Вы упомянули PROPACK . Fortran совместим с C, вам просто нужно знать, как работает соглашение о вызовах. Я не уверен, но я думаю, что функция, которую вы хотите вызвать в PROPACK, имеет значение dlansvd (при условии двойной точности), что задокументировано следующим образом:
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
В Фортране важно помнить, что все параметры передаются по ссылке , а не разреженные массивы хранятся в формате column-major . Итак, правильное объявление этой функции в C ++ должно быть следующим (непроверенным):
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);
Это настоящий зверь. Удачи!