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有人知道 C++ 的稀疏 SVD 求解器吗？我的问题涉及一些可能将列/行归零的条件不佳的矩阵。我的数据存储在 uBLAS 矩阵中，该矩阵是 Harwell-Boeing 稀疏格式。

我很难找到：

SVD 求解器

  1. 可以对稀疏矩阵进行运算的 SVD 求解器。Lapack似乎无法做到这一点？我想将稀疏矩阵传递给函数和稀疏矩阵输出。
  2. 一种重新组合结果的方法......这样我就可以从 x=b(A^-1) 中读取 xs。我希望这是 x=(b)(v.(d^-1).(u^t))

我希望从 GSL 重新创建以下两个步骤

gsl_linalg_SV_decomp_jacobi (gsl_matrix * A, gsl_matrix * V, gsl_vector * S) 
gsl_linalg_SV_solve (const gsl_matrix * U, const gsl_matrix * V, const gsl_vector * S, const gsl_vector * b, gsl_vector * x)

我也不知道如何在 C++ 中包装 FORTRAN 库。哪里/有任何 PROPACK c/c++ 绑定？

编辑 1：我在使用 PROPACK 时遇到了一些问题。PROPACK 输出稀疏矩阵吗？它似乎将 V 输出为“V(LDV,KMAX): DOUBLE PRECISION array”。这意味着它没有？

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3 回答 3

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SVDLIBC是一个 C 库，部分支持 Harwell-Boeing格式。我不熟悉该库，但表面上它似乎符合您的要求。

于 2011-07-06T01:38:22.273 回答
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你提到了 PROPACK。Fortran 与 C 兼容，您只需要知道调用约定是如何工作的。我不确定，但我认为您要在 PROPACK 中调用的函数是dlansvd（假设为双精度），记录如下：

  subroutine dlansvd(jobu,jobv,m,n,k,kmax,aprod,U,ldu,Sigma,bnd,
 c     V,ldv,tolin,work,lwork,iwork,liwork,doption,ioption,info,
 c     dparm,iparm)


c     DLANSVD: Compute the leading singular triplets of a large and
c     sparse matrix by Lanczos bidiagonalization with partial
c     reorthogonalization.
c
c     Parameters:
c
c     JOBU: CHARACTER*1. If JOBU.EQ.'Y' then compute the left singular vectors.
c     JOBV: CHARACTER*1. If JOBV.EQ.'Y' then compute the right singular 
c           vectors.
c     M: INTEGER. Number of rows of A.
c     N: INTEGER. Number of columns of A.
c     K: INTEGER. Number of desired singular triplets. K <= MIN(KMAX,M,N)
c     KMAX: INTEGER. Maximal number of iterations = maximal dimension of
c           the generated Krylov subspace.
c     APROD: Subroutine defining the linear operator A. 
c            APROD should be of the form:
c
c           SUBROUTINE DAPROD(TRANSA,M,N,X,Y,DPARM,IPARM)
c           CHARACTER*1 TRANSA
c           INTEGER M,N,IPARM(*)
c           DOUBLE PRECISION X(*),Y(*),DPARM(*)
c
c           If TRANSA.EQ.'N' then the function should compute the matrix-vector
c           product Y = A * X.
c           If TRANSA.EQ.'T' then the function should compute the matrix-vector
c           product Y = A^T * X.
c           The arrays IPARM and DPARM are a means to pass user supplied
c           data to APROD without the use of common blocks.
c     U(LDU,KMAX+1): DOUBLE PRECISION array. On return the first K columns of U
c               will contain approximations to the left singular vectors 
c               corresponding to the K largest singular values of A.
c               On entry the first column of U contains the starting vector
c               for the Lanczos bidiagonalization. A random starting vector
c               is used if U is zero.
c     LDU: INTEGER. Leading dimension of the array U. LDU >= M.
c     SIGMA(K): DOUBLE PRECISION array. On return Sigma contains approximation
c               to the K largest singular values of A.
c     BND(K)  : DOUBLE PRECISION array. Error estimates on the computed 
c               singular values. The computed SIGMA(I) is within BND(I)
c               of a singular value of A.
c     V(LDV,KMAX): DOUBLE PRECISION array. On return the first K columns of V
c               will contain approximations to the right singular vectors 
c               corresponding to the K largest singular values of A.
c     LDV: INTEGER. Leading dimension of the array V. LDV >= N.
c     TOLIN: DOUBLE PRECISION. Desired relative accuracy of computed singular 
c            values. The error of SIGMA(I) is approximately 
c            MAX( 16*EPS*SIGMA(1), TOLIN*SIGMA(I) )
c     WORK(LWORK): DOUBLE PRECISION array. Workspace of dimension LWORK.
c     LWORK: INTEGER. Dimension of WORK.
c            If JOBU.EQ.'N' and JOBV.EQ.'N' then  LWORK should be at least
c            M + N + 9*KMAX + 2*KMAX**2 + 4 + MAX(M+N,4*KMAX+4).
c            If JOBU.EQ.'Y' or JOBV.EQ.'Y' then LWORK should be at least
c            M + N + 9*KMAX + 5*KMAX**2 + 4 + 
c            MAX(3*KMAX**2+4*KMAX+4, NB*MAX(M,N)), where NB>1 is a block 
c            size, which determines how large a fraction of the work in
c            setting up the singular vectors is done using fast BLAS-3 
c            operation. 
c     IWORK: INTEGER array. Integer workspace of dimension LIWORK.
c     LIWORK: INTEGER. Dimension of IWORK. Should be at least 8*KMAX if
c             JOBU.EQ.'Y' or JOBV.EQ.'Y' and at least 2*KMAX+1 otherwise.
c     DOPTION: DOUBLE PRECISION array. Parameters for LANBPRO.
c        doption(1) = delta. Level of orthogonality to maintain among
c          Lanczos vectors.
c        doption(2) = eta. During reorthogonalization, all vectors with
c          with components larger than eta along the latest Lanczos vector
c          will be purged.
c        doption(3) = anorm. Estimate of || A ||.
c     IOPTION: INTEGER array. Parameters for LANBPRO.
c        ioption(1) = CGS.  If CGS.EQ.1 then reorthogonalization is done
c          using iterated classical GRAM-SCHMIDT. IF CGS.EQ.0 then 
c          reorthogonalization is done using iterated modified Gram-Schmidt.
c        ioption(2) = ELR. If ELR.EQ.1 then extended local orthogonality is
c          enforced among u_{k}, u_{k+1} and v_{k} and v_{k+1} respectively.
c     INFO: INTEGER. 
c         INFO = 0  : The K largest singular triplets were computed succesfully
c         INFO = J>0, J<K: An invariant subspace of dimension J was found.
c         INFO = -1 : K singular triplets did not converge within KMAX
c                     iterations.   
c     DPARM: DOUBLE PRECISION array. Array used for passing data to the APROD
c         function.   
c     IPARM: INTEGER array. Array used for passing data to the APROD
c         function.   
c
c     (C) Rasmus Munk Larsen, Stanford, 1999, 2004 
c

在 Fortran 中，要记住的重要一点是所有参数都通过引用传递，并且非稀疏数组以列优先格式存储。所以，这个函数在 C++ 中的正确声明应该如下（未经测试）：

extern "C"
void dlansvd(const char *jobu,
             const char *jobv,
             int *m,
             int *n,
             int *k,
             int *kmax,
             void (*aprod)(const char *transa,
                           int *m,
                           int *n,
                           int *iparm,
                           double *x,
                           double *y,
                           double *dparm),
             double *U,
             int *ldu,
             double *Sigma,
             double *bnd,
             double *V,
             int *ldv,
             double *tolin,
             double *work,
             int *lwork,
             int *iwork,
             int *liwork,
             double *doption,
             int *ioption,
             int *info,
             double *dparm,
             int *iparm);

真是一头野兽。祝你好运！

于 2011-07-05T04:34:42.147 回答
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查看 Tim Davis 的稀疏线性代数软件可能值得：http ://www.cise.ufl.edu/~davis/

一般来说，我发现他的软件非常有用，通常非常高效和强大。

似乎他一直在和一个学生一起研究一个稀疏的 SVD 包，但我不确定该项目处于什么阶段。

希望这可以帮助。

于 2011-07-05T01:34:37.227 回答