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 */
}
}
int main (void)
{
cs_dl *T, *A, *Eye, *AT, *C, *D ;
UF_long i, m ;
T = cs_dl_load (stdin) ; /* load triplet matrix T from stdin */
printf ("T:\n") ; cs_dl_print (T, 0) ; /* print T */
A = cs_dl_compress (T) ; /* A = compressed-column form of T */
printf ("A:\n") ; cs_dl_print (A, 0) ; /* print A */
cs_dl_spfree (T) ; /* clear T */
AT = cs_dl_transpose (A, 1) ; /* AT = A' */
printf ("AT:\n") ; cs_dl_print (AT, 0) ; /* print AT */
m = A ? A->m : 0 ; /* m = # of rows of A */
T = cs_dl_spalloc (m, m, m, 1, 1) ; /* create triplet identity matrix */
for (i = 0 ; i < m ; i++) cs_dl_entry (T, i, i, 1) ;
Eye = cs_dl_compress (T) ; /* Eye = speye (m) */
cs_dl_spfree (T) ;
C = cs_dl_multiply (A, AT) ; /* C = A*A' */
D = cs_dl_add (C, Eye, 1, cs_dl_norm (C)) ; /* D = C + Eye*norm (C,1) */
printf ("D:\n") ; cs_dl_print (D, 0) ; /* print D */
cs_dl_spfree (A) ; /* clear A AT C D Eye */
cs_dl_spfree (AT) ;
cs_dl_spfree (C) ;
cs_dl_spfree (D) ;
cs_dl_spfree (Eye) ;
return (0) ;
}
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
CS_INT n, nel, s ;
cs *A, *AT ;
if (nargout > 1 || nargin != 3)
{
mexErrMsgTxt ("Usage: C = cs_frand(n,nel,s)") ;
}
n = mxGetScalar (pargin [0]) ;
nel = mxGetScalar (pargin [1]) ;
s = mxGetScalar (pargin [2]) ;
n = CS_MAX (1,n) ;
nel = CS_MAX (1,nel) ;
s = CS_MAX (1,s) ;
AT = cs_dl_frand (n, nel, s) ;
A = cs_dl_transpose (AT, 1) ;
cs_dl_spfree (AT) ;
cs_dl_dropzeros (A) ;
pargout [0] = cs_dl_mex_put_sparse (&A) ;
}
/* 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_sparse: convert triplet form into compress-column form sparse matrix */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
if (nargout > 1 || nargin != 3)
{
mexErrMsgTxt ("Usage: A = cs_sparse(i,j,x)") ;
}
if (mxIsComplex (pargin [2]))
{
#ifndef NCOMPLEX
cs_cl *A, *C, *T, Tmatrix ;
T = &Tmatrix ; /* get i,j,x and copy to triplet form */
T->nz = mxGetM (pargin [0]) ;
T->p = cs_dl_mex_get_int (T->nz, pargin [0], &(T->n), 1) ;
T->i = cs_dl_mex_get_int (T->nz, pargin [1], &(T->m), 1) ;
cs_mex_check (1, T->nz, 1, 0, 0, 1, pargin [2]) ;
T->x = cs_cl_mex_get_double (T->nz, pargin [2]) ;
T->nzmax = T->nz ;
C = cs_cl_compress (T) ; /* create sparse matrix C */
cs_cl_dupl (C) ; /* remove duplicates from C */
cs_cl_dropzeros (C) ; /* remove zeros from C */
A = cs_cl_transpose (C, -1) ; /* A=C.' */
cs_cl_spfree (C) ;
pargout [0] = cs_cl_mex_put_sparse (&A) ; /* return A */
cs_free (T->p) ;
cs_free (T->i) ;
cs_free (T->x) ; /* free copy of complex values*/
#else
mexErrMsgTxt ("complex matrices not supported") ;
#endif
}
else
{
cs_dl *A, *C, *T, Tmatrix ;
T = &Tmatrix ; /* get i,j,x and copy to triplet form */
T->nz = mxGetM (pargin [0]) ;
T->p = cs_dl_mex_get_int (T->nz, pargin [0], &(T->n), 1) ;
T->i = cs_dl_mex_get_int (T->nz, pargin [1], &(T->m), 1) ;
cs_mex_check (1, T->nz, 1, 0, 0, 1, pargin [2]) ;
T->x = mxGetPr (pargin [2]) ;
T->nzmax = T->nz ;
C = cs_dl_compress (T) ; /* create sparse matrix C */
cs_dl_dupl (C) ; /* remove duplicates from C */
cs_dl_dropzeros (C) ; /* remove zeros from C */
A = cs_dl_transpose (C, 1) ; /* A=C' */
cs_dl_spfree (C) ;
pargout [0] = cs_dl_mex_put_sparse (&A) ; /* return A */
cs_free (T->p) ;
cs_free (T->i) ;
}
}
/* 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);
}
