netlib2.cs.utk.edu/linalg/templates.ps + + "Iterative Methods for Sparse Linear Systems, Second Edition", Saad, + SIAM Publications, 2003, ftp + ftp.cs.umn.edu/dept/users/saad/PS/all_ps.zip + + + CGS + + + "CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems" by Peter Sonneveld. + + + Original article + + + Article on ACM + + + Some theory around CGS + + + BICG + + + "Numerical Recipes: The Art of Scientific Computing." (third ed.) by William Press, Saul Teukolsky, William Vetterling, Brian Flannery. + + + http://apps.nrbook.com/empanel/index.html?pg=87 + + + Article on ACM + + + Some theory around BICG + + + BICGSTAB + + + "Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems" by Henk van der Vorst. 339 + + + Original article + + + Article on ACM + + + Some theory around BICG + + + + History + + + 5.5.0 + + Introduction + + + + + diff --git a/modules/sparse/help/en_US/iterativesolvers/gmres.xml b/modules/sparse/help/en_US/iterativesolvers/gmres.xml new file mode 100755 index 000000000..f54361ef0 --- /dev/null +++ b/modules/sparse/help/en_US/iterativesolvers/gmres.xml @@ -0,0 +1,252 @@ + + + + + gmres + Generalized Minimum RESidual method + + + Calling Sequence + [x,flag,err,iter,res] = gmres(A,b,[rstr,[tol,[maxi,[M,[x0]]]]]) + + + Arguments + + + A + + + n-by-n matrix or function returning A*x. If A is a function, it must have the following header : + + + + + + b + + right hand side vector + + + + x0 + + initial guess vector (default: zeros(n,1)) + + + + M + + + preconditioner: matrix of size n-by-n or function returning M*x (In the first case, default: eye(n,n)). If M is a function, it must have the following header : + + + + + + rstr + + number of iterations between restarts (default: 10) + + + + maxi + + maximum number of iterations (default: n) + + + + tol + + error tolerance (default: 1e-6) + + + + x + + solution vector + + + + err + + final residual norm + + + + iter + + number of iterations performed + + + + flag + + + + 0 = + + + gmres converged to the desired tolerance within maxi iterations + + + + + 1 = + + + no convergence given maxi + + + + + + + + res + + residual vector + + + + + + Description + + + GMRES + + + solves the linear system Ax=b using the Generalized Minimal residual method with restarts. + + + + + Details + + of this algorithm are described in : + "Templates for the Solution of Linear Systems: Building Blocks for + Iterative Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra, + Eijkhout, Pozo, Romine, and Van der Vorst, SIAM Publications, 1993 (ftp + netlib2.cs.utk.edu; cd linalg; get templates.ps). + + "Iterative Methods for Sparse Linear Systems, Second Edition" Saad, + SIAM Publications, 2003 (ftp ftp.cs.umn.edu; cd dept/users/saad/PS; get + all_ps.zip). + + + + + + + Examples + + + + See Also + + + conjgrad + + + qmr + + + + diff --git a/modules/sparse/help/en_US/iterativesolvers/qmr.xml b/modules/sparse/help/en_US/iterativesolvers/qmr.xml new file mode 100755 index 000000000..71b37cc11 --- /dev/null +++ b/modules/sparse/help/en_US/iterativesolvers/qmr.xml @@ -0,0 +1,374 @@ + + + + + qmr + quasi minimal residual method with preconditioning + + + Calling Sequence + [x,flag,err,iter,res] = qmr(A,Ap,b,x0,M1,M1p,M2,M2p,maxi,tol) + [x,flag,err,iter,res] = qmr(A,b,x0,M1,M2,maxi,tol) + + + + Arguments + + + A + + + matrix of size n-by-n or function. + + + + + matrix.If A is a matrix, it can be + dense or sparse + + + + + function.If A is a function which returns A*x, it must + have the following header : + + + + If A is a function which returns A*x or A'*x depending t. + If t = "notransp", the function returns A*x. + If t = "transp", the function returns A'*x. It must + have the following header : + + + + + + + + Ap + + + function returning A'*x. It must have the following header : + + + + + + b + + right hand side vector + + + + x0 + + initial guess vector (default: zeros(n,1)) + + + + M1 + + + left preconditioner : matrix or function (In the first case, default: eye(n,n)). If M1 is a function, she returns either, + + + + + only M1*x + + + or + + + + M1*x or M1'*x depending t. + + + + + + + M1p + + + must only be provided when M1 is a function returning M1*x. + In this case M1p is the function which returns M1'*x. + + + + + M2 + + + right preconditioner : matrix or function (In the first case, default: eye(n,n)). If M2 is a function, she returns either + + + + + only M2*x + + + or + + + + M2*x or M2'*x depending t. + + + + + + + M2p + + + must only be provided when M2 is a function returning M2*x. + In this case M2p is the function which returns M2'*x + + + + + maxi + + maximum number of iterations (default: n) + + + + + tol + + error tolerance (default: 1000*%eps) + + + + x + + solution vector + + + + flag + + + + + flag=0: qmr converged to the desired tolerance within maxi + iterations, + + + + + flag=1: no convergence given maxi, + + + + + -7 < flag < 0: A breakdown occurred because one of the scalar quantities calculated during + qmr was equal to zero. + + + + + + + res + + residual vector + + + + err + + final residual norm + + + + iter + + number of iterations performed + + + + + + Description + + Solves the linear system Ax=b using the Quasi Minimal Residual Method with preconditioning. + + + + Examples + + + + See Also + + + gmres + + + conjgrad + + + + + History + + + 5.4.0 + + Calling qmr(A, Ap) is deprecated. qmr(A) should be used instead. The following function is an example : + + + + + + diff --git a/modules/sparse/help/en_US/matrixmanip/CHAPTER b/modules/sparse/help/en_US/matrixmanip/CHAPTER new file mode 100755 index 000000000..a797a77e1 --- /dev/null +++ b/modules/sparse/help/en_US/matrixmanip/CHAPTER @@ -0,0 +1 @@ +title = Sparse Matrix Manipulation diff --git a/modules/sparse/help/en_US/matrixmanip/issparse.xml b/modules/sparse/help/en_US/matrixmanip/issparse.xml new file mode 100755 index 000000000..6bac33ba4 --- /dev/null +++ b/modules/sparse/help/en_US/matrixmanip/issparse.xml @@ -0,0 +1,70 @@ + + + + + issparse + determine whether input is sparse + + + Calling Sequence + res = issparse(S) + + + Arguments + + + S + + a scilab object + + + + res + + 1 is the matrix is a sparse and 0 otherwise/ + + + + + + Description + + res = issparse(S) returns 1 if S is a sparse + matrix and 0 otherwise. + + + + Examples + sp = sparse([1,2;4,5;3,10],[1,2,3]); + if issparse(sp) == 1 then + disp("It is a sparse"); + end + + A = 1; + if issparse(A) == 0 then + disp("It is not a sparse"); + end + + + + See Also + + + type + + + typeof + + + + diff --git a/modules/sparse/help/en_US/matrixmanip/nnz.xml b/modules/sparse/help/en_US/matrixmanip/nnz.xml new file mode 100755 index 000000000..9bb90e77f --- /dev/null +++ b/modules/sparse/help/en_US/matrixmanip/nnz.xml @@ -0,0 +1,62 @@ + + + + + nnz + number of non zero entries in a matrix + + + Calling Sequence + n=nnz(X) + + + Arguments + + + X + + real or complex sparse (or full) matrix + + + + n + + integer, the number of non zero elements in X + + + + + + Description + + nnz counts the number of non zero entries in a sparse or full matrix + + + + Examples + + + + See Also + + + spget + + + + diff --git a/modules/sparse/help/en_US/matrixmanip/speye.xml b/modules/sparse/help/en_US/matrixmanip/speye.xml new file mode 100755 index 000000000..a79e4d3ae --- /dev/null +++ b/modules/sparse/help/en_US/matrixmanip/speye.xml @@ -0,0 +1,96 @@ + + + + + speye + sparse identity matrix + + + Calling Sequence + Isp=speye(nrows,ncols) + Isp=speye(A) + + + + Arguments + + + nrows + + integer (number of rows) + + + + ncols + + integer (number os columns) + + + + A + + sparse matrix + + + + sp + + sparse identity matrix + + + + + + Description + + Isp=speye(nrows,ncols) returns a sparse identity + matrix Isp with nrows rows, + ncols columns. (Non square identity matrix have a + maximal number of ones along the main diagonal). + + + Isp=speye(A) returns a sparse identity matrix + with same dimensions as A. If + [m,n]=size(A), speye(m,n) and + speye(A) are equivalent. In particular + speye(3) is not equivalent to + speye(3,3). + + + + Examples + + + + See Also + + + sparse + + + full + + + eye + + + spzeros + + + spones + + + + diff --git a/modules/sparse/help/en_US/matrixmanip/spones.xml b/modules/sparse/help/en_US/matrixmanip/spones.xml new file mode 100755 index 000000000..76e2aec02 --- /dev/null +++ b/modules/sparse/help/en_US/matrixmanip/spones.xml @@ -0,0 +1,76 @@ + + + + + spones + sparse matrix + + + Calling Sequence + sp=spones(A) + + + Arguments + + + A + + sparse matrix + + + + sp + + sparse matrix + + + + + + Description + + sp=spones(A) generates a matrix with the same + sparsity structure as A, but with ones in the nonzero + positions. + + + + Examples + + + + See Also + + + sparse + + + full + + + eye + + + speye + + + spzeros + + + + diff --git a/modules/sparse/help/en_US/matrixmanip/sprand.xml b/modules/sparse/help/en_US/matrixmanip/sprand.xml new file mode 100755 index 000000000..69ee87075 --- /dev/null +++ b/modules/sparse/help/en_US/matrixmanip/sprand.xml @@ -0,0 +1,190 @@ + + + + + sprand + sparse random matrix + + + Calling Sequence + sp=sprand(nrows,ncols,density [,typ]) + + + Arguments + + + nrows + + integer (number of rows) + + + + ncols + + integer (number of columns) + + + + density + + filling coefficient (density) + + + + typ + + + character string, "uniform" (default) or + "normal" + + + + + sp + + sparse matrix + + + + + + Description + + sp=sprand(nrows,ncols,density) returns a sparse + matrix sp with nrows rows, + ncols columns and approximately + density*nrows*ncols non-zero entries. + + + The density parameter is expected to be in the + [0,1] interval. If not, it is automatically + projected into this interval. Therefore, using a density which is + lower than 0 or greater than 1 will generate neither an error, + nor a warning: the formula density=max(min(density,1),0) + is used. + + + If typ="uniform" uniformly distributed values on + [0,1] are generated. If typ="normal" normally + distributed values are generated (mean=0 and standard deviation=1). + + + The entries of the output matrix are computed from the given + distribution function typ. + The indices of the non-zeros entries are computed + randomly, so that the average number of nonzeros is equal to + density. + The actual indices values are computed from the exponential distribution + function, where the parameter of the distribution function is + computed accordingly. + + + + Examples + + In the following example, we generate a 100x1000 sparse matrix with + approximate density 0.001, i.e. with approximately + 100*1000*0.001=100 nonzero entries. + + + + In the following script, we check that the entries of the matrix + have the expected distribution. + We use the spget function in order to get the nonzero entries. + Then we compute the min, mean and max of the entries and compare + them with the limit values. + + + + In the following script, we check that the entry indices, which + are also chosen at random, have the correct distribution. + We generate kmax sparse random matrices with + uniform distribution. + For each matrix, we consider the indices of the nonzero + entries which were generated, i.e. we see if the event + Aij = {the entry (i,j) is nonzero} occurred for + each i and j, for i=1,2,...,nrows + and j=1,2,...,ncols. + The matrix C(i,j) stores the number of times that the event Aij + occurred. + The matrix R(k) stores the actual density of the try number k, + where k=1,2,...,kmax. + + 0); + NZratio = size(NZ,"*")/(nrows*ncols); + R=[R NZratio]; + C(NZ)=C(NZ)+1; + end + ]]> + + Now that this algorithm has been performed (which may require some time), + we can compute elementary statistics to check that the algorithm performed + well. + + + + + See Also + + + sparse + + + full + + + rand + + + speye + + + + diff --git a/modules/sparse/help/en_US/matrixmanip/spzeros.xml b/modules/sparse/help/en_US/matrixmanip/spzeros.xml new file mode 100755 index 000000000..32d23952f --- /dev/null +++ b/modules/sparse/help/en_US/matrixmanip/spzeros.xml @@ -0,0 +1,99 @@ + + + + + spzeros + sparse zero matrix + + + Calling Sequence + sp=spzeros(nrows,ncols) + sp=spzeros(A) + + + + Arguments + + + nrows + + integer (number of rows) + + + + ncols + + integer (number os columns) + + + + A + + sparse matrix + + + + sp + + sparse zero matrix + + + + + + Description + + sp=spzeros(nrows,ncols) returns a sparse zero + matrix sp with nrows rows, + ncols columns. (Equivalent to + sparse([],[],[nrow,ncols])) + + + sp=spzeros(A) returns a sparse zero matrix with + same dimensions as A. If + [m,n]=size(A), spzeros(m,n) and + spzeros(A) are equivalent. In particular + spzeros(3) is not equivalent to + spzeros(3,3). + + + + Examples + + + + See Also + + + sparse + + + full + + + eye + + + speye + + + spones + + + + diff --git a/modules/sparse/help/en_US/ordmmd.xml b/modules/sparse/help/en_US/ordmmd.xml new file mode 100755 index 000000000..f9d61c1a2 --- /dev/null +++ b/modules/sparse/help/en_US/ordmmd.xml @@ -0,0 +1,232 @@ + + + + + ordmmd + + Compute multiple minimum degree ordering + + + + Calling Sequence + + [perm,invp,nofsub]=ordmmd(xadj,iadj,n) + + + + Arguments + + + n + + a 1-by-1 matrix of doubles, integer value, the number of equations + + + + xadj + + (n+1)-by-1 matrix of doubles, integer value, pointer to the rows of A + + + + iadj + + nnz-by-1 matrix of doubles, integer value, the row indices of A + + + + perm + + n-by-1 matrix of doubles, integer value, the minimum degree ordering + + + + invp + + n-by-1 matrix of doubles, integer value, the inverse of perm + + + + nofsub + + + 1-by-1 matrix of doubles, integer value, + an upper bound on the number of nonzero subscripts for the compressed storage scheme + + + + + + + Description + + The minimum degree algorithm is used to permute the rows and + columns of a symmetric sparse matrix before applying the Cholesky decomposition. + This algorithm reduces the number of non-zeros in the Cholesky factor. + + + Given a n-by-n real symmetric sparse square matrix A, + the Cholesky factor U will typically suffer "fill in", that is have more + non-zeros than the upper triangle of A. + We seek a permutation matrix P, so that the matrix P'*A*P, + which is also symmetric, has the least possible fill in its Cholesky factor. + + + + Examples + + In the following example, we compute an ordering for a symmetric + sparse matrix. + We use the sp2adj function to compute the adjacency structure. + + + + In the following example, we compute an ordering for a symmetric + sparse matrix. + We check that invp is the inverse of perm. + + + + In the following example, we compare the sparsity pattern of the Cholesky + factor of a matrix A and the matrix P'*A*P. + See p. 3, "Chapter 1: Introduction" in + "Computer Solution of Large Sparse Positive Definite Systems". + We see that the number of nonzeros in the Cholesky decomposition is + 15, while the matrix P'*A*P has a Cholesky decomposition with + 9 nonzeros. + + + + A = [ + 4. 1. 2. 0.5 2. + 1. 0.5 0. 0. 0. + 2. 0. 3. 0. 0. + 0.5 0. 0. 0.625 0. + 2. 0. 0. 0. 16. + ]; + A = sparse(A); + U = sparse(chol(full(A))); + scf(); + subplot(2,1,1); + PlotSparse(U,"x"); + xtitle("Sparsity pattern of U, such that A=U''*U"); + [xadj,iadj,val]=sp2adj(A); + n = size(A,"r"); + [perm,invp,nofsub]=ordmmd(xadj,iadj,n); + P=spzeros(n,n); + for i=1:n + P(perm(i),i)=1; + end + U = sparse(chol(full(P'*A*P))); + subplot(2,1,2); + PlotSparse(U,"x"); + xtitle("Sparsity pattern of U, such that P''*A*P=U''*U"); + + + + Implementation notes + + This function is based on "ordmmd.f" a source code (1994) by Esmond G. Ng and Barry W. Peyton + from Mathematical Sciences Section, Oak Ridge National Laboratory. + The algorithm is based on the genmmd routine by Joseph W.H. Liu from the + SPARSPAK library. + + + + Bibliography + + "Minimum degree algorithm", Wikipedia contributors, Wikipedia, The Free Encyclopedia. http://en.wikipedia.org/wiki/Minimum_degree_algorithm + + + "A new release of SPARSPAK: the Waterloo sparse matrix package", Alan George and Esmond Ng. 1984. SIGNUM Newsl. 19, 4 (October 1984), 9-13. + + + "Computer Solution of Large Sparse Positive Definite Systems" by Alan George and Joseph Liu, Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1981 + + + "Implementation of Lipsol in Scilab", Rubio Scola, 1997, INRIA, No 0215 + + + + See Also + + + sp2adj + + + spchol + + + + diff --git a/modules/sparse/help/en_US/sparseconvert/CHAPTER b/modules/sparse/help/en_US/sparseconvert/CHAPTER new file mode 100755 index 000000000..42d5e0bf2 --- /dev/null +++ b/modules/sparse/help/en_US/sparseconvert/CHAPTER @@ -0,0 +1 @@ +title = Sparse Matrix Conversion diff --git a/modules/sparse/help/en_US/sparseconvert/adj2sp.xml b/modules/sparse/help/en_US/sparseconvert/adj2sp.xml new file mode 100755 index 000000000..1b90969ce --- /dev/null +++ b/modules/sparse/help/en_US/sparseconvert/adj2sp.xml @@ -0,0 +1,230 @@ + + + + + adj2sp + converts adjacency form into sparse matrix. + + + Calling Sequence + + A=adj2sp(xadj,iadj,v) + A=adj2sp(xadj,iadj,v,mn) + + + + Arguments + + + xadj + + + a (n+1)-by-1 matrix of floating point integers. + For j=1:n, the floating point integer + xadj(j+1)-xadj(j) is the number of non zero entries in + column j. + + + + + iadj + + + a nz-by-1 matrix of floating point integers, the row indices for the + nonzeros. + For j=1:n, for k = xadj(j):xadj(j+1)-1, the floating point integer + i = iadj(k) is the row index of the nonzero entry #k. + + + + + v + + + a nz-by-1 matrix of floating point integers, the non-zero entries of A. + For j=1:n, for k = xadj(j):xadj(j+1)-1, the floating point integer + Aij = v(k) is the value of the nonzero entry #k. + + + + + mn + + + a 1-by-2 or 2-by-1 matrix of floating point integers, optional, + mn(1) is the number of rows in A, + mn(2) is the number of columns in A. + If mn is not provided, then mn=[m,n] is the default with + m=max(iadj) and n=size(xadj,"*")-1. + + + + + A + + m-by-n real or complex sparse matrix (with nz non-zero entries) + + + + + + Description + + adj2sp converts a sparse matrix into its adjacency form format. + The values in the adjacency format are stored colum-by-column. + This is why this format is sometimes called "Compressed sparse column" or CSC. + + + + Examples + + In the following example, we create a sparse matrix from its adjacency format. + Then we check that it matches the expected sparse matrix. + + + + In the following example, we create a sparse matrix from its adjacency format. + Then we check that it matches the expected sparse matrix. + + + + In the following example, we check the use of the mn parameter. + The consistency between the mn parameter and the actual content of + xadj and iadj is checked by adj2sp. + + + + In the following example, create a 3-by-3 sparse matrix. + This example is adapted from the documentation of SciPy. + + + + The previous script produces the following output. + + full(adj2sp(xadj,iadj,v)) + ans = + 1. 0. 4. + 0. 0. 5. + 2. 3. 6. + ]]> + + In the following example, we check that the sp2adj and adj2sp functions + are inverse. + + + + + See Also + + + sp2adj + + + sparse + + + spcompack + + + spget + + + + + References + + "Implementation of Lipsol in Scilab", Hector E. Rubio Scola, INRIA, Decembre 1997, Rapport Technique No 0215 + + + "Solving Large Linear Optimization Problems with Scilab : Application to Multicommodity Problems", Hector E. Rubio Scola, Janvier 1999, Rapport Technique No 0227 + + + "Toolbox Scilab : Detection signal design for failure detection and isolation for linear dynamic systems User's Guide", Hector E. Rubio Scola, 2000, Rapport Technique No 0241 + + + "Computer Solution of Large Sparse Positive Definite Systems", A. George, Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1981. + + + diff --git a/modules/sparse/help/en_US/sparseconvert/full.xml b/modules/sparse/help/en_US/sparseconvert/full.xml new file mode 100755 index 000000000..8253f7991 --- /dev/null +++ b/modules/sparse/help/en_US/sparseconvert/full.xml @@ -0,0 +1,68 @@ + + + + + full + sparse to full matrix conversion + + + Calling Sequence + X=full(sp) + + + Arguments + + + sp + + real or complex sparse (or full) matrix + + + + X + + full matrix + + + + + + Description + + X=full(sp) converts the sparse matrix sp into its + full representation. (If sp is already full then X equals + sp). + + + + Examples + + + + See Also + + + sparse + + + sprand + + + speye + + + + diff --git a/modules/sparse/help/en_US/sparseconvert/mtlb_sparse.xml b/modules/sparse/help/en_US/sparseconvert/mtlb_sparse.xml new file mode 100755 index 000000000..cc8d8fdf6 --- /dev/null +++ b/modules/sparse/help/en_US/sparseconvert/mtlb_sparse.xml @@ -0,0 +1,76 @@ + + + + + mtlb_sparse + convert sparse matrix + + + Calling Sequence + Y=mtlb_sparse(X) + + + Arguments + + + X + + sparse matrix + + + + Y + + sparse matrix in Matlab format + + + + + + Description + + Y=mtlb_sparse(X) is used to convert X, a Scilab sparse matrix, to + Matlab format. Y is the a variable with type 7, + i.e. type(Y) is equal to 7. + This function should be used in mexfiles (a Matlab mexfile containing sparse + matrices can be used only if the Scilab sparse matrices are converted + to that format). The functions full and spget work + with this format. + + + Other operations and functions using this format + can be overloaded with Scilab functions using the prefix "%msp". + For instance the function + %msp_p(x) (see SCI/modules/overloading/macros directory) is used to + display such "type 7" objects. + + + + Examples + + + + See Also + + + full + + + spget + + + + diff --git a/modules/sparse/help/en_US/sparseconvert/sp2adj.xml b/modules/sparse/help/en_US/sparseconvert/sp2adj.xml new file mode 100755 index 000000000..90fd92c18 --- /dev/null +++ b/modules/sparse/help/en_US/sparseconvert/sp2adj.xml @@ -0,0 +1,229 @@ + + + + + sp2adj + converts sparse matrix into adjacency form + + + Calling Sequence + + [xadj,iadj,v]=sp2adj(A) + + + + Arguments + + + A + + m-by-n real or complex sparse matrix (with nz non-zero entries) + + + + xadj + + + a (n+1)-by-1 matrix of floating point integers, pointers to the starting + index in iadj and v for each column. + For j=1:n, the floating point integer + xadj(j+1)-xadj(j) is the number of non zero entries in + column j. + + + + + iadj + + + a nz-by-1 matrix of floating point integers, the row indices for the + nonzeros. + For j=1:n, for k = xadj(j):xadj(j+1)-1, the floating point integer + i = iadj(k) is the row index of the nonzero entry #k. + + + + + v + + + a nz-by-1 matrix of floating point integers, the non-zero entries of A. + For j=1:n, for k = xadj(j):xadj(j+1)-1, the floating point integer + Aij = v(k) is the value of the nonzero entry #k. + + + + + + + Description + + sp2adj converts a sparse matrix into its adjacency format. + The values in the adjacency format are stored colum-by-column. + This is why this format is sometimes called "Compressed sparse column" or CSC. + + + + Examples + + In the following example, we create a full matrix, which entries + goes from 1 to 10. + Then we convert it into a sparse matrix, which removes the zeros. + Finally, we compute the adjacency represention of this matrix. + The matrix v contains only the nonzero entries of A. + + + + The previous script produces the following output. + + + + Let us consider the column #1. + The equality xadj(2)-xadj(1)=2 indicates that there are two + nonzeros in the column #1. + The row indices are stored in iadj, which tells us that the + nonzero entries in column #1 are at rows #3 and #5. + The v matrix tells us the actual entries are equal to 1 and 2. + + + In the following example, we browse the nonzero entries of + a sparse matrix by looping on the adjacency structure. + + + + In the following example, we check that the sp2adj and adj2sp functions + are inverse. + + + + + See Also + + + adj2sp + + + sparse + + + spcompack + + + spget + + + + + References + + "Implementation of Lipsol in Scilab", Hector E. Rubio Scola, INRIA, Decembre 1997, Rapport Technique No 0215 + + + "Solving Large Linear Optimization Problems with Scilab : Application to Multicommodity Problems", Hector E. Rubio Scola, Janvier 1999, Rapport Technique No 0227 + + + "Toolbox Scilab : Detection signal design for failure detection and isolation for linear dynamic systems User's Guide", Hector E. Rubio Scola, 2000, Rapport Technique No 0241 + + + "Computer Solution of Large Sparse Positive Definite Systems", A. George, Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1981. + + + diff --git a/modules/sparse/help/en_US/sparseconvert/sparse.xml b/modules/sparse/help/en_US/sparseconvert/sparse.xml new file mode 100755 index 000000000..6f9aec111 --- /dev/null +++ b/modules/sparse/help/en_US/sparseconvert/sparse.xml @@ -0,0 +1,143 @@ + + + + + sparse + sparse matrix definition + + + Calling Sequence + sp=sparse(X) + sp=sparse(ij,v [,mn]) + + + + Arguments + + + X + + real or complex or boolean full (or sparse) matrix + + + + ij + + two columns integer matrix (indices of non-zeros entries) + + + + v + + vector + + + + mn + + integer vector with two entries (row-dimension, column-dimension) + + + + sp + + sparse matrix + + + + + + Description + + sparse is used to build a sparse matrix. Only non-zero entries + are stored. + + + sp = sparse(X) converts a full matrix to sparse form by + squeezing out any zero elements. (If X is already sparse + sp is X). + + + sp=sparse(ij,v [,mn]) builds an mn(1)-by-mn(2) + sparse matrix with sp(ij(k,1),ij(k,2))=v(k). + ij and v must have the same column dimension. + If optional mn parameter is not given the sp + matrix dimensions are the max value of ij(:,1) and ij(:,2) + respectively. + + + Operations (concatenation, addition, etc,) with sparse matrices are + made using the same syntax as for full matrices. + + + Elementary functions are also available (abs,maxi,sum,diag,...) + for sparse matrices. + + + Mixed operations (full-sparse) are allowed. Results are full or sparse + depending on the operations. + + + Note : Any operation involing dense matrices of the same size, either as argument (e.g. sp=sparse(d)) + or as result (e.g. d= sp + 1.) is provided for convenience purposes but should of course be avoided. + Furthermore, random access to elements (sp(r,c)), especially for insertions, is not efficient, so + any performance-constrained access should be done in batches with spget for read access + and the three arguments constructor sp=sparse(ij, v, mn) for write access. + + + + Examples + + + + See Also + + + full + + + spget + + + sprand + + + speye + + + lufact + + + + diff --git a/modules/sparse/help/en_US/sparseconvert/spcompack.xml b/modules/sparse/help/en_US/sparseconvert/spcompack.xml new file mode 100755 index 000000000..13deb634c --- /dev/null +++ b/modules/sparse/help/en_US/sparseconvert/spcompack.xml @@ -0,0 +1,107 @@ + + + + + spcompack + converts a compressed adjacency representation + + + Arguments + + + xadj + + integer vector of length (n+1). + + + + xlindx + + integer vector of length n+1 (pointers). + + + + lindx + + integer vector + + + + adjncy + + integer vector + + + + + + Description + + + + Examples + + + + See Also + + + sp2adj + + + adj2sp + + + spget + + + + diff --git a/modules/sparse/help/en_US/sparseconvert/spget.xml b/modules/sparse/help/en_US/sparseconvert/spget.xml new file mode 100755 index 000000000..20cb9db9d --- /dev/null +++ b/modules/sparse/help/en_US/sparseconvert/spget.xml @@ -0,0 +1,86 @@ + + + + + spget + retrieves entries of sparse matrix + + + Calling Sequence + [ij,v,mn]=spget(sp) + + + Arguments + + + sp + + real, complex or boolean sparse matrix + + + + ij + + two columns integer matrix (indices of non-zeros or true entries) + + + + mn + + integer vector with two entries (row-dimension, column-dimension) + + + + v + + column vector + + + + + + Description + + spget is used to convert the internal representation of sparse + matrices into the standard ij, v representation. + + + Non zero entries (or entries set to true for a boolean sparse matrix) of sp are located in rows and columns + with indices in ij. + + + + Examples + + + + See Also + + + sparse + + + sprand + + + speye + + + lufact + + + + diff --git a/modules/sparse/help/fr_FR/addchapter.sce b/modules/sparse/help/fr_FR/addchapter.sce new file mode 100755 index 000000000..5744e12ad --- /dev/null +++ b/modules/sparse/help/fr_FR/addchapter.sce @@ -0,0 +1,11 @@ +// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab +// Copyright (C) 2009 - DIGITEO +// +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + +add_help_chapter("Matrices creuses",SCI+"/modules/sparse/help/fr_FR",%T); + diff --git a/modules/sparse/help/fr_FR/chfact.xml b/modules/sparse/help/fr_FR/chfact.xml new file mode 100755 index 000000000..67b1eb75d --- /dev/null +++ b/modules/sparse/help/fr_FR/chfact.xml @@ -0,0 +1,68 @@ + + + + + chfact + Factorisation de Cholesky creuse + + + Séquence d'appel + spcho=chfact(A) + + + Paramètres + + + A + + matrice creuse réelle ou complexe + + + + + spcho + + liste contenant les facteurs de Cholesky + + + + + + + Description + + Si A est creuse et hermitienne (symétrique dans le cas réel) définie positive, spcho=chfact(A) calcule les facteurs de sa factorisation de Cholesky. + Cette fonction est basée sur le programme Ng-Peyton (ORNL). Voir le programme Fortran pour une description complète des variables de la liste spcho. Cette fonction est à utiliser conjointement avec chsolve. + + + + Voir aussi + + + chsolve + + + sparse + + + lufact + + + luget + + + spchol + + + + diff --git a/modules/sparse/help/fr_FR/chsolve.xml b/modules/sparse/help/fr_FR/chsolve.xml new file mode 100755 index 000000000..6b054fcde --- /dev/null +++ b/modules/sparse/help/fr_FR/chsolve.xml @@ -0,0 +1,82 @@ + + + + + chsolve + solveur de Cholesky creux + + + Séquence d'appel + sol=chsolve(spcho,rhs) + + + Paramètres + + + spcho + + liste contenant les facteurs de Cholesky renvoyés par chfact + + + + + rhs, sol + + vecteurs + + + + + + + Description + + sol=chsolve(spcho,rhs) calcule la solution de + rhs=A*sol, où A est une matrice symétrique + définie positive. Cette fonction est basée sur le programme Ng-Peyton + (ORNL). Voir le programme Fortran pour une description complète des + variables de la liste spcho. + + + + Exemples + + + + Voir aussi + + + chfact + + + sparse + + + lufact + + + luget + + + spchol + + + + diff --git a/modules/sparse/help/fr_FR/decomposition/CHAPTER b/modules/sparse/help/fr_FR/decomposition/CHAPTER new file mode 100755 index 000000000..41ee03202 --- /dev/null +++ b/modules/sparse/help/fr_FR/decomposition/CHAPTER @@ -0,0 +1 @@ +title = Décompositions Creuses diff --git a/modules/sparse/help/fr_FR/decomposition/ludel.xml b/modules/sparse/help/fr_FR/decomposition/ludel.xml new file mode 100755 index 000000000..8ed809f20 --- /dev/null +++ b/modules/sparse/help/fr_FR/decomposition/ludel.xml @@ -0,0 +1,58 @@ + + + + + ludel + libération de la mémoire allouée à des facteurs LU creux + + + Séquence d'appel + ludel(hand) + + + Paramètres + + + hand + + pointeur vers des facteurs L,U creux déjà calculés (sortie de lufact) + + + + + + + Description + + Cette fonction est à utiliser conjointement avec lufact. Elle libère la mémoire allouée pour le stockage des facteurs L,U creux renvoyés par lufact. + + + La suite de commandes [p,r]=lufact(A);x=lusolve(p,b);ludel(p); + résout le système linéaire creux A*x = b et libère les facteurs creux dont p est le pointeur. + + + + Voir aussi + + + sparse + + + lufact + + + luget + + + + diff --git a/modules/sparse/help/fr_FR/decomposition/lufact.xml b/modules/sparse/help/fr_FR/decomposition/lufact.xml new file mode 100755 index 000000000..21a82f726 --- /dev/null +++ b/modules/sparse/help/fr_FR/decomposition/lufact.xml @@ -0,0 +1,109 @@ + + + + + lufact + factorisation LU d'une matrice creuse + + + Séquence d'appel + [hand,rk]=lufact(A,prec) + + + Paramètres + + + A + + matrice réelle carrée creuse + + + + + hand + + pointeur vers des facteurs L,U creux + + + + + rk + + entier (rang de A) + + + + + prec + + + vecteur à 2 composantes prec=[eps,reps] (tolérances absolue et relative). + + + + + + + Description + + [hand,rk]=lufact(A) calcule la factorisation LU d'une matrice creuse A. + hand (variable non affichable) est utilisé par lusolve (pour la résolution d'un système linéaire Ax=B) et luget (pour récupérer L et U à partir du pointeur hand). + hand doit être détruit après utilisation (par luget ou lusolve) : ludel(hand); + + + La matrice A n'est pas obligatoirement de rang plein mais doit être carrée + (puisque A est supposée creuse on peut lui ajouter des lignes ou des colonnes nulles pour la rendre carrée). + + + + eps : + + + La valeur absolue qu'un élément de A doit avoir pour être utilisé comme pivot, sauf éventuellement en dernier recours. Ce nombre doit être significativement plus petit que le plus petit élément diagonal attendu dans la matrice. La valeur par défaut est %eps. + + + + + reps : + + + Ce nombre donne le seuil relatif pour les pivots. Il doit être compris entre zéro et un. S'il vaut un, la méthode se comporte comme un pivot total, qui est très lent et qui a tendance à remplir la matrice. S'il est proche de zéro, la méthode de pivotage est de type Markowitz stricte sans utilisation de seuil. Ce seuil est utilisé pour éliminer les pivots qui causeraient une croissance excessive des termes de la matrice. La croissance des éléments est source d'erreurs d'arrondi, et peut avoir lieu même si la matrice est bien conditionnée. Prendre reps grand réduit cette croissance excessive, et donc les erreurs d'arrondi, mais le prendre trop grand risque d'augmenter le temps d'exécution, ainsi que le remplissage de la matrice. La précision peut donc ainsi être dégradée à cause du nombre élevé d'opérations à effectuer à cause du remplissage. Une valeur correcte semble être 0.001 qui est la valeur par défaut (cette valeur par défaut est aussi utilisée si reps>1 ou reps<0). Cette valeur doit être augmentée et la factorisation doit être recommencée si la croissance s'avère trop importante. Changer le seuil sur les pivots n'améliore pas les performances pour les matrices où la croissance est faible, comme c'est souvent le cas pour les matrices mal conditionnées. La valeur par défaut de reps a été choisie pour un usage de lufact avec des matrices à diagonale à peu près dominante (matrices provenant de problèmes de type éléments finis). Pour ces matrices un pivotage diagonal donne les meilleurs résultats. Pour les matrices à diagonale non dominante, on obtient de meilleurs résultats en prenant un seuil plus élevé, comme 0.01 ou 0.1. + + + + + + + Exemples + + + + Voir aussi + + + sparse + + + lusolve + + + luget + + + + diff --git a/modules/sparse/help/fr_FR/decomposition/luget.xml b/modules/sparse/help/fr_FR/decomposition/luget.xml new file mode 100755 index 000000000..68076a9cb --- /dev/null +++ b/modules/sparse/help/fr_FR/decomposition/luget.xml @@ -0,0 +1,105 @@ + + + + + luget + extraction de facteurs LU creux + + + Séquence d'appel + [P,L,U,Q]=luget(hand) + + + Paramètres + + + hand + + pointeur vers des facteurs L,U creux déjà calculés (sortie de lufact) + + + + + P + + matrice de permutation (creuse) + + + + + L + + + matrice creuse, triangulaire inférieure si hand provient de la factorisation d'une matrice régulière. + + + + + U + + matrice carrée creuse, régulière, triangulaire supérieure à diagonale unité. + + + + + Q + + matrice de permutation (creuse) + + + + + + + Description + + [P,L,U,Q]=luget(hand) avec hand obtenue avec la commande [hand,rk]=lufact(A) avec A une matrice creuse, renvoie quatre matrices P,L,U,Q telles que P*L*U*Q=A. + + + La matrice A n'est pas obligatoirement de rang plein mais doit être carrée + (puisque A est supposée creuse on peut lui ajouter des lignes ou des colonnes nulles pour la rendre carrée). + + + Si A est singulière, la matrice L est à colonnes compressées (avec + rk colonnes indépendantes non nulles) : la matrice creuse régulière + Q'*inv(U) compresse les colonnes de A. + + + + Exemples + + + + Voir aussi + + + sparse + + + lusolve + + + luget + + + clean + + + + diff --git a/modules/sparse/help/fr_FR/decomposition/lusolve.xml b/modules/sparse/help/fr_FR/decomposition/lusolve.xml new file mode 100755 index 000000000..e9fc2fe80 --- /dev/null +++ b/modules/sparse/help/fr_FR/decomposition/lusolve.xml @@ -0,0 +1,99 @@ + + + + + lusolve + solveur de système linéaire creux + + + Séquence d'appel + x=lusolve(hand,b) + x=lusolve(A,b) + + + + Paramètres + + + b + + matrice réelle pleine + + + + + A + + matrice réelle carrée creuse inversible + + + + + hand + + pointeur vers des facteurs L,U creux déjà calculés (sortie de lufact) + + + + + x + + matrice réelle pleine + + + + + + Description + + x=lusolve(hand,b) résout le système linéaire + A*x = b, où hand est obtenu par un appel + préliminaire à lufact :[hand,rk]=lufact(A). + + + x=lusolve(A,b) résout le système linéaire creux + A*x = b + + + + Exemples + + + + Voir aussi + + + sparse + + + lufact + + + slash + + + backslash + + + + diff --git a/modules/sparse/help/fr_FR/decomposition/spchol.xml b/modules/sparse/help/fr_FR/decomposition/spchol.xml new file mode 100755 index 000000000..6a74c4fc7 --- /dev/null +++ b/modules/sparse/help/fr_FR/decomposition/spchol.xml @@ -0,0 +1,110 @@ + + + + + spchol + Factorisation de Cholesky creuse + + + Séquence d'appel + [R,P] = spchol(X) + + + Paramètres + + + X + + matrice creuse réelle symétrique et définie positive. + + + + + P + + matrice de permutation + + + + + R + + facteur de Cholesky + + + + + + + Description + + [R,P] = spchol(X) produit une matrice triangulaire inférieure R telle que P*R*R'*P' = X. + + + + Exemples + + + + Voir aussi + + + sparse + + + lusolve + + + luget + + + chol + + + + diff --git a/modules/sparse/help/fr_FR/matrixmanip/CHAPTER b/modules/sparse/help/fr_FR/matrixmanip/CHAPTER new file mode 100755 index 000000000..7a8eeab21 --- /dev/null +++ b/modules/sparse/help/fr_FR/matrixmanip/CHAPTER @@ -0,0 +1 @@ +title = Manipulation des Matrices Creuses diff --git a/modules/sparse/help/fr_FR/matrixmanip/nnz.xml b/modules/sparse/help/fr_FR/matrixmanip/nnz.xml new file mode 100755 index 000000000..89d92c41f --- /dev/null +++ b/modules/sparse/help/fr_FR/matrixmanip/nnz.xml @@ -0,0 +1,64 @@ + + + + + nnz + nombre de termes non nuls dans une matrice + + + Séquence d'appel + n=nnz(X) + + + Paramètres + + + X + + matrice réelle ou complexe (pleine ou creuse) + + + + + n + + entier, le nombre de termes non nuls + + + + + + + Description + + nnz compte le nombre de termes non nuls dans une matrice pleine ou creuse. + + + + Exemples + + + + Voir aussi + + + spget + + + + diff --git a/modules/sparse/help/fr_FR/matrixmanip/speye.xml b/modules/sparse/help/fr_FR/matrixmanip/speye.xml new file mode 100755 index 000000000..191953450 --- /dev/null +++ b/modules/sparse/help/fr_FR/matrixmanip/speye.xml @@ -0,0 +1,84 @@ + + + + speye + matrice identité creuse + + + Séquence d'appel + Isp=speye(nrows,ncols) + Isp=speye(A) + + + + Paramètres + + + nrows + + entier (nombre de lignes) + + + + ncols + + entier (nombre de colonnes) + + + + A + + matrice creuse + + + + sp + + matrice identité creuse + + + + + + Description + + Isp=speye(nrows,ncols) renvoie une matrice + identité creuse Isp avec nrows + lignes et ncols colonnes. + + + Isp=speye(A) renvoie une matrice identité creuse + de même taille que A. Si + [m,n]=size(A), les commandes + speye(m,n) et speye(A) sont + équivalentes. En particulier speye(3) n'est pas + équivalent à speye(3,3). + + + + Exemples + + + + Voir aussi + + + sparse + + + full + + + eye + + + spzeros + + + spones + + + + diff --git a/modules/sparse/help/fr_FR/matrixmanip/spones.xml b/modules/sparse/help/fr_FR/matrixmanip/spones.xml new file mode 100755 index 000000000..31f894370 --- /dev/null +++ b/modules/sparse/help/fr_FR/matrixmanip/spones.xml @@ -0,0 +1,65 @@ + + + + spones + matrice creuse dont les termes valent 1 + + + Séquence d'appel + sp = spones(A) + + + Paramètres + + + A + + matrice creuse + + + + sp + + matrice creuse + + + + + + Description + + sp=spones(A) génère une matrice creuse de même + structure que A, mais où les termes non-nuls ont été + remplacés par la valeur 1. + + + + Exemples + + + + Voir aussi + + + sparse + + + full + + + eye + + + speye + + + spzeros + + + + diff --git a/modules/sparse/help/fr_FR/matrixmanip/sprand.xml b/modules/sparse/help/fr_FR/matrixmanip/sprand.xml new file mode 100755 index 000000000..9ac2048f7 --- /dev/null +++ b/modules/sparse/help/fr_FR/matrixmanip/sprand.xml @@ -0,0 +1,86 @@ + + + + sprand + matrice creuse aléatoire + + + Séquence d'appel + sp=sprand(nrows,ncols,fill [,typ]) + + + Paramètres + + + nrows + + entier (nombre de lignes) + + + + ncols + + entier (nombre de colonnes) + + + + fill + + coefficient de remplissage (densité) + + + + typ + + + chaîne de caractères ('uniform' (par + défaut) ou 'normal') + + + + + sp + + matrice creuse + + + + + + Description + + sp=sprand(nrows,ncols,fill) renvoie une matrice + creuse sp avec nrows lignes, + ncols colonnes et approximativement + fill*nrows*ncols termes non-nuls. + + + Si typ='uniform' les termes non nuls suivent une + loi uniforme sur [0,1]. Si typ='normal' les termes non + nuls suivent une loi normale centrée réduite. + + + + Exemples + + + + Voir aussi + + + sparse + + + full + + + rand + + + speye + + + + diff --git a/modules/sparse/help/fr_FR/matrixmanip/spzeros.xml b/modules/sparse/help/fr_FR/matrixmanip/spzeros.xml new file mode 100755 index 000000000..cc4398e84 --- /dev/null +++ b/modules/sparse/help/fr_FR/matrixmanip/spzeros.xml @@ -0,0 +1,88 @@ + + + + spzeros + matrice creuse nulle + + + Séquence d'appel + sp = spzeros(nrows, ncols) + sp = spzeros(A) + + + + Paramètres + + + nrows + + entier (nombre de lignes) + + + + ncols + + entier (nombre de colonnes) + + + + A + + matrice creuse + + + + sp + + matrice creuse nulle + + + + + + Description + + sp=spzeros(nrows,ncols) renvoie une matrice + creuse nulle sp avec nrows lignes et + ncols colonnes (Équivalent à + sparse([],[],[nrow,ncols])). + + + sp=spzeros(A) renvoie une matrice creuse nulle de + mêmes dimensions que A. Si + [m,n]=size(A), les commandes + spzeros(m,n) et spzeros(A) sont + équivalentes. En particulier spzeros(3) n'est pas + équivalent à spzeros(3,3). + + + + Exemples + + + + Voir aussi + + + sparse + + + full + + + eye + + + speye + + + spones + + + + diff --git a/modules/sparse/help/ja_JP/addchapter.sce b/modules/sparse/help/ja_JP/addchapter.sce new file mode 100755 index 000000000..f63ec568a --- /dev/null +++ b/modules/sparse/help/ja_JP/addchapter.sce @@ -0,0 +1,11 @@ +// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab +// Copyright (C) 2009 - DIGITEO +// +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + +add_help_chapter("Sparses Matrix",SCI+"/modules/sparse/help/ja_JP",%T); + diff --git a/modules/sparse/help/ja_JP/chfact.xml b/modules/sparse/help/ja_JP/chfact.xml new file mode 100755 index 000000000..867ce4744 --- /dev/null +++ b/modules/sparse/help/ja_JP/chfact.xml @@ -0,0 +1,148 @@ + + + + + + + + + chfact + + 疎行列のコレスキー分解 + + + + + + 呼び出し手順 + + spcho=chfact(A) + + + + + + 引数 + + + + + + A + + + + 正方正定対称疎行列 + + + + + + + + spcho + + + + コード形式のコレスキー分解を含むリスト + + + + + + + + + + + + 説明 + + + + spcho=chfact(A) は, + + 正定対称行列と仮定して疎行列Aの + + コレスキー分解を計算します. + + この関数は,Ng-Peyton プログラム (ORNL)に基づいています. + + spchoの変数の詳細な説明については, + + Fortran プログラムを参照ください. + + この関数は chsolveと共に使用されます. + + + + + + + + 例 + + + + + + + + 参照 + + + + + + chsolve + + + + + + sparse + + + + + + lufact + + + + + + luget + + + + + + spchol + + + + + + + + + diff --git a/modules/sparse/help/ja_JP/chsolve.xml b/modules/sparse/help/ja_JP/chsolve.xml new file mode 100755 index 000000000..8a95951ba --- /dev/null +++ b/modules/sparse/help/ja_JP/chsolve.xml @@ -0,0 +1,145 @@ + + + + + + + + + chsolve + + 疎行列のコレスキーソルバ + + + + + + 呼び出し手順 + + sol=chsolve(spcho,rhs) + + + + + + 引数 + + + + + + spcho + + + + chfact から返されたコード形式のコレスキー分解を含むリスト + + + + + + + + rhs, sol + + + + フル列ベクトル + + + + + + + + + + + + 説明 + + + + sol=chsolve(spcho,rhs) は, + + Aを疎行列の正定対称行列として + + rhs=A*solの解を計算します. + + この関数は,Ng-Peyton プログラム (ORNL)に基づいています. + + spchoの変数の詳細な説明については, + + Fortran プログラムを参照ください. + + + + + + + + 例 + + + + + + + + 参照 + + + + + + chfact + + + + + + sparse + + + + + + lufact + + + + + + luget + + + + + + spchol + + + + + + + + + diff --git a/modules/sparse/help/ja_JP/decomposition/CHAPTER b/modules/sparse/help/ja_JP/decomposition/CHAPTER new file mode 100755 index 000000000..ccebc80d8 --- /dev/null +++ b/modules/sparse/help/ja_JP/decomposition/CHAPTER @@ -0,0 +1 @@ +title = Sparse Decompositions diff --git a/modules/sparse/help/ja_JP/decomposition/ludel.xml b/modules/sparse/help/ja_JP/decomposition/ludel.xml new file mode 100755 index 000000000..30ccb122d --- /dev/null +++ b/modules/sparse/help/ja_JP/decomposition/ludel.xml @@ -0,0 +1,126 @@ + + + + + + + + + ludel + + lufactで使用されるユーティリティ関数 + + + + + + 呼び出し手順 + + ludel(hand) + + + + + + 引数 + + + + + + hand + + + + 疎行列LU分解のハンドル (lufactの出力) + + + + + + + + + + + + 説明 + + + + この関数は,lufactと組み合わせて使用されます. + + この関数は,lufactの結果を保存するために使用される + + 内部メモリ空間を消去します. + + + + + + 一連のコマンド,[p,r]=lufact(A);x=lusolve(p,b);ludel(p); + + により線形疎行列システムA*x = bを解き, + + pを消去することができます. + + + + + + + + 例 + + + + + + + + 参照 + + + + + + sparse + + + + + + lufact + + + + + + luget + + + + + + + + + diff --git a/modules/sparse/help/ja_JP/decomposition/lufact.xml b/modules/sparse/help/ja_JP/decomposition/lufact.xml new file mode 100755 index 000000000..49e6e99c4 --- /dev/null +++ b/modules/sparse/help/ja_JP/decomposition/lufact.xml @@ -0,0 +1,271 @@ + + + + + + + + + lufact + + 疎行列LU分解 + + + + + + 呼び出し手順 + + [hand,rk]=lufact(A,prec) + + + + + + 引数 + + + + + + A + + + + 正方疎行列 + + + + + + + + hand + + + + 疎行列LU分解へのハンドル + + + + + + + + rk + + + + 整数 (Aのランク) + + + + + + + + prec + + + + + + 大きさ2のベクトルprec=[eps,reps]で, + + 絶対および相対閾値を指定します. + + + + + + + + + + + + + + 説明 + + + + [hand,rk]=lufact(A)は, + + 疎行列AのLU分解を行ないます. + + hand (表示されません) が, + + (線形システムを解く)lusolveおよび + + (LU分解を取得する)lugetで + + 使用されます. + + hand は以下のコマンドにより消去します: ludel(hand); + + + + + + 行列Aは,フルランクである必要はありませんが,正方である必要があります + + (Aは疎行列であると仮定されるため,必要に応じてAの下に正方にするための + + ゼロを追加することができます). + + + + + + + + eps : + + + + + + 最終的に要素がピボットの候補とみなされる大きさ. + + この数は行列の中で存在すると思われる最も小さい対角項よりも + + 著しく小さな値に設定する必要があります. + + デフォルトは%epsです. + + + + + + + + + + reps : + + + + この数は,ピポット相対閾値を定義します. + + この値は,0と1の間とする必要があります. + + 1の場合,ピボット選択は完全ピボット選択となり, + + 非常に遅く,通常の行列に近くなるまで要素が埋められる + + 傾向があります. 0 に近い値を設定した場合, + + ピボット選択は閾値なしの厳密なMarkowitz法となります. + + ピボットの閾値はこれらが使用された場合には + + 要素が増加しすぎるようなピボット候補を消去する際に使用されます. + + 要素の増加が丸め誤差の原因です. + + 要素の増加は条件の良い行列においても発生します. + + reps に大きな値を設定することで, + + 要素の増加と丸め誤差が減少しますが, + + 大きすぎる値を設定すると実行時間が過大となり, + + 代入の数が過大となります. + + このような場合, + + 多くの代入に必要な行列の操作の回数が多くなるため,実際の + + 精度は低下します. + + 良い値は 0.001 と思われ,これがデフォルト値です. + + このデフォルト値は,1より大きいか,0以下の値を指定することにより + + 選択されます. + + この値は,過度な要素数の増加が認められた場合には, + + 増加させ,行列を決定する必要があります. + + ピボット閾値の変更は,要素数の増加が小さい行列においては, + + 条件が悪い行列において期待されるような性能の改善効果を, + + 得ることはできません. + + reps は, ノードおよび修正ノードアドミタンス行列のような + + 近似的に対角優位の行列で使用するように選択されています. + + これらの行列では,通常は対角ピボット選択を使用するのが最良です. + + 大きな対角項がない行列の場合は, + + 通常は0.01または0.1のようなより大きな閾値を使用するのが最善です. + + + + + + + + + + + + + + 例 + + + + + + + + 参照 + + + + + + sparse + + + + + + lusolve + + + + + + luget + + + + + + + + + diff --git a/modules/sparse/help/ja_JP/decomposition/luget.xml b/modules/sparse/help/ja_JP/decomposition/luget.xml new file mode 100755 index 000000000..c5a2b3943 --- /dev/null +++ b/modules/sparse/help/ja_JP/decomposition/luget.xml @@ -0,0 +1,202 @@ + + + + + + + + + luget + + 疎行列LU分解の展開 + + + + + + 呼び出し手順 + + [P,L,U,Q]=luget(hand) + + + + + + 引数 + + + + + + hand + + + + + + ハンドル, lufactの出力 + + + + + + + + + + P + + + + 疎交換行列 + + + + + + + + L + + + + + + 疎行列, lower triangular if handが + + 正則行列から得られた場合は上三角 + + + + + + + + + + U + + + + 正方正則上三角疎行列(主対角項は1) + + + + + + + + Q + + + + 疎交換行列 + + + + + + + + + + + + 説明 + + + + 疎行列 Aに関して + + コマンド[hand,rk]=lufact(A)により得られた + + handを指定すると,[P,L,U,Q]=luget(hand) + + は,P*L*U*Q=Aとなるような4つの疎行列を返します. + + + + + + 行列Aはフルランクである必要はありませんが正方行列である必要があります + + (Aは疎行列と仮定されるため,正方化するために必要に応じて0を追加することができます). + + + + + + Aが正則でない場合, + + 行列Lは(rk個の + + 独立した非ゼロ列について)列圧縮されます + + 正則な疎行列 Q'*inv(U) は + + Aを列圧縮します. + + + + + + + + 例 + + + + + + + + 参照 + + + + + + sparse + + + + + + lusolve + + + + + + luget + + + + + + clean + + + + + + + + + diff --git a/modules/sparse/help/ja_JP/decomposition/lusolve.xml b/modules/sparse/help/ja_JP/decomposition/lusolve.xml new file mode 100755 index 000000000..a0befa06e --- /dev/null +++ b/modules/sparse/help/ja_JP/decomposition/lusolve.xml @@ -0,0 +1,175 @@ + + + + + + + + + lusolve + + 疎な線形システムの解を得る + + + + + + 呼び出し手順 + + x=lusolve(hand,b) + + x=lusolve(A,b) + + + + + + + + 引数 + + + + + + b + + + + 通常の実数行列 + + + + + + + + A + + + + 可逆な実数正方疎行列 + + + + + + + + hand + + + + 疎行列LU分解を計算した際のハンドル(lufactの出力) + + + + + + + + x + + + + 通常の実数行列 + + + + + + + + + + + + 説明 + + + + x=lusolve(hand,b) は疎な線形システム + + A*x = bを解きます. + + + + + + [hand,rk]=lufact(A) は lufact の出力です. + + + + + + x=lusolve(A,b)は,疎な線形システム + + A*x = bを解きます. + + + + + + + + 例 + + + + + + + + 参照 + + + + + + sparse + + + + + + lufact + + + + + + slash + + + + + + backslash + + + + + + + + + diff --git a/modules/sparse/help/ja_JP/decomposition/spchol.xml b/modules/sparse/help/ja_JP/decomposition/spchol.xml new file mode 100755 index 000000000..f9369d81b --- /dev/null +++ b/modules/sparse/help/ja_JP/decomposition/spchol.xml @@ -0,0 +1,173 @@ + + + + + + + + + spchol + + 疎行列コレスキー分解 + + + + + + 呼び出し手順 + + [R,P] = spchol(X) + + + + + + 引数 + + + + + + X + + + + 対称正定実疎行列 + + + + + + + + P + + + + 順列行列 + + + + + + + + R + + + + コレスキー分解 + + + + + + + + + + + + 説明 + + + + [R,P] = spchol(X) は, + + P*R*R'*P' = Xとなるような + + 上三角行列R を出力します. + + + + + + + + 例 + + + + + + + + 参照 + + + + + + sparse + + + + + + lusolve + + + + + + luget + + + + + + chol + + + + + + + + + diff --git a/modules/sparse/help/ja_JP/iterativesolvers/CHAPTER b/modules/sparse/help/ja_JP/iterativesolvers/CHAPTER new file mode 100755 index 000000000..c59edd550 --- /dev/null +++ b/modules/sparse/help/ja_JP/iterativesolvers/CHAPTER @@ -0,0 +1 @@ +title = Linear Equations (Iterative Solvers) diff --git a/modules/sparse/help/ja_JP/iterativesolvers/conjgrad.xml b/modules/sparse/help/ja_JP/iterativesolvers/conjgrad.xml new file mode 100755 index 000000000..a8c61a1bb --- /dev/null +++ b/modules/sparse/help/ja_JP/iterativesolvers/conjgrad.xml @@ -0,0 +1,402 @@ + + + + + conjgrad + 共役勾配ソルバ + + + 呼び出し手順 + + [x, flag, err, iter, res] = conjgrad(A, b [, method [, tol [, maxIter [, M [, M2 [, x0 [, verbose]]]]]]]) + [x, flag, err, iter, res] = conjgrad(A, b [, method [, key=value,...]]) + + + + 引数 + + + A + + + + 指令した各xについてA*xを計算する + 行列または関数またはリスト. + Aのそれぞれの型に関する A*x の計算に関して以下に示します. + + + + + 行列.Aが行列の場合, 通常または疎行列が使用可能 + + + + + 関数.Aが関数の場合, 以下のヘッダを有する + 必要があります : + + + + + + リスト.Aがリストの場合, + リストの最初の要素には関数を指定し, + 添字2から最後までのリストの他の要素には関数の引数を指定します. + この関数がコールされた際, + xのカレントの値が関数の最初の引数に指定され, + その他の引数にはリストで指定されたものが指定されます. + + + + + + + b + + 右辺ベクトル (大きさ: nx1) + + + + mehtod + + スカラー文字列, "pcg", "cgs", "bicg" または "bicgstab" (デフォルト "bicgstab") + + + + tol + + 相対許容誤差 (デフォルト: 1e-8). + 終了基準は残差 r=b-Ax の二乗ノルムを右辺 b の二乗ノルムで割ったものに + 基づきます. + + + + + maxIter + + 最大反復回数 (デフォルト: n) + + + + M + + プリコンディショナ: 通常または疎行列または + M\x を返す関数 (デフォルト: none) + + + + + M2 + + + プリコンディショナ: 通常または疎行列または各xの + M2\x を返す関数 (デフォルト: none) + + + + + x0 + + 初期推定ベクトル (デフォルト: zeros(n,1)) + + + + verbose + + 冗長なログを有効にする場合は1を指定 (デフォルト 0) + + + + x + + 解ベクトル + + + + flag + + + conjgrad が反復回数maxi以内に + 許容誤差以内に収束した場合は 0, + それ以外は 1 + + + + + err + + 残差ノルムの最終値 (右辺 b の二乗ノルムを使用) + + + + iter + + 実行した反復回数 + + + + res + + 相対ノルム残差のベクトル + + + + + + 説明 + + プリコンディショニング有りまたは無しの + 共役勾配法により線形システムAx=b を解きます. + プリコンディショナは対称正定行列M,または + M=M1*M2となる2つの行列 + M1とM2 + により定義されます. + この場合,この関数はinv(M)*A*x = inv(M)*bを + xについて解きます. + M, M1 および + M2 は, 呼び出し手順y=Milx(x) + で対応する左除算y=Mi\xを計算するScilab関数と + することができます. + + + 入力引数 method は,使用するソルバを指定します: + + + "pcg" プリコンディショナ付き共役勾配法 + + + "cgs" プリコンディショナ付き二乗共役勾配法 + + + "bicg" プリコンディショナ付き双共役勾配法 + + + "bicgstab" プリコンディショナ付き安定化双共役勾配法 (デフォルト) + + + + + method="pcg"の場合, A 行列は + 対称正定行列(通常または疎行列)または呼び出し手順y=Ax(x)で + y=A*xを計算する関数とする必要があります. + その他の場合 (method="cgs", "bicg" or "bicgstab"), + A は正方行列であることのみ必要です. + + + + 良条件および悪条件の問題の例 + + + 以下の例では, 2つの線形システムを解きます. + 最初の行列は条件数が ~0.02で,アルゴリズムは10回で収束します. + これは行列の大きさと同じで,共役勾配法で期待される動作です. + 2番目の行列は条件数が1.d-6と小さく,アルゴリズムは収束までに22回と + より多くの反復を要します.これがパラメータ maxIter が 30 に設定されている + 理由です. + "key=value" 構文の他の例については以下を参照ください. + + + + + Aに疎行列または関数またはリストを指定する例 + + + 以下の例は,この手法が疎行列を同様に処理できることを示すものです. + また,この例は右辺を計算する関数を"conjgrad"のプリミティブに指定する + ケースも示します. + この例の最後のケースは, + リストをプリミティブに指定すた場合です. + + + + + key=value 構文の例 + + 以下の例は"key=value"構文で引数を指定する方法を示すものです. + これにより,位置を固定せずに引数を指定でき, + つまり, 引数リストにおける順序に依存せずに, + 引数を設定できます. + 有効なキーはオプション引数の名前,つまり, + tol, maxIter, %M, %M2, x0, verbose です. + 以下の例では, verbose オプションが maxIterオプションの + 前に指定されていることに注意してください. + "key=value"構文ではない場合は引数の位置が固定されるため, + maxIter は先, verbose は後で使用する必要があります. + + + + + 参照 + + + backslash + + + qmr + + + gmres + + + + + 参考文献 + + PCG + + "Templates for the Solution of Linear Systems: Building Blocks for + Iterative Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra, + Eijkhout, Pozo, Romine, and Van der Vorst, SIAM Publications, 1993, ftp + netlib2.cs.utk.edu/linalg/templates.ps + + "Iterative Methods for Sparse Linear Systems, Second Edition", Saad, + SIAM Publications, 2003, ftp + ftp.cs.umn.edu/dept/users/saad/PS/all_ps.zip + + + CGS + + + "CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems" by Peter Sonneveld. + + + Original article + + + Article on ACM + + + Some theory around CGS + + + BICG + + + "Numerical Recipes: The Art of Scientific Computing." (third ed.) by William Press, Saul Teukolsky, William Vetterling, Brian Flannery. + + + http://apps.nrbook.com/empanel/index.html?pg=87 + + + Article on ACM + + + Some theory around BICG + + + BICGSTAB + + + "Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems" by Henk van der Vorst. 339 + + + Original article + + + Article on ACM + + + Some theory around BICG + + + + 履歴 + + + 5.5.0 + + 導入 + + + + + diff --git a/modules/sparse/help/ja_JP/iterativesolvers/gmres.xml b/modules/sparse/help/ja_JP/iterativesolvers/gmres.xml new file mode 100755 index 000000000..46bff29f2 --- /dev/null +++ b/modules/sparse/help/ja_JP/iterativesolvers/gmres.xml @@ -0,0 +1,406 @@ + + + + + + + + + gmres + + Generalized Minimum RESidual 法 + + + + + + 呼び出し手順 + + [x,flag,err,iter,res] = gmres(A,b,[rstr,[tol,[maxi,[M,[x0]]]]]) + + + + + + 引数 + + + + + + A + + + + + + n行n列行列またはA*xを返す関数. + + Aが関数の場合,以下のようなヘッダを有すること: + + + + + + + + + + + + b + + + + 右辺ベクトル + + + + + + + + x0 + + + + 初期推定値ベクトル(デフォルト: zeros(n,1)) + + + + + + + + M + + + + + + プリコンディショナ: n行n列行列（デフォルト: eye(n,n)）または + + M*xを返す関数. + + M が関数の場合,以下のようなヘッダを有すること: + + + + + + + + + + + + rstr + + + + リスタートまでの反復回数 (デフォルト: 10) + + + + + + + + maxi + + + + 最大反復回数 (デフォルト: n) + + + + + + + + tol + + + + 許容誤差 (デフォルト: 1e-6) + + + + + + + + x + + + + 解のベクトル + + + + + + + + err + + + + 最終残差ノルム + + + + + + + + iter + + + + 実行した反復回数 + + + + + + + + flag + + + + + + + + 0 = + + + + + + gmresは, + + maxi回の反復内に + + 指定した許容誤差に収束しました + + + + + + + + + + 1 = + + + + + + 指定した maxi回では収束しませんでした + + + + + + + + + + + + + + + + res + + + + 残差ベクトル + + + + + + + + + + + + 説明 + + + + + + GMRES + + + + + + 線形システムAx=bをリスタート付きの + + Generalized Minimal residual法により解きます. + + + + + + + + + + 詳細 + + + + このアルゴリズムの詳細は以下の文献に記述されています : + + "Templates for the Solution of Linear Systems: Building Blocks for + + Iterative Methods", Barrett, Berry, Chan, Demmel, Donato, Dongarra, + + Eijkhout, Pozo, Romine, and Van der Vorst, SIAM Publications, 1993 (ftp + + netlib2.cs.utk.edu; cd linalg; get templates.ps). + + + + "Iterative Methods for Sparse Linear Systems, Second Edition" Saad, + + SIAM Publications, 2003 (ftp ftp.cs.umn.edu; cd dept/users/saad/PS; get + + all_ps.zip). + + + + + + + + + + + + + + 例 + + + + + + + + 参照 + + + + + + conjgrad + + + + + + qmr + + + + + + + + + diff --git a/modules/sparse/help/ja_JP/iterativesolvers/qmr.xml b/modules/sparse/help/ja_JP/iterativesolvers/qmr.xml new file mode 100755 index 000000000..5d5b392b4 --- /dev/null +++ b/modules/sparse/help/ja_JP/iterativesolvers/qmr.xml @@ -0,0 +1,490 @@ + + + + + + + + + qmr + + プリコンディショナ付きのQuasi Minimal Residual法 + + + + + + 呼び出し手順 + + [x,flag,err,iter,res] = qmr(A,b,x0,M1,M1p,M2,M2p,maxi,tol) + + + + + + Parameters + + + + + + A + + + + + + 大きさn行n列の行列またはA*xを返す関数 + + + + + + + + + + b + + + + 右辺ベクトル + + + + + + + + x0 + + + + 初期推定ベクトル (デフォルト: zeros(n,1)) + + + + + + + + M1 + + + + + + 左プリコンディショナ: 行列またはM1*xを返す関数 + + (前者のデフォルト値: eye(n,n)) + + + + + + + + + + M1p + + + + + + M1が関数の場合のみ指定する + + 必要があります. この場合, M1p は + + M1'*xを返す関数です. + + + + + + + + + + M2 + + + + + + 右プリコンディショナ: 行列またはM2*xを + + 返す関数 (前者のデフォルト値: eye(n,n)) + + + + + + + + + + M2p + + + + + + M2が関数の場合のみ指定する + + 必要があります. この場合, + + M2pはM2'*xを返す関数です. + + + + + + + + + + maxi + + + + 最大反復回数 (デフォルト: n) + + + + + + + + + + tol + + + + 許容誤差 (デフォルト: 1000*%eps) + + + + + + + + x + + + + 解ベクトル + + + + + + + + flag + + + + + + + + 0 = + + + + + + gmres は + + maxi回の反復の間に + + 許容誤差内に収束しました + + + + + + + + + + 1 = + + + + + + 指定したmaxi回の反復の間に + + 収束しませんでした + + + + + + + + + + + + + + + + res + + + + 残差ベクトル + + + + + + + + err + + + + 最終残差ノルム + + + + + + + + iter + + + + 実行した反復回数 + + + + + + + + + + + + 説明 + + + + プリコンディショナ付きのQuasi Minimal Residual法により, + + 線形システムAx=bを解きます. + + + + + + + + 例 + + + + + + + + 参照 + + + + + + gmres + + + + + + conjgrad + + + + + + + + + + 履歴 + + + + + + 5.4.0 + + + + qmr(A, Ap) のコールは廃止されました. + + qmr(A) を代わりに使用してください. + + 以下の関数が例となります : + + + + + + + + + + + + + diff --git a/modules/sparse/help/ja_JP/matrixmanip/CHAPTER b/modules/sparse/help/ja_JP/matrixmanip/CHAPTER new file mode 100755 index 000000000..a797a77e1 --- /dev/null +++ b/modules/sparse/help/ja_JP/matrixmanip/CHAPTER @@ -0,0 +1 @@ +title = Sparse Matrix Manipulation diff --git a/modules/sparse/help/ja_JP/matrixmanip/issparse.xml b/modules/sparse/help/ja_JP/matrixmanip/issparse.xml new file mode 100755 index 000000000..19ce3bf8d --- /dev/null +++ b/modules/sparse/help/ja_JP/matrixmanip/issparse.xml @@ -0,0 +1,69 @@ + + + + + issparse + 入力値が疎行列かどうかを調べる + + + 呼び出し手順 + res = issparse(S) + + + 引数 + + + S + + scilabオブジェクト + + + + res + + 1: 行列は疎行列, 0: その他 + + + + + + 説明 + + res = issparse(S) は、S が疎行列の時に1, + それ以外の時に0を返します. + + + + 例 + sp = sparse([1,2;4,5;3,10],[1,2,3]); + if issparse(sp) == 1 then + disp("It is a sparse"); + end + A = 1; + if issparse(A) == 0 then + disp("It is not a sparse"); + end + + + + 参照 + + + type + + + typeof + + + + diff --git a/modules/sparse/help/ja_JP/matrixmanip/nnz.xml b/modules/sparse/help/ja_JP/matrixmanip/nnz.xml new file mode 100755 index 000000000..c0826a9ea --- /dev/null +++ b/modules/sparse/help/ja_JP/matrixmanip/nnz.xml @@ -0,0 +1,111 @@ + + + + + + + + + nnz + + 行列における非ゼロ要素の数 + + + + + + 呼び出し手順 + + n=nnz(X) + + + + + + 引数 + + + + + + X + + + + 実数または複素疎(または通常)行列 + + + + + + + + n + + + + 整数, Xの非ゼロ要素の数 + + + + + + + + + + + + 説明 + + + + nnz は疎行列または通常の行列における + + 非ゼロ要素の数を数えます. + + + + + + + + 例 + + + + + + + + 参照 + + + + + + spget + + + + + + + + + diff --git a/modules/sparse/help/ja_JP/matrixmanip/speye.xml b/modules/sparse/help/ja_JP/matrixmanip/speye.xml new file mode 100755 index 000000000..b224401de --- /dev/null +++ b/modules/sparse/help/ja_JP/matrixmanip/speye.xml @@ -0,0 +1,182 @@ + + + + + + + + + speye + + 疎単位行列 + + + + + + 呼び出し手順 + + Isp=speye(nrows,ncols) + + Isp=speye(A) + + + + + + + + 引数 + + + + + + nrows + + + + 整数 (行数) + + + + + + + + ncols + + + + 整数 (列数) + + + + + + + + A + + + + 疎行列 + + + + + + + + sp + + + + 疎単位行列 + + + + + + + + + + + + 説明 + + + + Isp=speye(nrows,ncols) は, + + nrows 行, + + ncols 列の + + 疎単位行列Ispを返します. + + (非正方行列は主対角項に1を有します). + + + + + + Isp=speye(A)はAと + + 同じ次元の疎単位行列を返します. + + [m,n]=size(A)の場合, speye(m,n) および + + speye(A)は等価です. なお, + + speye(3) は + + speye(3,3)と等価ではありません. + + + + + + + + 例 + + + + + + + + 参照 + + + + + + sparse + + + + + + full + + + + + + eye + + + + + + spzeros + + + + + + spones + + + + + + + + + diff --git a/modules/sparse/help/ja_JP/matrixmanip/spones.xml b/modules/sparse/help/ja_JP/matrixmanip/spones.xml new file mode 100755 index 000000000..64971b973 --- /dev/null +++ b/modules/sparse/help/ja_JP/matrixmanip/spones.xml @@ -0,0 +1,137 @@ + + + + + + + + + spones + + 疎行列 + + + + + + 呼び出し手順 + + sp=spones(A) + + + + + + 引数 + + + + + + A + + + + 疎行列 + + + + + + + + sp + + + + 疎行列 + + + + + + + + + + + + 説明 + + + + sp=spones(A) は + + Aと同じ疎構造を有し + + その非ゼロ要素の位置に1を有する,行列を生成します. + + + + + + + + 例 + + + + + + + + 参照 + + + + + + sparse + + + + + + full + + + + + + eye + + + + + + speye + + + + + + spzeros + + + + + + + + + diff --git a/modules/sparse/help/ja_JP/matrixmanip/sprand.xml b/modules/sparse/help/ja_JP/matrixmanip/sprand.xml new file mode 100755 index 000000000..6aacb19fa --- /dev/null +++ b/modules/sparse/help/ja_JP/matrixmanip/sprand.xml @@ -0,0 +1,332 @@ + + + + + + + + + sprand + + ランダム疎行列 + + + + + + 呼び出し手順 + + sp=sprand(nrows,ncols,density [,typ]) + + + + + + 引数 + + + + + + nrows + + + + 整数 (行数) + + + + + + + + ncols + + + + 整数 (列数) + + + + + + + + density + + + + 占有率 (密度) + + + + + + + + typ + + + + + + 文字列, "uniform" (デフォルト) または + + "normal" + + + + + + + + + + sp + + + + 疎行列 + + + + + + + + + + + + 説明 + + + + sp=sprand(nrows,ncols,density) は, + + nrows 行ncols列, + + 近似的にdensity*nrows*ncols個の非ゼロ + + エントリを有する疎行列spを返します. + + + + + + densityパラメータは + + [0,1] の範囲で指定されます. + + そうでない場合, + + 自動的にこの範囲に変換されます. + + このため, 0 より小さいか 1より大きい density を使用しても, + + エラーも警告も発生しません: + + 式density=max(min(density,1),0)が使用されます. + + + + + + typ="uniform"の場合, 一様分布の + + 値 [0,1]が生成されます. + + typ="normal" の場合,正規分布の + + 値が生成されます (平均=0 および標準偏差=1). + + + + + + 出力行列のエントリは指定された分布関数typに + + 基づき計算されます. + + 非ゼロ要素のインデックスはランダムに計算され, + + 非ゼロの平均的な数はdensityとなります. + + 実際のインデックスの値は,指数分布関数により計算されます. + + ただし,分布関数のパラメータは同時に計算されます. + + + + + + + + 例 + + + + 以下の例では,近似的に密度0.001の + + 100x1000疎行列を生成します. + + すなわち,およそ 100*1000*0.001=100個の非ゼロエントリとなります. + + + + + + + + 以下のスクリプトは, + + 行列のエントリが指定した分布を有することを確認します. + + 非ゼロエントリを取得するためにspget関数を用います. + + 次に,エントリの最小値,最大値,平均を計算し, + + limit値と比較します. + + + + + + + + 以下のスクリプトでは,ランダムに選択したエントリのインデックスを調べ, + + 正しい分布を有することを確認します. + + 一様分布のkmaxランダム疎行列を生成します. + + ここで,各行列について,生成する非ゼロのエントリのインデックスについて + + 考えます. + + すなわち, + + i=1,2,...,nrows + + および j=1,2,...,ncolsｒとなる + + 各i および jについて + + イベント Aij = {エントリ (i,j) が非ゼロ} + + が発生するかどうかを調べます. + + 行列C(i,j)はイベントAij + + が発生する回数を保存します. + + 行列 R(k) は,k=1,2,...,kmax + + について試行回数kの実際の密度を保存します. + + + + 0); + NZratio = size(NZ,"*")/(nrows*ncols); + R=[R NZratio]; + C(NZ)=C(NZ)+1; + end + ]]> + + + + このアルゴリズムが実行される場合(時々必要となる可能性があります), + + アルゴリズムが正しく実行されていることを確認するために + + 要素の統計値を計算することができます. + + + + + + + + + + 参照 + + + + + + sparse + + + + + + full + + + + + + rand + + + + + + speye + + + + + + + + + diff --git a/modules/sparse/help/ja_JP/matrixmanip/spzeros.xml b/modules/sparse/help/ja_JP/matrixmanip/spzeros.xml new file mode 100755 index 000000000..f4128e96f --- /dev/null +++ b/modules/sparse/help/ja_JP/matrixmanip/spzeros.xml @@ -0,0 +1,100 @@ + + + + + spzeros + 疎ゼロ行列 + + + 呼び出し手順 + sp=spzeros(nrows,ncols) + sp=spzeros(A) + + + + パラメータ + + + nrows + + 整数 (行数) + + + + ncols + + 整数 (列数) + + + + A + + 疎行列 + + + + sp + + 疎ゼロ行列 + + + + + + 説明 + + sp=spzeros(nrows,ncols)は, + nrows 行, + ncols 列の + 疎ゼロ行列を返します. + (sparse([],[],[nrow,ncols])と等価です) + + + sp=spzeros(A) は, + Aと同じ次元を有する疎ゼロ行列を返します. + [m,n]=size(A)の場合, spzeros(m,n) および + spzeros(A) は等価です. なお, + spzeros(3) は + spzeros(3,3)と等しくなりません. + + + + 例 + + + + 参照 + + + sparse + + + full + + + eye + + + speye + + + spones + + + + diff --git a/modules/sparse/help/ja_JP/ordmmd.xml b/modules/sparse/help/ja_JP/ordmmd.xml new file mode 100755 index 000000000..6095241eb --- /dev/null +++ b/modules/sparse/help/ja_JP/ordmmd.xml @@ -0,0 +1,388 @@ + + + + + + + + + ordmmd + + + + 複数の最小次元順序付けを計算する + + + + + + + + 呼び出し手順 + + + + [perm,invp,nofsub]=ordmmd(xadj,iadj,n) + + + + + + + + 引数 + + + + + + n + + + + double、整数値の1行1列の行列,方程式の数 + + + + + + + + xadj + + + + double、整数値の(n+1)行1列の行列,Aの行へのポインタ + + + + + + + + iadj + + + + double、整数値のnnz行1列の行列,Aの行添字 + + + + + + + + perm + + + + double、整数値のn行1列の行列,最小次元規則配列 + + + + + + + + invp + + + + double、整数値のn行1列の行列,permの逆行列 + + + + + + + + nofsub + + + + + + double、整数値の1行1列の行列,圧縮記憶方式における非ゼロ要素の数の上限 + + + + + + + + + + + + + + 説明 + + + + コレスキー分解を適用する前に対称疎行列の行および列を交換する際に + + 最小次元アルゴリズムが使用されます. + + このアルゴリズムはコレスキー分解の非ゼロ要素の数を減らします. + + + + + + n行n列の実対称疎行列Aを指定すると, + + このコレスキー分解 U は,通常, + + Aの上三角要素よりも非ゼロ要素が多くなる + + "塗りつぶし(fill in)"に苦しめられます. + + 行列P'*A*Pが同じく対称で, + + そのコレスキー分解の非ゼロ要素の数が最小となる + + 交換行列 Pを探します. + + + + + + + + 例 + + + + 以下の例では,対称疎行列の順序付けを計算します. + + 隣接構造体を計算する際にsp2adj を使用します. + + + + + + + + 以下の例では,対称疎行列の順序付けを計算します. + + invpがpermの + + 逆行列であることを確認します. + + + + + + + + 以下の例では, 行列Aと行列P'*A*P + + のコレスキー分解の疎パターンを計算します. + + "Computer Solution of Large Sparse Positive Definite Systems"のp.3 "Chapter 1: Introduction"を参照. + + コレスキー分解の非ゼロ要素の数は15,一方,行列P'*A*Pのコレスキー分解は + + 9個の非ゼロ要素を有することがわかります. + + + + + + + + A = [ + + 4. 1. 2. 0.5 2. + + 1. 0.5 0. 0. 0. + + 2. 0. 3. 0. 0. + + 0.5 0. 0. 0.625 0. + + 2. 0. 0. 0. 16. + + ]; + + A = sparse(A); + + U = sparse(chol(full(A))); + + scf(); + + subplot(2,1,1); + + PlotSparse(U,"x"); + + xtitle("Sparsity pattern of U, such that A=U''*U"); + + [xadj,iadj,val]=sp2adj(A); + + n = size(A,"r"); + + [perm,invp,nofsub]=ordmmd(xadj,iadj,n); + + P=spzeros(n,n); + + for i=1:n + + P(perm(i),i)=1; + + end + + U = sparse(chol(full(P'*A*P))); + + subplot(2,1,2); + + PlotSparse(U,"x"); + + xtitle("Sparsity pattern of U, such that P''*A*P=U''*U"); + + + + + + + + 実装に関する注記 + + + + この関数はMathematical Sciences Section, Oak Ridge National Laboratoryの + + Esmond G. Ng および Barry W. Peytonによる + + ソースコード "ordmmd.f",に基づいています. + + アルゴリズムはSPARSPAKライブラリのJoseph W.H. Liuによる genmmdルーチンに基づいています. + + + + + + + + 参考文献 + + + + "Minimum degree algorithm", Wikipedia contributors, Wikipedia, The Free Encyclopedia. http://en.wikipedia.org/wiki/Minimum_degree_algorithm + + + + + + "A new release of SPARSPAK: the Waterloo sparse matrix package", Alan George and Esmond Ng. 1984. SIGNUM Newsl. 19, 4 (October 1984), 9-13. + + + + + + "Computer Solution of Large Sparse Positive Definite Systems" by Alan George and Joseph Liu, Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1981 + + + + + + "Implementation of Lipsol in Scilab", Rubio Scola, 1997, INRIA, No 0215 + + + + + + + + 参照 + + + + + + sp2adj + + + + + + spchol + + + + + + + + + diff --git a/modules/sparse/help/ja_JP/sparseconvert/CHAPTER b/modules/sparse/help/ja_JP/sparseconvert/CHAPTER new file mode 100755 index 000000000..42d5e0bf2 --- /dev/null +++ b/modules/sparse/help/ja_JP/sparseconvert/CHAPTER @@ -0,0 +1 @@ +title = Sparse Matrix Conversion diff --git a/modules/sparse/help/ja_JP/sparseconvert/adj2sp.xml b/modules/sparse/help/ja_JP/sparseconvert/adj2sp.xml new file mode 100755 index 000000000..816ab53b8 --- /dev/null +++ b/modules/sparse/help/ja_JP/sparseconvert/adj2sp.xml @@ -0,0 +1,384 @@ + + + + + + + + + adj2sp + + 隣接形式を疎行列に変換. + + + + + + 呼び出し手順 + + + + A=adj2sp(xadj,iadj,v) + + A=adj2sp(xadj,iadj,v,mn) + + + + + + + + 引数 + + + + + + xadj + + + + + + 長さ (n+1)の整数ベクトル. + + j=1:nの場合, + + 浮動小数点整数 + + xadj(j+1)-xadj(j) は + + j列における非ゼロエントリの数です. + + + + + + + + + + iadj + + + + + + nz行1列の浮動小数点整数の行列, 非ゼロエントリの行添字. + + j=1:nおよび, + + k = xadj(j):xadj(j+1)-1に関して, + + 浮動小数点整数 i = iadj(k) は + + 非ゼロエントリ #k の行添字です. + + + + + + + + + + v + + + + + + nz行1列の浮動小数点整数の行列, Aの非ゼロエントリ. + + j=1:nおよび, + + k = xadj(j):xadj(j+1)-1に関して, + + 浮動小数点整数Aij = v(k)は + + 非ゼロエントリ #k の値です. + + + + + + + + + + mn + + + + + + 1行2列または2行1列の浮動小数点整数の行列(オプション), + + mn(1) はAの行数, + + mn(2) はAの列数です. + + mn が指定されない場合, + + mn=[m,n] は, + + m=max(iadj) および + + n=size(xadj,"*")-1がデフォルトとなります. + + + + + + + + + + A + + + + m行n列実数または複素数の疎行列 (nz 個の非ゼロエントリ) + + + + + + + + + + + + 説明 + + + + adj2sp は,隣接形式を疎行列に変換します. + + 隣接形式の値は列毎に保存されています. + + これは,この形式がしばしば + + "Compressed sparse column" または CSCと呼ばれる理由です. + + + + + + + + 例 + + + + 以下の例では,隣接形式から疎行列を作成します. + + その後,期待した疎行列と一致するかどうかを確認します. + + + + + + + + 以下の例では,隣接形式から疎行列を作成します. + + その後,期待した疎行列と一致するかどうかを確認します. + + + + + + + + 以下の例では,mnパラメータの使用法を確認します. + + mnパラメータとxadjおよびiadjの実際の内容の整合性をadj2spで確認します. + + + + + + + + 以下の例では,3行3列の疎行列を作成します. + + この例は, SciPyの文書からの引用です. + + + + + + + + 前のスクリプトは以下の出力を生成します. + + + + full(adj2sp(xadj,iadj,v)) + ans = + 1. 0. 4. + 0. 0. 5. + 2. 3. 6. + ]]> + + + + 以下の例では,sp2adjおよびadj2sp関数が逆関数であることを + + 確認します. + + + + + + + + + + 参照 + + + + + + sp2adj + + + + + + sparse + + + + + + spcompack + + + + + + spget + + + + + + + + + + 参考文献 + + + + "Implementation of Lipsol in Scilab", Hector E. Rubio Scola, INRIA, Decembre 1997, Rapport Technique No 0215 + + + + + + "Solving Large Linear Optimization Problems with Scilab : Application to Multicommodity Problems", Hector E. Rubio Scola, Janvier 1999, Rapport Technique No 0227 + + + + + + "Toolbox Scilab : Detection signal design for failure detection and isolation for linear dynamic systems User's Guide", Hector E. Rubio Scola, 2000, Rapport Technique No 0241 + + + + + + "Computer Solution of Large Sparse Positive Definite Systems", A. George, Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1981. + + + + + + + diff --git a/modules/sparse/help/ja_JP/sparseconvert/full.xml b/modules/sparse/help/ja_JP/sparseconvert/full.xml new file mode 100755 index 000000000..753d84dbb --- /dev/null +++ b/modules/sparse/help/ja_JP/sparseconvert/full.xml @@ -0,0 +1,125 @@ + + + + + + + + + full + + 疎行列を通常の行列に変換する + + + + + + 呼び出し手順 + + X=full(sp) + + + + + + 引数 + + + + + + sp + + + + 実数または複素数の疎(または通常の)行列 + + + + + + + + X + + + + 通常の行列 + + + + + + + + + + + + 説明 + + + + X=full(sp) は疎行列 sp を + + 通常の行列表現に変換します. + + (sp が既に通常の行列の場合,X は + + spに等しくなります). + + + + + + + + 例 + + + + + + + + 参照 + + + + + + sparse + + + + + + sprand + + + + + + speye + + + + + + + + + diff --git a/modules/sparse/help/ja_JP/sparseconvert/mtlb_sparse.xml b/modules/sparse/help/ja_JP/sparseconvert/mtlb_sparse.xml new file mode 100755 index 000000000..a1a26114c --- /dev/null +++ b/modules/sparse/help/ja_JP/sparseconvert/mtlb_sparse.xml @@ -0,0 +1,145 @@ + + + + + + + + + mtlb_sparse + + 疎行列に変換 + + + + + + 呼び出し手順 + + Y=mtlb_sparse(X) + + + + + + 引数 + + + + + + X + + + + 疎行列 + + + + + + + + Y + + + + Matlab形式の疎行列 + + + + + + + + + + + + せつ + + + + Y=mtlb_sparse(X) は + + Scilab疎行列XをMatlab形式に変換する際に + + 使用されます. + + Y は7型の変数,すなわち, + + type(Y)は7となります. + + この関数は, mexfilesで使用されます (疎行列を含むMatlab mexileはScilab疎行列を + + この形式に変換した場合のみ使用できます). + + 関数full および spgetはこの形式でも + + 動作します. + + + + + + この形式を用いるその他の処理および関数は, + + 接頭辞 "%msp" を用いて + + Scilab関数によりオーバーロードすることができます. + + 例えば,関数 + + %msp_p(x) (SCIDIR/macros/percent ディレクトリ参照)は + + このような"7型"オブジェクトを表示する際に使用されます. + + + + + + + + 例 + + + + + + + + 参照 + + + + + + full + + + + + + spget + + + + + + + + + diff --git a/modules/sparse/help/ja_JP/sparseconvert/sp2adj.xml b/modules/sparse/help/ja_JP/sparseconvert/sp2adj.xml new file mode 100755 index 000000000..0f0e77986 --- /dev/null +++ b/modules/sparse/help/ja_JP/sparseconvert/sp2adj.xml @@ -0,0 +1,369 @@ + + + + + + + + + sp2adj + + 疎行列を隣接形式に変換する + + + + + + 呼び出し手順 + + + + [xadj,iadj,v]=sp2adj(A) + + + + + + + + 引数 + + + + + + A + + + + + + m行n列の実数または複素数の疎行列 (nz 個の非ゼロエントリ) + + + + + + + + + + xadj + + + + + + (n+1)行1列の浮動小数点整数の行列で, + + 各列のiadjとvの先頭の添字を指します. + + j=1:nの場合, + + 浮動小数点整数 + + xadj(j+1)-xadj(j) は + + j列の非ゼロエントリの数になります. + + + + + + + + + + iadj + + + + + + nz行1列の浮動小数点整数の行列, 非ゼロエントリの行添字. + + j=1:nおよび, + + k = xadj(j):xadj(j+1)-1に関して, + + 浮動小数点整数 i = iadj(k) は + + 非ゼロエントリ #k の行添字です. + + + + + + + + + + v + + + + + + nz行1列の浮動小数点整数の行列, Aの非ゼロエントリ. + + j=1:nおよび, + + k = xadj(j):xadj(j+1)-1に関して, + + 浮動小数点整数Aij = v(k)は + + 非ゼロエントリ #k の値です. + + + + + + + + + + + + + + 説明 + + + + sp2adjは,疎行列を隣接形式に変換します. + + 隣接形式の値は列毎に保存されています. + + これは,この形式がしばしば + + "Compressed sparse column" または CSCと呼ばれる理由です. + + + + + + + + 例 + + + + 以下の例では,1から10のエントリを有する通常の行列を作成します. + + 次に,これを疎行列に変換し,ゼロを除きます. + + 最後に,この行列の隣接形式を計算します. + + 行列bはAの非ゼロ要素のみを有します. + + + + + + + + 前のスクリプトは以下の出力を生成します. + + + + + + + + 列 #1について考えてみましょう. + + 等式 xadj(2)-xadj(1)=2 は列 #1に非ゼロ要素が2個あることを示します. + + 行添字は iadjに保存され, 列 #1 の非ゼロエントリは + + 行 #3 および #5であることを示します. + + 行列 v は実際のエントリが 1および2であることを示します. + + + + + + 以下の例では,疎行列の非ゼロエントリを隣接構造でループ処理を + + することにより,調べます. + + + + + + + + 以下の例では,sp2adjおよびadj2sp関数が逆関数であることを + + 確認します. + + + + + + + + + + 参照 + + + + + + adj2sp + + + + + + sparse + + + + + + spcompack + + + + + + spget + + + + + + + + + + 参考文献 + + + + "Implementation of Lipsol in Scilab", Hector E. Rubio Scola, INRIA, Decembre 1997, Rapport Technique No 0215 + + + + + + "Solving Large Linear Optimization Problems with Scilab : Application to Multicommodity Problems", Hector E. Rubio Scola, Janvier 1999, Rapport Technique No 0227 + + + + + + "Toolbox Scilab : Detection signal design for failure detection and isolation for linear dynamic systems User's Guide", Hector E. Rubio Scola, 2000, Rapport Technique No 0241 + + + + + + "Computer Solution of Large Sparse Positive Definite Systems", A. George, Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1981. + + + + + + + diff --git a/modules/sparse/help/ja_JP/sparseconvert/sparse.xml b/modules/sparse/help/ja_JP/sparseconvert/sparse.xml new file mode 100755 index 000000000..7b6095c57 --- /dev/null +++ b/modules/sparse/help/ja_JP/sparseconvert/sparse.xml @@ -0,0 +1,277 @@ + + + + + + + + + sparse + + 疎行列を定義 + + + + + + 呼び出し手順 + + sp=sparse(X) + + sp=sparse(ij,v [,mn]) + + + + + + + + 引数 + + + + + + X + + + + 実数または複素数の通常の(または疎)行列 + + + + + + + + ij + + + + 2列の整数行列 (非ゼロエントリのインデックス) + + + + + + + + v + + + + ベクトル + + + + + + + + mn + + + + 2つのエントリ(行の次元, 列の次元c)を有する整数ベクトル + + + + + + + + sp + + + + 疎行列 + + + + + + + + + + + + 説明 + + + + sparseは疎行列を作成するために使用されます. + + ゼロでないエントリのみが保存されます. + + + + + + sp = sparse(X) は, + + 0要素を除外することにより,通常の行列を疎行列に変換します. + + (Xが既に疎行列の場合, + + spはXとなります). + + + + + + sp=sparse(ij,v [,mn])は, + + sp(ij(k,1),ij(k,2))=v(k)となる + + mn(1)行mn(2)列の疎行列 + + を作成します. + + ij および vは列の次元が + + 同じである必要があります. + + オプションのmnパラメータが指定されない場合, + + 行列spの次元は,それぞれ + + ij(:,1) および ij(:,2)の + + 最大値となります. + + + + + + 疎行列に関する操作(結合,加算,等,)は通常の行列と同じ構文により + + 行ないます. + + + + + + 基本的な関数(abs,maxi,sum,diag,...)は疎行列でも + + 利用可能です. + + + + + + (通常の行列と疎行列の)混用も可能です. + + 結果は処理に応じて通常または疎行列となります. + + + + + + 注意 : + + 同じ大きさの通常の行列を含む任意の演算は, + + 引数(例: sp=sparse(d)), + + または,結果(例 d= sp + 1.) のどちら + + についても利便性のために提供されていますが,当然避けるべきです. + + 更に,要素(sp(r,c))へのランダムアクセス, + + 特に挿入,は効率的ではありません. + + このため,性能面の制約があるアクセスでは, + + 読込みアクセスはspget, + + 書込みアクセスはsp=sparse(ij, v, mn)による + + バッチ処理により行う必要があります. + + + + + + + + 例 + + + + + + + + 参照 + + + + + + full + + + + + + spget + + + + + + sprand + + + + + + speye + + + + + + lufact + + + + + + + + + diff --git a/modules/sparse/help/ja_JP/sparseconvert/spcompack.xml b/modules/sparse/help/ja_JP/sparseconvert/spcompack.xml new file mode 100755 index 000000000..12a02f148 --- /dev/null +++ b/modules/sparse/help/ja_JP/sparseconvert/spcompack.xml @@ -0,0 +1,165 @@ + + + + + + + + + spcompack + + 圧縮隣接表現に変換する + + + + + + 引数 + + + + + + xadj + + + + 長さ (n+1)の整数ベクトル. + + + + + + + + xlindx + + + + 長さ n+1の整数ベクトル(ポインタ). + + + + + + + + lindx + + + + 整数ベクトル + + + + + + + + adjncy + + + + 整数ベクトル + + + + + + + + + + + + 説明 + + + + + + + + 例 + + + + + + + + 参照 + + + + + + sp2adj + + + + + + adj2sp + + + + + + spget + + + + + + + + + diff --git a/modules/sparse/help/ja_JP/sparseconvert/spget.xml b/modules/sparse/help/ja_JP/sparseconvert/spget.xml new file mode 100755 index 000000000..4d20506b5 --- /dev/null +++ b/modules/sparse/help/ja_JP/sparseconvert/spget.xml @@ -0,0 +1,87 @@ + + + + + spget + 疎行列のエントリを取得 + + + 呼び出し手順 + [ij,v,mn]=spget(sp) + + + 引数 + + + sp + + 実数または複素数の疎行列 + + + + ij + + 2列の整数行列t (非ゼロエントリのインデックス) + + + + mn + + 2つのエントリ(行の次元, 列の次元)を有する整数ベクトル + + + + v + + 列ベクトル + + + + + + 説明 + + spget は疎行列の内部形式を + 標準的なij, v 形式に変換する際に使用されます. + + + spの非ゼロエントリは, + ijのインデックスにより行および列の + 位置が決定されます. + + + + 例 + + + + 参照 + + + sparse + + + sprand + + + speye + + + lufact + + + + diff --git a/modules/sparse/help/pt_BR/addchapter.sce b/modules/sparse/help/pt_BR/addchapter.sce new file mode 100755 index 000000000..848ab0920 --- /dev/null +++ b/modules/sparse/help/pt_BR/addchapter.sce @@ -0,0 +1,11 @@ +// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab +// Copyright (C) 2009 - DIGITEO +// +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + +add_help_chapter("Matrizes Esparsas",SCI+"/modules/sparse/help/pt_BR",%T); + diff --git a/modules/sparse/help/pt_BR/chfact.xml b/modules/sparse/help/pt_BR/chfact.xml new file mode 100755 index 000000000..12f52dbca --- /dev/null +++ b/modules/sparse/help/pt_BR/chfact.xml @@ -0,0 +1,72 @@ + + + + + chfact + fatorao esparsa de Cholesky + + + Seqncia de Chamamento + spcho=chfact(A) + + + Parmetros + + + A + + uma matriz simtrica, positiva e esparsa + + + + spcho + + lista contendo os fatores de Cholesky em forma + codificada + + + + + + + Descrio + + spcho=chfact(A) computa os fatores esparsos de + Cholesky da matriz esparsa A, assumida simtrica e + positiva definida. A funo baseada nos programas Ng-Peyton (ORNL). Ver + os programas FORTRAN para uma completa descrio das variveis em + spcho. Esta funo deve ser usada com a funo + chsolve. + + + + Ver Tambm + + + chsolve + + + sparse + + + lufact + + + luget + + + spchol + + + + diff --git a/modules/sparse/help/pt_BR/chsolve.xml b/modules/sparse/help/pt_BR/chsolve.xml new file mode 100755 index 000000000..a72657022 --- /dev/null +++ b/modules/sparse/help/pt_BR/chsolve.xml @@ -0,0 +1,82 @@ + + + + + chsolve + solucionador esparso de Cholesky + + + Seqncia de Chamamento + sol=chsolve(spcho,rhs) + + + Parmetros + + + spcho + + lista contendo os fatores de Cholesky na forma codificada + retornados por chfact + + + + + rhs, sol + + vetores colunas cheios + + + + + + Descrio + + sol=chsolve(spcho,rhs) computa a soluo de + rhs=A*sol, com A uma matriz + simtrica e positiva definida. Esta funo baseada nos programas + Ng-Peyton (ORNL). Veja os programas FORTRAN para uma descrio completa + das variveis em spcho. + + + + Exemplos + + + + Ver Tambm + + + chfact + + + sparse + + + lufact + + + luget + + + spchol + + + + diff --git a/modules/sparse/help/pt_BR/decomposition/CHAPTER b/modules/sparse/help/pt_BR/decomposition/CHAPTER new file mode 100755 index 000000000..ccebc80d8 --- /dev/null +++ b/modules/sparse/help/pt_BR/decomposition/CHAPTER @@ -0,0 +1 @@ +title = Sparse Decompositions diff --git a/modules/sparse/help/pt_BR/decomposition/ludel.xml b/modules/sparse/help/pt_BR/decomposition/ludel.xml new file mode 100755 index 000000000..427bc9743 --- /dev/null +++ b/modules/sparse/help/pt_BR/decomposition/ludel.xml @@ -0,0 +1,60 @@ + + + + + ludel + função utilitária usada com lufact + + + Seqüência de Chamamento + ludel(hand) + + + Parâmetros + + + hand + + manipulador para fatores lu esparsos (saída de lufact) + + + + + + Descrição + + Esta função é usada de modo conjunto com lufact. + Ela limpa o espaço de memória interna usado para guardar o resultado de + lufact. + + A seqüência de comandos + [p,r]=lufact(A);x=lusolve(p,b);ludel(p); resolve o + sistema linear esparso A*x = b e limpa + p. + + + + Ver Também + + + sparse + + + lufact + + + luget + + + + diff --git a/modules/sparse/help/pt_BR/decomposition/lufact.xml b/modules/sparse/help/pt_BR/decomposition/lufact.xml new file mode 100755 index 000000000..b90c5d284 --- /dev/null +++ b/modules/sparse/help/pt_BR/decomposition/lufact.xml @@ -0,0 +1,136 @@ + + + + + lufact + fatoração LU esparsa + + + Seqüência de Chamamento + [hand,rk]=lufact(A,prec) + + + Parâmetros + + + A + + matriz quadrada esparsa + + + + hand + + manipulador para fatores LU esparsos + + + + rk + + inteiro (posto de A) + + + + prec + + + vetor de tamanho 2 prec=[eps,reps] + fornecendo os limiares absoluto e relativo. + + + + + + + Descrição + + [hand,rk]=lufact(A) realiza a fatoração LU da + matriz esparsa A. hand (sem + exibição) é usado por lusolve (para resolver sistemas + lineares) e luget (para retirar os fatores). + hand deve ser limpo pelo comando: + ludel(hand); + + A matriz A não precisa ser de posto cheio, mas deve ser quadrada + (desde que A é assumida como sendo esparsa, pode-se adicionar 0, se + necessário, para quadrá-la). + + + + eps : + + a magnitude absoluta que um elemento deve ter para ser + considerado um candidato a pivô, exceto como último recurso. Este + número deve ser posto de modo a ser significantemente menor que o + menor elemento da diagonal que se espera estar localizado na matriz. + O valor padrão é %eps. + + + + + reps : + + Este número determina qual será o limiar relativo do pivô. + Deve estar entre 0 e 1. Se for 1, então o método de pivoteamento + torna-se pivotação completa, que é muito lento e tende a completar a + matriz. Se o número acertado é próximo de 0, o método de + pivoteamento torna-se estritamente de Markowitz, sem limiar. O + limiar de pivô é usado para eliminar candidatos a pivô que poderiam + causar crescimento excessivo de elementos se fossem usados. + Crescimento de elementos é a causa dos erros de arredondamento. + Crescimento de elementos ocorre mesmo em matrizes bem condicionadas. + Definir o reps como um número grande reduzirá o crescimento de + elementos e os erros de arredondamento, mas colocá-lo muito grande + aumentará muito o tempo de execução e resultará num grande número de + preenchimentos. Se isto ocorrer, a precisão pode ficar prejudicada + por causa do grande número de operações requeridas na matriz devido + ao grande número de preenchimentos. 0.001 parece um bom valor, e é o + valor default. O default é escolhido fornecendo-se um valor maior + que 1 ou menor que ou igual a 0. Este valor deve ser aumentado e a + matriz resolvida se o crescimento for excessivo. Mudar o limiar do + pivô não melhora o desempenho em matrizes onde o crescimento é + baixo, como é geralmente o caso de matrizes mal-condicionadas. reps + foi escolhido para uso com matrizes quase diagonalmente dominantes + como uma matriz de admissão de nó e nó modificado. Para estas + matrizes, geralmente o melhor é usar pivotação diagonal. Para + matrizes sem uma diagonal forte, geralmente é melhor usar um limiar + maior, como 0.01 ou 0.1. + + + + + + + Exemplos + + + + Ver Também + + + sparse + + + lusolve + + + luget + + + + diff --git a/modules/sparse/help/pt_BR/decomposition/luget.xml b/modules/sparse/help/pt_BR/decomposition/luget.xml new file mode 100755 index 000000000..2025bac26 --- /dev/null +++ b/modules/sparse/help/pt_BR/decomposition/luget.xml @@ -0,0 +1,110 @@ + + + + + luget + extração dos fatores LU esparsos + + + Seqüência de Chamamento + [P,L,U,Q]=luget(hand) + + + Parâmetros + + + hand + + + manipulador, saída de lufact + + + + + P + + matriz de permutação esparsa + + + + L + + + matriz esparsa, triangular infeiror se hand + é obtida de uma matriz não-singular + + + + + U + + matriz quadrada triangular superior esparsa não-snigular + preenchida com 1 ao longo da diagonal principal + + + + + Q + + matriz de permutação esparsa + + + + + + Descrição + + [P,L,U,Q]=luget(hand) com hand + obtida pelo comando [hand,rk]=lufact(A) com + A uma matriz esparsa retorna quatro matrizes esparsas + tais que P*L*U*Q=A. + + A matriz A não precisa ser de posto cheio, mas deve ser quadrada + (desde que A é assumida esparsa, pode-se adicionar 0, se necessário, para + quadrar A). + + + Se A é singular, a matriz L é + de colunas comprimidas (com rk colunas independentes + não-nulas): a matriz não-singular esparsa Q'*inv(U) + comprime em colunas A. + + + + Exemplos + + + + Ver Também + + + sparse + + + lusolve + + + luget + + + clean + + + + diff --git a/modules/sparse/help/pt_BR/decomposition/lusolve.xml b/modules/sparse/help/pt_BR/decomposition/lusolve.xml new file mode 100755 index 000000000..3011c9513 --- /dev/null +++ b/modules/sparse/help/pt_BR/decomposition/lusolve.xml @@ -0,0 +1,100 @@ + + + + + lusolve + solucionador de sistemas lineares esparsos + + + Seqüência de Chamamento + x=lusolve(hand,b) + x=lusolve(A,b) + + + + Parâmetros + + + b + + matriz de reais completa + + + + A + + matriz quadrada de reais esparsa e invertível + + + + hand + + manipulador para fatores de lu esparsos previamente computados + (saída de lufact) + + + + + x + + matriz de reais completa + + + + + + Descrição + + x=lusolve(hand,b) resolve o sistema linear + esparso A*x = b. + + + [hand,rk]=lufact(A) é a saída de lufact. + + + x=lusolve(A,b) resolve o sistema linear esparso + A*x = b + + + + Exemplos + + + + Ver Também + + + sparse + + + lufact + + + slash + + + backslash + + + + diff --git a/modules/sparse/help/pt_BR/decomposition/spchol.xml b/modules/sparse/help/pt_BR/decomposition/spchol.xml new file mode 100755 index 000000000..7388acd2e --- /dev/null +++ b/modules/sparse/help/pt_BR/decomposition/spchol.xml @@ -0,0 +1,91 @@ + + + + + spchol + fatoração esparsa de Cholesky + + + Seqüência de Chamamento + [R,P] = spchol(X) + + + Parâmetros + + + X + + matriz simétrica, esparsa e positiva definida de reais + + + + P + + matriz de permutação + + + + R + + fator de Cholesky + + + + + + Descrição + + [R,P] = spchol(X) produz uma matriz triângular + inferior R tal que P*R*R'*P' = + X + + . + + + + Exemplos + + + + Ver Também + + + sparse + + + lusolve + + + luget + + + chol + + + + diff --git a/modules/sparse/help/pt_BR/matrixmanip/CHAPTER b/modules/sparse/help/pt_BR/matrixmanip/CHAPTER new file mode 100755 index 000000000..a797a77e1 --- /dev/null +++ b/modules/sparse/help/pt_BR/matrixmanip/CHAPTER @@ -0,0 +1 @@ +title = Sparse Matrix Manipulation diff --git a/modules/sparse/help/pt_BR/matrixmanip/nnz.xml b/modules/sparse/help/pt_BR/matrixmanip/nnz.xml new file mode 100755 index 000000000..eb9971745 --- /dev/null +++ b/modules/sparse/help/pt_BR/matrixmanip/nnz.xml @@ -0,0 +1,63 @@ + + + + + nnz + número de entradas não-nulas de uma matriz + + + Seqüência de Chamamento + n=nnz(X) + + + Parâmetros + + + X + + matriz de reais ou complexos esparsa (ou cheia) + + + + n + + inteiro, número de elementos não-nulos de X. + + + + + + Descrição + + nnz conta o número de entradas não-nulas de uma + matriz esparsa ou cheia. + + + + Exemplos + + + + Ver Também + + + spget + + + + diff --git a/modules/sparse/help/pt_BR/matrixmanip/speye.xml b/modules/sparse/help/pt_BR/matrixmanip/speye.xml new file mode 100755 index 000000000..fe21e17d6 --- /dev/null +++ b/modules/sparse/help/pt_BR/matrixmanip/speye.xml @@ -0,0 +1,97 @@ + + + + + speye + matriz identidade esparsa + + + Seqncia de Chamamento + Isp=speye(nrows,ncols) + Isp=speye(A) + + + + Parmetros + + + nrows + + inteiro (nmero de linhas) + + + + ncols + + inteiro (nmero de colunas) + + + + A + + matriz esparsa + + + + sp + + matriz identidade esparsa + + + + + + Descrio + + Isp=speye(nrows,ncols) retorna uma matriz + identidade esparsa Isp com nrows + linhas e , ncols colunas (matrizes identidades + no-quadradas tm um nmero mximo de algarismos 1 na diagonal + principal). + + + Isp=speye(A) retorna uma matriz identidade + esparsa com as mesmas dimenses de A. + Se[m,n]=size(A), speye(m,n) e + speye(A) so equivalentes. Em particular + speye(3) no equivalente a + speye(3,3). + + + + Exemplos + + + + Ver Tambm + + + sparse + + + full + + + eye + + + spzeros + + + spones + + + + diff --git a/modules/sparse/help/pt_BR/matrixmanip/spones.xml b/modules/sparse/help/pt_BR/matrixmanip/spones.xml new file mode 100755 index 000000000..f9f099ae6 --- /dev/null +++ b/modules/sparse/help/pt_BR/matrixmanip/spones.xml @@ -0,0 +1,76 @@ + + + + + spones + matriz esparsa + + + Seqncia de Chamamento + sp=spones(A) + + + Parmetros + + + A + + matriz esparsa + + + + sp + + matriz esparsa + + + + + + Descrio + + sp=spones(A) gera uma matriz com a mesma + estrutura de espargimento de A, mas com 1 em posies + no-nulas; + + + + Exemplos + + + + Ver Tambm + + + sparse + + + full + + + eye + + + speye + + + spzeros + + + + diff --git a/modules/sparse/help/pt_BR/matrixmanip/sprand.xml b/modules/sparse/help/pt_BR/matrixmanip/sprand.xml new file mode 100755 index 000000000..00d9e12bd --- /dev/null +++ b/modules/sparse/help/pt_BR/matrixmanip/sprand.xml @@ -0,0 +1,98 @@ + + + + + sprand + matriz esparsa randmica + + + Seqncia de Chamamento + sp=sprand(nrows,ncols,fill [,typ]) + + + Parmetros + + + nrows + + inteiro (nmero de linhas) + + + + ncols + + inteiro (nmero de colunas) + + + + fill + + coeficiente de preenchimento (densidade) + + + + typ + + + string ('uniform' (padro) ou + 'normal') + + + + + sp + + matriz esparsa + + + + + + Descrio + + sp=sprand(nrows,ncols,fill) retorna uma matriz + esparsa sp com nrows linhas e + ncols colunas e aproximadamente + fill*nrows*ncols entradas no-nulas. + + + Se typ='uniform' valores uniformemente + distribudos em [0,1] so gerados. Se typ='normal' + valores normalmente distribudos so gerados (mdia=0 e desvio + padro=1). + + + + Exemplos + + + + Ver Tambm + + + sparse + + + full + + + rand + + + speye + + + + diff --git a/modules/sparse/help/pt_BR/matrixmanip/spzeros.xml b/modules/sparse/help/pt_BR/matrixmanip/spzeros.xml new file mode 100755 index 000000000..ade8f85a8 --- /dev/null +++ b/modules/sparse/help/pt_BR/matrixmanip/spzeros.xml @@ -0,0 +1,99 @@ + + + + + spzeros + matriz nula esparsa + + + Seqncia de Chamamento + sp=spzeros(nrows,ncols) + sp=spzeros(A) + + + + Parmetros + + + nrows + + inteiro (nmero de linhas) + + + + ncols + + inteiro (nmero de colunas) + + + + A + + matriz esparsa + + + + sp + + matriz nula esparsa + + + + + + Descrio + + sp=spzeros(nrows,ncols) retorna uma matriz nula + esparsa sp com nrows linhas e, + ncols colunas. (Equivalente a + sparse([],[],[nrow,ncols])) + + + sp=spzeros(A) retorna uma matriz nula esparsa com + as mesmas dimenses que A. Se + [m,n]=size(A), spzeros(m,n) e + spzeros(A) so equivalentes. Em particular + spzeros(3) no equivalente a + spzeros(3,3). + + + + Exemplos + + + + Ver Tambm + + + sparse + + + full + + + eye + + + speye + + + spones + + + + diff --git a/modules/sparse/help/pt_BR/sparseconvert/CHAPTER b/modules/sparse/help/pt_BR/sparseconvert/CHAPTER new file mode 100755 index 000000000..42d5e0bf2 --- /dev/null +++ b/modules/sparse/help/pt_BR/sparseconvert/CHAPTER @@ -0,0 +1 @@ +title = Sparse Matrix Conversion diff --git a/modules/sparse/help/pt_BR/sparseconvert/adj2sp.xml b/modules/sparse/help/pt_BR/sparseconvert/adj2sp.xml new file mode 100755 index 000000000..b792725d7 --- /dev/null +++ b/modules/sparse/help/pt_BR/sparseconvert/adj2sp.xml @@ -0,0 +1,101 @@ + + + + + adj2sp + converte forma de adjacncia para matriz esparsa + + + Parmetros + + + xadj + + vetor de inteiros de comprimento (n+1). + + + + adjncy + + vetor de inteiros de comprimento nz contendo os ndices de + linha para os elementos correspondentes em anz + + + + + anz + + vetor coluna de comprimento nz contendo os elementos no-nulos + de A + + + + + mn + + + vetor linha com duas entradas, mn=size(A) + (opcional). + + + + + A + + matriz quadrada esparsa de reais ou complexos (nz entradas + no-nulas) + + + + + + + Descrio + + + xadj(j+1)-xadj(j) = nmero de entradas no-nulas + na linha j. adjncy = ndice de coluna das entradas + no-nulas nas linha 1, linha 2..., linha n. anz = + valores das entradas no-nulas nas linha 1, linha 2,..., linha n. + xadj um vetor (coluna) de tamanho n+1 e + adjncy um vetor (coluna) de inteiros de tamanho + nz=nnz(A). anz um vetor de reais + de tamanho nz=nnz(A). + + + + Exemplos + + + + Ver Tambm + + + sp2adj + + + spcompack + + + + diff --git a/modules/sparse/help/pt_BR/sparseconvert/full.xml b/modules/sparse/help/pt_BR/sparseconvert/full.xml new file mode 100755 index 000000000..b362e23aa --- /dev/null +++ b/modules/sparse/help/pt_BR/sparseconvert/full.xml @@ -0,0 +1,69 @@ + + + + + full + conversão de matriz esparsa para cheia (completa) + + + Seqüência de Chamamento + X=full(sp) + + + Parâmetros + + + sp + + matriz esparsa (ou cheia) de reais ou complexos + + + + X + + matriz cheia (completa) + + + + + + Descrição + + X=full(sp) converte a matriz esparsa + sp em sua representação cheia (completa). (Se + sp já é cheia, então X é igual a + sp). + + + + Exemplos + + + + Ver Também + + + sparse + + + sprand + + + speye + + + + diff --git a/modules/sparse/help/pt_BR/sparseconvert/mtlb_sparse.xml b/modules/sparse/help/pt_BR/sparseconvert/mtlb_sparse.xml new file mode 100755 index 000000000..7d6072515 --- /dev/null +++ b/modules/sparse/help/pt_BR/sparseconvert/mtlb_sparse.xml @@ -0,0 +1,75 @@ + + + + + mtlb_sparse + converte matriz esparsa + + + Seqüência de Chamamento + Y=mtlb_sparse(X) + + + Parâmetros + + + X + + matriz esparsa + + + + Y + + matriz esparsa em formato Matlab + + + + + + Descrição + + Y=mtlb_sparse(X) é usado para converter + X, uma matriz esparsa Scilab, para formato Matlab. + Y é uma variável de tipo 7, i.e., + type(Y) é igual a 7. Esta função deve ser usada em + mexfiles (um mexfile Matlab contendo matrizes esparsas pode ser usado + apenas se as matrizes esparsas do Scilab forem convertidas para este + formato). As funções full e spget + funcionam com este formato. + + Outras operações e funções usando este formato podem ficar + sobrecarregadas com funções do Scilab usando o prefixo "%msp". Por + exemplo, a função %msp_p(x) (ver diretório + SCI/modules/overloading/macros) é usada para exibir tais objetos "tipo 7". + + + + Exemplos + + + + Ver Também + + + full + + + spget + + + + diff --git a/modules/sparse/help/pt_BR/sparseconvert/sp2adj.xml b/modules/sparse/help/pt_BR/sparseconvert/sp2adj.xml new file mode 100755 index 000000000..f4b6d1009 --- /dev/null +++ b/modules/sparse/help/pt_BR/sparseconvert/sp2adj.xml @@ -0,0 +1,100 @@ + + + + + sp2adj + converte uma matriz esparsa para forma de + adjacncia + + + + Parmetros + + + A + + matriz esparsa de reais ou complexos (nz entradas no-nulas) + + + + + xadj + + vetor de inteiros de comprimento (n+1). + + + + adjncy + + vetor de inteiros de comprimento nz contendo os ndices de + linha para os elementos correspondentes em anz + + + + + anz + + vetor coluna de comprimento nz contendo os elementos no-nulos + de A + + + + + + + Descrio + + + xadj(j+1)-xadj(j) = nmero de entradas no-nulas + na linha j. adjncy = ndice de coluna das entradas + no-nulas nas linha 1, linha 2,..., linha n. anz = + valores de entradas no-nulas nas linha 1, linha 2,..., linha n. + xadj um vetor (coluna) de tamanho n+1 e + adjncy um vetor (coluna) de inteiros de tamanho + nz=nnz(A). anz um vetor de reais + de tamanho nz=nnz(A). + + + + Exemplos + + + + Ver Tambm + + + adj2sp + + + sparse + + + spcompack + + + spget + + + + diff --git a/modules/sparse/help/pt_BR/sparseconvert/sparse.xml b/modules/sparse/help/pt_BR/sparseconvert/sparse.xml new file mode 100755 index 000000000..7950c5676 --- /dev/null +++ b/modules/sparse/help/pt_BR/sparseconvert/sparse.xml @@ -0,0 +1,122 @@ + + + + + sparse + definição de matriz esparsa + + + Seqüência de Chamamento + sp=sparse(X) + sp=sparse(ij,v [,mn]) + + + + Parâmetros + + + X + + matriz completa (ou esparsa) de reais ou complexos + + + + ij + + matriz de inteiros de duas colunas (índices das entradas não + nulas) + + + + + v + + vetor + + + + mn + + vetor de inteiros com duas entradas (dimensão de linha, + dimensão de coluna) + + + + + sp + + matriz esparsa + + + + + + Descrição + + sparse é usado para construir uma matriz esparsa. + Apenas entradas não-nulas são armazenadas. + + + sp = sparse(X) converte uma matriz completa para + sua forma esparsa retirando qualquer elemento nulo. (Se + X já é esparsa sp é + X). + + + sp=sparse(ij,v [,mn]) constrói uma matriz esparsa + mn(1)-por-mn(2) sparse matrix com + sp(ij(k,1),ij(k,2))=v(k). ij e + v devem ter a mesma dimensão de coluna. Se o parâmetro + opcional mn não for dado, as dimensões da matriz + sp são os valores máximos de ij(:,1) + e ij(:,2) respectivamente. + + Operações (concatenação, adição, etc,) com matrizes esparsas são + feitas usando a mesma sintaxe para matrizes completas. + + Funções elementares também estão disponíveis + (abs,maxi,sum,diag,...) para matrizes esparsas. + + Operações mistas (completas-esparsas) são permitidas. Os resultados + são completos ou esparsos dependendo das operações. + + + + Exemplos + + + + Ver Também + + + full + + + spget + + + sprand + + + speye + + + lufact + + + + diff --git a/modules/sparse/help/pt_BR/sparseconvert/spcompack.xml b/modules/sparse/help/pt_BR/sparseconvert/spcompack.xml new file mode 100755 index 000000000..a9de7f93d --- /dev/null +++ b/modules/sparse/help/pt_BR/sparseconvert/spcompack.xml @@ -0,0 +1,109 @@ + + + + + spcompack + converte uma representação de adjacência comprimida em + representação de adjacência padrão + + + + Parâmetros + + + xadj + + vetor de inteiros de comprimento (n+1). + + + + xlindx + + vetor de inteiros de comprimento n+1 (ponteiros). + + + + lindx + + vetor de inteiros + + + + adjncy + + vetor de inteiros + + + + + + Descrição + + + + Exemplos + + + + Ver Também + + + sp2adj + + + adj2sp + + + spget + + + + diff --git a/modules/sparse/help/pt_BR/sparseconvert/spget.xml b/modules/sparse/help/pt_BR/sparseconvert/spget.xml new file mode 100755 index 000000000..725d52944 --- /dev/null +++ b/modules/sparse/help/pt_BR/sparseconvert/spget.xml @@ -0,0 +1,93 @@ + + + + + spget + recupera entradas de matriz esparsa + + + Seqüência de Chamamento + [ij,v,mn]=spget(sp) + + + Parâmetros + + + sp + + matriz esparsa de reais ou complexos + + + + ij + + matriz de inteiros de duas colunas (índices das entradas + não-nulas) + + + + + mn + + vetor de inteiros com duas entradas (dimensão de linha, + dimensão de coluna) + + + + + v + + vetor coluna + + + + + + Descrição + + spget é usado para converter a representação + interna de matrizes esparsas na representação padrão ij, + v + + . + + + Entradas não-nulas de sp estão localizadas em + linhas e colunas com índices em ij. + + + + Exemplos + + + + Ver Também + + + sparse + + + sprand + + + speye + + + lufact + + + + diff --git a/modules/sparse/help/ru_RU/addchapter.sce b/modules/sparse/help/ru_RU/addchapter.sce new file mode 100755 index 000000000..22a8a387a --- /dev/null +++ b/modules/sparse/help/ru_RU/addchapter.sce @@ -0,0 +1,11 @@ +// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab +// Copyright (C) 2009 - DIGITEO +// +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + +add_help_chapter("Sparse Matrix",SCI+"/modules/sparse/help/ru_RU",%T); + -- cgit