void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
if (nargout > 1 || nargin < 2 || nargin > 4)
{
mexErrMsgTxt ("Usage: C = cs_add(A,B,alpha,beta)") ;
}
if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])
|| (nargin > 2 && mxIsComplex (pargin [2]))
|| (nargin > 3 && mxIsComplex (pargin [3])))
{
#ifndef NCOMPLEX
cs_complex_t alpha, beta ;
cs_cl Amatrix, Bmatrix, *A, *B, *C, *D ;
A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
B = cs_cl_mex_get_sparse (&Bmatrix, 0, pargin [1]) ; /* get B */
alpha = (nargin < 3) ? 1 : get_complex (pargin [2]) ; /* get alpha */
beta = (nargin < 4) ? 1 : get_complex (pargin [3]) ; /* get beta */
C = cs_cl_add (A,B,alpha,beta) ; /* C = alpha*A + beta *B */
cs_cl_dropzeros (C) ; /* drop zeros */
D = cs_cl_transpose (C, 1) ; /* sort result via double transpose */
cs_cl_spfree (C) ;
C = cs_cl_transpose (D, 1) ;
cs_cl_spfree (D) ;
pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */
#else
mexErrMsgTxt ("complex matrices not supported") ;
#endif
}
else
{
double alpha, beta ;
cs_dl Amatrix, Bmatrix, *A, *B, *C, *D ;
A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ; /* get B */
alpha = (nargin < 3) ? 1 : mxGetScalar (pargin [2]) ; /* get alpha */
beta = (nargin < 4) ? 1 : mxGetScalar (pargin [3]) ; /* get beta */
C = cs_dl_add (A,B,alpha,beta) ; /* C = alpha*A + beta *B */
cs_dl_dropzeros (C) ; /* drop zeros */
D = cs_dl_transpose (C, 1) ; /* sort result via double transpose */
cs_dl_spfree (C) ;
C = cs_dl_transpose (D, 1) ;
cs_dl_spfree (D) ;
pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */
}
}
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
cs_dl *A, Amatrix ;
double *x ;
CS_INT i, m, n, *parent, *post, *rowcount ;
if (nargout > 1 || nargin != 3)
{
mexErrMsgTxt ("Usage: r = cs_rowcnt(A,parent,post)") ;
}
/* get inputs */
A = cs_dl_mex_get_sparse (&Amatrix, 1, 0, pargin [0]) ;
n = A->n ;
parent = cs_dl_mex_get_int (n, pargin [1], &i, 0) ;
post = cs_dl_mex_get_int (n, pargin [2], &i, 1) ;
rowcount = rowcnt (A, parent, post) ;
pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ;
x = mxGetPr (pargout [0]) ;
for (i = 0 ; i < n ; i++) x [i] = rowcount [i] ;
cs_dl_free (rowcount) ;
}
/* C = cs_transpose (A), computes C=A', where A must be sparse.
C = cs_transpose (A,kind) computes C=A.' if kind <= 0, C=A' if kind > 0 */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
CS_INT values ;
if (nargout > 1 || nargin < 1 || nargin > 2)
{
mexErrMsgTxt ("Usage: C = cs_transpose(A,kind)") ;
}
values = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ;
values = (values <= 0) ? -1 : 1 ;
if (mxIsComplex (pargin [0]))
{
#ifndef NCOMPLEX
cs_cl Amatrix, *A, *C ;
A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
C = cs_cl_transpose (A, values) ; /* C = A' */
pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */
#else
mexErrMsgTxt ("complex matrices not supported") ;
#endif
}
else
{
cs_dl Amatrix, *A, *C ;
A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
C = cs_dl_transpose (A, values) ; /* C = A' */
pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */
}
}
/* cs_lusol: solve A*x=b using a sparse LU factorization */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
double tol ;
CS_INT order ;
if (nargout > 1 || nargin < 2 || nargin > 4)
{
mexErrMsgTxt ("Usage: x = cs_lusol(A,b,order,tol)") ;
}
order = (nargin < 3) ? 2 : mxGetScalar (pargin [2]) ;
order = CS_MAX (order, 0) ;
order = CS_MIN (order, 3) ;
if (nargin == 2)
{
tol = 1 ; /* normal partial pivoting */
}
else if (nargin == 3)
{
tol = (order == 1) ? 0.001 : 1 ; /* tol = 0.001 for amd(A+A') */
}
else
{
tol = mxGetScalar (pargin [3]) ;
}
if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
{
#ifndef NCOMPLEX
cs_cl *A, Amatrix ;
cs_complex_t *x ;
A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */
x = cs_cl_mex_get_double (A->n, pargin [1]) ; /* x = b */
if (!cs_cl_lusol (order, A, x, tol)) /* x = A\x */
{
mexErrMsgTxt ("failed (singular or out of memory)") ;
}
cs_cl_free (A->x) ; /* complex copy no longer needed */
pargout [0] = cs_cl_mex_put_double (A->n, x) ; /* return x */
#else
mexErrMsgTxt ("complex matrices not supported") ;
#endif
}
else
{
cs_dl *A, Amatrix ;
double *x, *b ;
A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */
b = cs_dl_mex_get_double (A->n, pargin [1]) ; /* get b */
x = cs_dl_mex_put_double (A->n, b, &(pargout [0])) ; /* x = b */
if (!cs_dl_lusol (order, A, x, tol)) /* x = A\x */
{
mexErrMsgTxt ("failed (singular or out of memory)") ;
}
}
}
/* cs_qrsol: solve least squares or underdetermined problem */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
CS_INT k, order ;
if (nargout > 1 || nargin < 2 || nargin > 3)
{
mexErrMsgTxt ("Usage: x = cs_qrsol(A,b,order)") ;
}
order = (nargin < 3) ? 3 : mxGetScalar (pargin [2]) ;
order = CS_MAX (order, 0) ;
order = CS_MIN (order, 3) ;
if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
{
#ifndef NCOMPLEX
cs_cl *A, Amatrix ;
cs_complex_t *x, *b ;
A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
b = cs_cl_mex_get_double (A->m, pargin [1]) ; /* get b */
x = cs_dl_calloc (CS_MAX (A->m, A->n), sizeof (cs_complex_t)) ;
for (k = 0 ; k < A->m ; k++) x [k] = b [k] ; /* x = b */
cs_free (b) ;
if (!cs_cl_qrsol (order, A, x)) /* x = A\x */
{
mexErrMsgTxt ("QR solve failed") ;
}
pargout [0] = cs_cl_mex_put_double (A->n, x) ; /* return x */
#else
mexErrMsgTxt ("complex matrices not supported") ;
#endif
}
else
{
cs_dl *A, Amatrix ;
double *x, *b ;
A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
b = cs_dl_mex_get_double (A->m, pargin [1]) ; /* get b */
x = cs_dl_calloc (CS_MAX (A->m, A->n), sizeof (double)) ; /* x = b */
for (k = 0 ; k < A->m ; k++) x [k] = b [k] ;
if (!cs_dl_qrsol (order, A, x)) /* x = A\x */
{
mexErrMsgTxt ("QR solve failed") ;
}
cs_dl_mex_put_double (A->n, x, &(pargout [0])) ; /* return x */
cs_free (x) ;
}
}
/* cs_sqr: symbolic sparse QR factorization */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
double s ;
cs_dls *S ;
cs_dl Amatrix, *A ;
CS_INT m, n, order, *p ;
if (nargout > 7 || nargin != 1)
{
mexErrMsgTxt ("Usage: [vnz,rnz,parent,c,leftmost,p,q] = cs_sqr(A)") ;
}
A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
m = A->m ;
n = A->n ;
if (m < n) mexErrMsgTxt ("A must have # rows >= # columns") ;
order = (nargout == 7) ? 3 : 0 ; /* determine ordering */
S = cs_dl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/
if (!S) mexErrMsgTxt ("cs_sqr failed") ;
s = S->lnz ;
cs_dl_mex_put_double (1, &s, &(pargout [0])) ; /* return nnz(V) */
s = S->unz ;
cs_dl_mex_put_double (1, &s, &(pargout [1])) ; /* return nnz(R) */
pargout [2] = cs_dl_mex_put_int (S->parent, n, 1, 0) ; /* return parent */
pargout [3] = cs_dl_mex_put_int (S->cp, n, 0, 0) ; /* return c */
pargout [4] = cs_dl_mex_put_int (S->leftmost, m, 1, 0) ;/* return leftmost*/
p = cs_dl_pinv (S->pinv, S->m2) ; /* p = pinv' */
pargout [5] = cs_dl_mex_put_int (p, S->m2, 1, 1) ; /* return p */
if (nargout > 6)
{
pargout [6] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */
}
cs_dl_sfree (S) ;
}
/* cs_updown: sparse Cholesky update/downdate (rank-1 or multiple rank) */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
CS_INT ignore, j, k, n, lnz, *parent, sigma = 1, cp [2], ok ;
char sigma_string [20] ;
if (nargout > 1 || nargin < 3 || nargin > 4)
{
mexErrMsgTxt ("Usage: L = cs_updown(L,C,parent,sigma)") ;
}
if (nargin > 3 && mxIsChar (pargin [3]))
{
mxGetString (pargin [3], sigma_string, 8) ;
sigma = (sigma_string [0] == '-') ? (-1) : 1 ;
}
n = mxGetN (pargin [0]) ;
parent = cs_dl_mex_get_int (n, pargin [2], &ignore, 0) ; /* get parent*/
if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
{
#ifndef NCOMPLEX
cs_cl Lmatrix, *Lin, Cmatrix, *C, *L, Cvector, *Cvec ;
/* get input L, and copy MATLAB complex to C complex type */
Lin = cs_cl_mex_get_sparse (&Lmatrix, 1, pargin [0]) ;
/* make a copy of L (this can take more work than updating L itself) */
lnz = Lin->p [n] ;
L = cs_cl_spalloc (n, n, lnz, 0, 0) ;
for (j = 0 ; j <= n ; j++) L->p [j] = Lin->p [j] ;
for (k = 0 ; k < lnz ; k++) L->i [k] = Lin->i [k] ;
/* complex values already copied into Lin->x, use shallow copy for L */
L->x = Lin->x ;
cs_mex_check (0, n, -1, 0, 1, 1, pargin [1]) ; /* get C */
C = cs_cl_mex_get_sparse (&Cmatrix, 0, pargin [1]) ;
/* do the update one column at a time */
Cvec = &Cvector ;
Cvec->m = n ;
Cvec->n = 1 ;
Cvec->p = cp ;
Cvec->nz = -1 ;
cp [0] = 0 ;
for (k = 0 ; k < C->n ; k++)
{
/* extract C(:,k) */
cp [1] = C->p [k+1] - C->p [k] ;
Cvec->nzmax = cp [1] ;
Cvec->i = C->i + C->p [k] ;
Cvec->x = C->x + C->p [k] ;
/* update/downdate */
ok = cs_cl_updown (L, sigma, Cvec, parent) ;
if (!ok) mexErrMsgTxt ("matrix is not positive definite") ;
}
/* return new L */
pargout [0] = cs_cl_mex_put_sparse (&L) ;
cs_free (C->x) ; /* free complex copy of C */
#else
mexErrMsgTxt ("complex matrices not supported") ;
#endif
}
else
{
cs_dl Lmatrix, *Lin, Cmatrix, *C, *L, Cvector, *Cvec ;
/* get input L */
Lin = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ;
/* make a copy of L (this can take more work than updating L itself) */
lnz = Lin->p [n] ;
L = cs_dl_spalloc (n, n, lnz, 1, 0) ;
for (j = 0 ; j <= n ; j++) L->p [j] = Lin->p [j] ;
for (k = 0 ; k < lnz ; k++) L->i [k] = Lin->i [k] ;
for (k = 0 ; k < lnz ; k++) L->x [k] = Lin->x [k] ;
cs_mex_check (0, n, -1, 0, 1, 1, pargin [1]) ; /* get C */
C = cs_dl_mex_get_sparse (&Cmatrix, 0, 1, pargin [1]) ;
/* do the update one column at a time */
Cvec = &Cvector ;
Cvec->m = n ;
Cvec->n = 1 ;
Cvec->p = cp ;
Cvec->nz = -1 ;
cp [0] = 0 ;
for (k = 0 ; k < C->n ; k++)
{
/* extract C(:,k) */
cp [1] = C->p [k+1] - C->p [k] ;
Cvec->nzmax = cp [1] ;
Cvec->i = C->i + C->p [k] ;
Cvec->x = C->x + C->p [k] ;
/* update/downdate */
ok = cs_dl_updown (L, sigma, Cvec, parent) ;
if (!ok) mexErrMsgTxt ("matrix is not positive definite") ;
}
/* return new L */
pargout [0] = cs_dl_mex_put_sparse (&L) ;
}
}
/*
[C, [E]] = provaKoren (A,B), computes Corr(A,B), where A and B must be sparse.
[C, [E]] = provaKoren (A,B,mode) computes Corr(A,b). If mode=0, the column average is calculated on common elements, otherwise column average is calculated on all non-zeros elements (DEFAULT)
E is a matrix contaninng the number of common elements
*/
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
CS_INT modeAllElement ;
if (nargout > 2 || nargin < 2 || nargin > 3)
{
mexErrMsgTxt ("Usage: [C, [E]] = provaKoren (A,B,[mode=0])") ;
}
modeAllElement = (nargin > 2) ? mxGetScalar (pargin [2]) : 1 ; /* default = 1 */
modeAllElement = (modeAllElement == 0) ? 0 : 1 ;
if (modeAllElement && log) fprintf(stdout,"average computed on all non-zeros elements\n");
cs_dl Amatrix, Bmatrix, *A, *B, *C;
A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ; /* get B */
UF_long i, p, pp, Am, An, Anzmax, Anz, *Ap, *Ai ;
UF_long j, q, qq, Bm, Bn, Bnzmax, Bnz, *Bp, *Bi ;
double *Ax, *Bx;
if (!A || !B) { if (log) printf ("(null)\n") ; return ; }
Am = A->m ; An = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; Anzmax = A->nzmax ; Anz = A->nz ;
Bm = B->m ; Bn = B->n ; Bp = B->p ; Bi = B->i ; Bx = B->x ; Bnzmax = B->nzmax ; Bnz = B->nz ;
if (log) fprintf(stdout,"A: mxn = %dx%d\n",Am,An);
if (log) fprintf(stdout,"B: mxn = %dx%d\n",Bm,Bn);
/* allocate result */
cs *corrMatrix = cs_spalloc (An, Bn, An*Bn, 1, 1) ;
cs *commonElementMatrix = cs_spalloc (An, Bn, An*Bn, 1, 1) ;
for (i = 0 ; i < An ; i++)
{
for (j = 0 ; j < Bn ; j++)
{
p=Ap[i];
q=Bp[j];
pp = Ap[i+1];
qq = Bp[j+1];
/* mean on common elements*/
double meanA=0, meanB=0;
long countElementsA=0, countElementsB=0;
if (modeAllElement)
{
for (p=Ap[i] ; p<pp ; p++)
{
meanA += Ax[p];
countElementsA++;
}
for (q=Bp[j] ; q<qq ; q++)
{
meanB += Bx[q];
countElementsB++;
}
}
else
{
while (pp && qq && p<pp && q<qq)
{
/* fprintf(stdout,"i=%d, j=%d, p=%d, q=%d, pp=%d, qq=%d, rowA=%d, rowB=%d \n",i,j,p,q,pp,qq,Ai[p],Bi[q]); */
if (Ai[p]==Bi[q])
{
meanA += Ax[p];
meanB += Bx[q];
countElementsA++;
countElementsB++;
/* fprintf(stdout,"(%d,%d) - sum A = %f, sum B = %f \n",Ai[p],Bi[q],meanA,meanB); */
p++;
q++;
/* values Ax[p] and Bx[q] referring to the same row */
}
else if (Ai[p]>Bi[q])
{
q++;
}
else
{
p++;
}
}
}
meanA = meanA / ((double)countElementsA);
meanB = meanB / ((double)countElementsB);
/* fprintf(stdout,"common elements = %d - mean A = %f, mean B = %f \n",countCommonElements,meanA,meanB); */
/* correleation on common elements*/
double corr;
double corrNum=0, corrDenA=0, corrDenB=0;
double entryA, entryB;
p=Ap[i];
q=Bp[j];
pp = Ap[i+1];
qq = Bp[j+1];
long countCommonElements=0;
while (pp && qq && p<pp && q<qq)
{
/* fprintf(stdout,"i=%d, j=%d, p=%d, q=%d, pp=%d, qq=%d, rowA=%d, rowB=%d \n",i,j,p,q,pp,qq,Ai[p],Bi[q]); */
if (Ai[p]==Bi[q])
{
entryA=Ax[p]-meanA;
entryB=Bx[q]-meanB;
corrNum += entryA * entryB;
corrDenA += entryA*entryA;
corrDenB += entryB*entryB;
p++;
q++;
countCommonElements++;
/* values Ax[p] and Bx[q] referring to the same row */
}
else if (Ai[p]>Bi[q])
{
q++;
}
else
{
p++;
}
}
/* fprintf(stdout,"corrNum=%f, corrDenA=%f, corrDenB=%f\n",corrNum,corrDenA,corrDenB); */
corrDenA = (corrDenA==0) ? 1 : corrDenA;
corrDenB = (corrDenB==0) ? 1 : corrDenB;
corr = corrNum / (sqrt(corrDenA*corrDenB));
/* fprintf(stdout,"corr(%d,%d)=%f\n",i,j,corr); */
cs_entry(corrMatrix,i,j,corr);
cs_entry(commonElementMatrix,i,j,countCommonElements);
}
}
if (log) fprintf(stdout,"provaKoren: outputing computed matrices \n");
corrMatrix=cs_compress(corrMatrix);
pargout [0] = cs_dl_mex_put_sparse (&corrMatrix) ; /* return C */
if (nargout>1)
{
commonElementMatrix=cs_compress(commonElementMatrix);
pargout [1] = cs_dl_mex_put_sparse (&commonElementMatrix) ; /* return E */
}
}
/* cs_lu: sparse LU factorization, with optional fill-reducing ordering */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
CS_INT n, order, *p ;
double tol ;
if (nargout > 4 || nargin > 3 || nargin < 1)
{
mexErrMsgTxt ("Usage: [L,U,p,q] = cs_lu (A,tol)") ;
}
if (nargin == 2) /* determine tol and ordering */
{
tol = mxGetScalar (pargin [1]) ;
order = (nargout == 4) ? 1 : 0 ; /* amd (A+A'), or natural */
}
else
{
tol = 1 ;
order = (nargout == 4) ? 2 : 0 ; /* amd(S'*S) w/dense rows or I */
}
if (mxIsComplex (pargin [0]))
{
#ifndef NCOMPLEX
cs_cls *S ;
cs_cln *N ;
cs_cl Amatrix, *A, *D ;
A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */
n = A->n ;
S = cs_cl_sqr (order, A, 0) ; /* symbolic ordering, no QR bound */
N = cs_cl_lu (A, S, tol) ; /* numeric factorization */
if (!N) mexErrMsgTxt ("cs_lu failed (singular, or out of memory)") ;
cs_cl_free (A->x) ; /* complex copy no longer needed */
cs_cl_dropzeros (N->L) ; /* drop zeros from L and sort it */
D = cs_cl_transpose (N->L, 1) ;
cs_cl_spfree (N->L) ;
N->L = cs_cl_transpose (D, 1) ;
cs_cl_spfree (D) ;
cs_cl_dropzeros (N->U) ; /* drop zeros from U and sort it */
D = cs_cl_transpose (N->U, 1) ;
cs_cl_spfree (N->U) ;
N->U = cs_cl_transpose (D, 1) ;
cs_cl_spfree (D) ;
p = cs_cl_pinv (N->pinv, n) ; /* p=pinv' */
pargout [0] = cs_cl_mex_put_sparse (&(N->L)) ; /* return L */
pargout [1] = cs_cl_mex_put_sparse (&(N->U)) ; /* return U */
pargout [2] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */
/* return Q */
if (nargout == 4) pargout [3] = cs_dl_mex_put_int (S->q, n, 1, 0) ;
cs_cl_nfree (N) ;
cs_cl_sfree (S) ;
#else
mexErrMsgTxt ("complex matrices not supported") ;
#endif
}
else
{
cs_dls *S ;
cs_dln *N ;
cs_dl Amatrix, *A, *D ;
A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */
n = A->n ;
S = cs_dl_sqr (order, A, 0) ; /* symbolic ordering, no QR bound */
N = cs_dl_lu (A, S, tol) ; /* numeric factorization */
if (!N) mexErrMsgTxt ("cs_lu failed (singular, or out of memory)") ;
cs_dl_dropzeros (N->L) ; /* drop zeros from L and sort it */
D = cs_dl_transpose (N->L, 1) ;
cs_dl_spfree (N->L) ;
N->L = cs_dl_transpose (D, 1) ;
cs_dl_spfree (D) ;
cs_dl_dropzeros (N->U) ; /* drop zeros from U and sort it */
D = cs_dl_transpose (N->U, 1) ;
cs_dl_spfree (N->U) ;
N->U = cs_dl_transpose (D, 1) ;
cs_dl_spfree (D) ;
p = cs_dl_pinv (N->pinv, n) ; /* p=pinv' */
pargout [0] = cs_dl_mex_put_sparse (&(N->L)) ; /* return L */
pargout [1] = cs_dl_mex_put_sparse (&(N->U)) ; /* return U */
pargout [2] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */
/* return Q */
if (nargout == 4) pargout [3] = cs_dl_mex_put_int (S->q, n, 1, 0) ;
cs_dl_nfree (N) ;
cs_dl_sfree (S) ;
}
}
/* cs_qr: sparse QR factorization */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
CS_INT m, n, order, *p ;
if (nargout > 5 || nargin != 1)
{
mexErrMsgTxt ("Usage: [V,beta,p,R,q] = cs_qr(A)") ;
}
order = (nargout == 5) ? 3 : 0 ; /* determine ordering */
m = mxGetM (pargin [0]) ;
n = mxGetN (pargin [0]) ;
if (m < n) mexErrMsgTxt ("A must have # rows >= # columns") ;
if (mxIsComplex (pargin [0]))
{
#ifndef NCOMPLEX
cs_cls *S ;
cs_cln *N ;
cs_cl Amatrix, *A, *D ;
A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
S = cs_cl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/
N = cs_cl_qr (A, S) ; /* numeric QR factorization */
cs_free (A->x) ;
if (!N) mexErrMsgTxt ("qr failed") ;
cs_cl_dropzeros (N->L) ; /* drop zeros from V and sort */
D = cs_cl_transpose (N->L, 1) ;
cs_cl_spfree (N->L) ;
N->L = cs_cl_transpose (D, 1) ;
cs_cl_spfree (D) ;
cs_cl_dropzeros (N->U) ; /* drop zeros from R and sort */
D = cs_cl_transpose (N->U, 1) ;
cs_cl_spfree (N->U) ;
N->U = cs_cl_transpose (D, 1) ;
cs_cl_spfree (D) ;
m = N->L->m ; /* m may be larger now */
p = cs_cl_pinv (S->pinv, m) ; /* p = pinv' */
pargout [0] = cs_cl_mex_put_sparse (&(N->L)) ; /* return V */
cs_dl_mex_put_double (n, N->B, &(pargout [1])) ; /* return beta */
pargout [2] = cs_dl_mex_put_int (p, m, 1, 1) ; /* return p */
pargout [3] = cs_cl_mex_put_sparse (&(N->U)) ; /* return R */
pargout [4] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */
cs_cl_nfree (N) ;
cs_cl_sfree (S) ;
#else
mexErrMsgTxt ("complex matrices not supported") ;
#endif
}
else
{
cs_dls *S ;
cs_dln *N ;
cs_dl Amatrix, *A, *D ;
A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
S = cs_dl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/
N = cs_dl_qr (A, S) ; /* numeric QR factorization */
if (!N) mexErrMsgTxt ("qr failed") ;
cs_dl_dropzeros (N->L) ; /* drop zeros from V and sort */
D = cs_dl_transpose (N->L, 1) ;
cs_dl_spfree (N->L) ;
N->L = cs_dl_transpose (D, 1) ;
cs_dl_spfree (D) ;
cs_dl_dropzeros (N->U) ; /* drop zeros from R and sort */
D = cs_dl_transpose (N->U, 1) ;
cs_dl_spfree (N->U) ;
N->U = cs_dl_transpose (D, 1) ;
cs_dl_spfree (D) ;
m = N->L->m ; /* m may be larger now */
p = cs_dl_pinv (S->pinv, m) ; /* p = pinv' */
pargout [0] = cs_dl_mex_put_sparse (&(N->L)) ; /* return V */
cs_dl_mex_put_double (n, N->B, &(pargout [1])) ; /* return beta */
pargout [2] = cs_dl_mex_put_int (p, m, 1, 1) ; /* return p */
pargout [3] = cs_dl_mex_put_sparse (&(N->U)) ; /* return R */
pargout [4] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */
cs_dl_nfree (N) ;
cs_dl_sfree (S) ;
}
}
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
int iterations;
double mu, lrate,lrateB, lambda,lambdaB;
double *buin, *biin, *qin, *xin, *yin, *pin, *zin;
double *bu, *bi, *q, *x, *y, *p, *z;
int ls;
int itemsNum, usersNum;
cs_dl Amatrix, *A;
bool useruser = false;
FILE *verbose;
if (nargout < 5 || nargout > 7 || nargin < 10 || nargin > 12)
{
mexErrMsgTxt ("Usage: [bu,bi,q,x,y,[p,z]]=learnFactorModel(urm,mu,bu,bi,iterations,lrate,lrateB,lambda,lambdaB,q,x,y,[p,z]) \n urm must be sparse, bu and bi must be dense") ;
}
if (nargout>5 && nargin>11)
{
useruser=true; /* enable the integration of the user-user model into the item-item model */
if (log) fprintf(stdout,"user-user model enabled\n");
}
int indexArgin = 0, indexArgout = 0;;
if (log>1)
{
verbose = fopen("/home/roby/verbose.txt", "w+");
fprintf(stdout, "verbose mode");
}
if (log) fprintf(stdout,"--input started\n");
A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [indexArgin]) ; usersNum = mxGetM(pargin[indexArgin++]); /* get A=urm */
mu = mxGetScalar (pargin [indexArgin++]);
buin = mxGetPr(pargin[indexArgin++]);
biin = mxGetPr(pargin[indexArgin++]);
iterations = mxGetScalar (pargin [indexArgin++]);
lrate = mxGetScalar (pargin [indexArgin++]);
lrateB = mxGetScalar (pargin [indexArgin++]);
lambda = mxGetScalar (pargin [indexArgin++]);
lambdaB = mxGetScalar (pargin [indexArgin++]);
qin = mxGetPr(pargin[indexArgin]); ls = mxGetM(pargin[indexArgin]); itemsNum = mxGetN(pargin[indexArgin++]);
xin = mxGetPr(pargin[indexArgin++]);
yin = mxGetPr(pargin[indexArgin++]);
if (useruser)
{
pin = mxGetPr(pargin[indexArgin++]);
zin = mxGetPr(pargin[indexArgin++]);
if (log) fprintf(stdout," read: p and z \n");
}
if (log) fprintf(stdout,"users=%d, items=%d\n",usersNum,itemsNum);
if (log) fprintf(stdout,"number of factors=%d, number of iterations=%d\n",ls,iterations);
if (log) fprintf(stdout," bu =[%d x %d] \n", mxGetM(pargin[2]), mxGetN(pargin[2]));
if (log) fprintf(stdout," bi =[%d x %d] \n", mxGetM(pargin[3]), mxGetN(pargin[3]));
if (log) fprintf(stdout,"--input completed\n");
UF_long Am, An, Anzmax, Anz, *Ap, *Ai ;
double *Ax ;
if (!A) { printf ("(null)\n") ; return ; }
Am = A->m ; An = A->n ; Ap = A->p ; Ai = A->i ;
Ax = A->x ; Anzmax = A->nzmax ; Anz = A->nz ;
/*
B = transpose of URM
*/
cs_dl *B;
UF_long Bm, Bn, Bnzmax, Bnz, *Bp, *Bi ;
double *Bx ;
B = cs_dl_transpose (A, 1) ; /* B = A' = urm' */
Bm = B->m ; Bn = B->n ; Bp = B->p ; Bi = B->i ;
Bx = B->x ; Bnzmax = B->nzmax ; Bnz = B->nz ;
int ii;
pargout[indexArgout]=mxCreateDoubleMatrix(usersNum,1,mxREAL);
bu=mxGetPr(pargout[indexArgout++]);
for (ii=0;ii<usersNum;ii++) bu[ii] = buin[ii];
pargout[indexArgout]=mxCreateDoubleMatrix(itemsNum,1,mxREAL);
bi=mxGetPr(pargout[indexArgout++]);
for (ii=0;ii<itemsNum;ii++) bi[ii] = biin[ii];
pargout[indexArgout]=mxCreateDoubleMatrix(ls,itemsNum,mxREAL);
q=mxGetPr(pargout[indexArgout++]);
for (ii=0;ii<ls*itemsNum;ii++) q[ii] = qin[ii];
pargout[indexArgout]=mxCreateDoubleMatrix(ls,itemsNum,mxREAL);
x=mxGetPr(pargout[indexArgout++]);
for (ii=0;ii<ls*itemsNum;ii++) x[ii] = xin[ii];
pargout[indexArgout]=mxCreateDoubleMatrix(ls,itemsNum,mxREAL);
y=mxGetPr(pargout[indexArgout++]);
for (ii=0;ii<ls*itemsNum;ii++) y[ii] = yin[ii];
if (useruser)
{
pargout[indexArgout]=mxCreateDoubleMatrix(ls,usersNum,mxREAL);
p=mxGetPr(pargout[indexArgout++]);
for (ii=0;ii<ls*usersNum;ii++) p[ii] = pin[ii];
if (log) fprintf(stdout," p initialized \n");
pargout[indexArgout]=mxCreateDoubleMatrix(ls,usersNum,mxREAL);
z=mxGetPr(pargout[indexArgout++]);
for (ii=0;ii<ls*usersNum;ii++) z[ii] = zin[ii];
if (log) fprintf(stdout," z initialized \n");
}
if (log) fprintf(stdout," \n allocated %d outputs \n",indexArgout);
int count, u, i, j, k;
int iii;
int itemj;
int numRatedItems, numRatingUsers;
double puCoeff, zvCoeff;
double *pu=calloc(ls, sizeof(double));
double *zv=calloc(ls, sizeof(double));
double sum[ls];
double *sumUU=calloc(ls, sizeof(double));
double cumerror=0.0, pseudoRMSE=0.0;
long numTests=0;
int anomaliesCounter=0;
const int maxAnomalies=100000;
time_t t1,t2, t0;
(void) time(&t0);
for (count=0;count<iterations;count++) /* FOR count=1,#iterations DO */
{
(void) time(&t1);
cumerror=0.0;
numTests = 0;
anomaliesCounter = 0;
for (u=0;u<usersNum;u++) /* FOR u=1,..,m DO */
{
double errorUU=0;
for (iii=0;iii<ls;iii++) pu[iii]=0.0; /* pu[ls] <- 0 */
numRatedItems = (int) (Bp [u+1] - Bp [u]);
if (numRatedItems==0) continue;
/* compute the component independent of i*/
for (j=Bp[u]; j<Bp[u+1]; j++)
{
double ruj, biasi, xjk, yjk;
itemj = Bi[j];
ruj=Bx[j]; /* r_uj */
biasi=bi[itemj];
puCoeff = (ruj - (mu + bu[u] + biasi)) / (sqrt((double) numRatedItems)); /* |R(u)|^-1/2 * (r_uj - b_uj) */
for (k=0;k<ls;k++) /* compute pu for each feature k*/
{
xjk = x[ls*itemj+k]; /* x[ls*itemj+k] = x[ls,itemj] */
yjk = y[ls*itemj+k]; /* y[ls*itemj+k] = y[ls,itemj] */
pu[k] = pu[k] + (puCoeff * xjk);
pu[k] = pu[k] + (yjk / (sqrt((double) numRatedItems)));
}
}
for (iii=0;iii<ls;iii++) sum[iii]=0.0; /* sum[ls] <- 0 */
if (useruser)
{
for (iii=0;iii<ls;iii++) sumUU[iii]=0.0; /* sumUU[ls] <- 0 */
}
/* FOR ALL i (itemj) IN R(u) DO */
for (j=Bp[u]; j<Bp[u+1]; j++)
{
double r_hat_ui=0.0, e_ui;
double biasi;
itemj = Bi[j];
if (useruser) /* if user-user is enabled */
{
int useri;
numRatingUsers = Ap [itemj+1] - Ap [itemj]; /* |R(i)| */
for (iii=0;iii<ls;iii++) zv[iii]=0.0; /* zv[ls] <- 0 */
biasi = bi[itemj]; /* bias item j */
for (i=Ap[itemj]; i<Ap[itemj+1]; i++)
{
double rvj, biasvj, zjk;
useri = Ai[i];
rvj=Ax[i];
biasvj=bu[useri];
zvCoeff = (rvj - (mu + biasvj + biasi)) / (sqrt((double) numRatingUsers)); /* |R(i)|^-1/2 * (r_vj - b_vj) */
for (k=0;k<ls;k++) /* compute pu for each feature k*/
{
zjk = z[ls*useri+k]; /* z[ls*useri+k] = z[ls,itemj] */
zv[k] += (zvCoeff * zjk);
}
}
for (k=0; k<ls; k++) /* p_u' * z_v */
{
r_hat_ui += ( p[ls*u+k] * zv[k] ); /* p_u(k) * zv(k) */
}
}
for (k=0; k<ls; k++) /* q_i' * pu */
{
r_hat_ui += ( q[ls*itemj+k] * pu[k] ); /* q_i(k) * pu(k) */
}
r_hat_ui += (mu + bu[u] + bi[itemj]); /* r_hat_ui = mu + bu + bi + q_i'*pu */
e_ui = Bx[j] - r_hat_ui; /* e_ui = r_ui - r_hat_ui */
if (log>1) fprintf(verbose,"(%d,%d)=%f\n",u,itemj,e_ui);
if (mxIsNaN(e_ui) || mxIsInf(e_ui) || absolute(e_ui)>100000)
{
fprintf(stdout, " -!- [%d] -!- user=%d, item=%d, r=%f, r_hat=%f, e_ui=%f gradient error too large \n",anomaliesCounter,u,itemj,Bx[j],r_hat_ui,e_ui);
fprintf(stdout, " biasu=%f, biasi=%f \n", bu[u], bi[itemj]);
if (log>1) fclose(verbose);
return;
}
if (absolute(e_ui)>7)
{
fprintf(stdout, " -!- [%d] -!- user=%d, item=%d, r=%f, r_hat=%f, e_ui=%f gradient error too large \n",anomaliesCounter,u,itemj,Bx[j],r_hat_ui,e_ui);
fprintf(stdout, " biasu=%f, biasi=%f \n", bu[u], bi[itemj]);
if (log>1) fclose(verbose);
anomaliesCounter++;
if (anomaliesCounter>maxAnomalies) return;
}
cumerror += (e_ui*e_ui);
numTests++;
for (k=0; k<ls; k++) /* sum <- sum + e_ui * q_i */
{
sum[k] += (e_ui*q[ls*itemj+k]); /* sum(k) = e_ui * q_i(k) */
}
if (useruser) /* sumUU <- sumUU + e_ui * p_u */
{
for (k=0; k<ls; k++)
{
sumUU[k] += (e_ui*p[ls*u+k]); /* sumUU(k) = e_ui * p_u(k) */
}
}
/* perform gradient step on qi, bu, bi AND on "pu" if user-user model is enabled */
bu[u] += (lrateB * (e_ui - lambdaB*bu[u])); /* bu <- bu + gamma*(e_ui-lambdaB*bu) */
bi[itemj] += (lrateB * (e_ui - lambdaB*bi[itemj])); /* bi <- bi + gamma*(e_ui-lambdaB*bi) */
for (k=0; k<ls; k++)
{
q[ls*itemj+k] += (lrate * (e_ui*pu[k] - lambda* q[ls*itemj+k])); /* q_i <- q_i + gamma*(e_ui*pu-lambda*q_i) */
if (useruser)
{
p[ls*u+k] += (lrate * (e_ui*zv[k] - lambda* p[ls*u+k])); /* p_u <- p_u + gamma*(e_ui*zv-lambda*p_u) */
}
}
}
/* FOR ALL i IN R(u) DO */
for (j=Bp[u]; j<Bp[u+1]; j++) /* perform gradient step on xi*/
{
itemj = Bi[j];
double ruj = Bx[j];
double biasi = bi[itemj];
puCoeff = (1/sqrt(numRatedItems)) * (ruj - (mu + bu[u] + biasi)); /* |R(u)|^-1/2 * (r_ui - b_ui) */
for (k=0; k<ls; k++)
{
x[ls*itemj+k] += (lrate * ( puCoeff*sum[k] - lambda*x[ls*itemj+k] )); /* update of every feature of xi */
}
if (useruser)
{
int useri;
numRatingUsers = Ap [itemj+1] - Ap [itemj]; /* |R(i)| */
/* FOR ALL useri IN R(i) DO */
for (i=Ap[itemj]; i<Ap[itemj+1]; i++) /* perform gradient step on zv*/
{
double rvj = Ax[i];
double biasvj;
useri = Ai[i]; /* we are looping on all useri who rated itemj*/
biasvj = bu[useri]; /* bias user v*/
zvCoeff = (1/sqrt(numRatingUsers)) * (rvj - (mu + biasvj + biasi)); /* |R(i)|^-1/2 * (r_vj - b_vj) */
for (k=0; k<ls; k++)
{
z[ls*useri+k] += (lrate * ( zvCoeff*sumUU[k] - lambda*z[ls*useri+k] ) ); /* update of every feature of zv */
}
}
}
}
/* FOR ALL i IN N(u) DO */
for (j=Bp[u]; j<Bp[u+1]; j++) /* perform gradient step on yi*/
{
itemj = Bi[j];
double ruj = Bx[j];
puCoeff = (1/sqrt(numRatedItems)); /* |N(u)|^-1/2 */
for (k=0; k<ls; k++)
{
y[ls*itemj+k] += (lrate * ( puCoeff*sum[k] - lambda*y[ls*itemj+k] ) ); /* update of every feature of yi */
}
}
if (log && ( ((u-1) % 10000 == 0)) )
{
(void) time(&t2);
fprintf(stdout, "[%d] time for last group (up to user %d) is %d secs - remaining Time =%d secs\n", (int) t2-t0,u, (int) t2-t1, (int) ( ( (t2-t0)/((double) u))*((double)((usersNum-u)*(count+1)))));
if ((((double) (t2-t1))/10000.0)>1.0) fprintf (stdout, "warning... high computing time");
if (file_exists("~/stopnow")) return;
(void) time(&t1);
}
}
pseudoRMSE = cumerror / ((double) numTests);
if (log)
{
fprintf(stdout, " cumulative error iteration %d = %g (%d tests) \n", count, pseudoRMSE,numTests);
if (file_exists("~/stopiter")) return;
}
if (mxIsNaN(pseudoRMSE))
{
fprintf(stdout, " -!- STOPPED -!- ");
return;
}
}
if (log>1) fclose(verbose);
}
