void solver (int n) {
int i, lda, ldb, nrhs, info, *ipiv;
double *a, *b;
// Get matrix dimension and allocate arrays
lda = n;
ldb = n;
nrhs = 1;
a = (double *) malloc(sizeof(double) * n * n);
b = (double *) malloc(sizeof(double) * n);
ipiv = (int *) malloc(sizeof(int) * n);
// Fill matrix a and vector b with random values
for (i=0; i<n*n; i++)
a[i] = drand48();
for (i=0; i<n; i++)
b[i] = drand48();
dgesv(&n, &nrhs, a, &lda, ipiv, b, &ldb, &info);
free(a);
free(b);
free(ipiv);
return;
}
int main(void)
{
int n=4096;
int nrhs = n;
int lda = n;
int ldb = n;
int info = 0;
// Define matrix variables
double *A;
int *ipiv;
double *B;
// Allocate matrices
A = (double*) malloc(lda*n*sizeof(double));
ipiv = (int*) malloc(n*sizeof(int));
B = (double*) malloc(ldb*nrhs*sizeof(double));
// Add some random data
fillRandomDouble(lda, n, A, -10.0f, 10.0f);
fillRandomDouble(ldb, nrhs, B, -10.0f, 10.0f);
// Solve the system A*X=B using Intel MKL libraries
dgesv(&n, &nrhs, A, &lda, ipiv, B, &ldb, &info);
// Free the memory
free(A);
free(ipiv);
free(B);
}
void lusolve(Matrix A, Vector x, int** ipiv)
{
if (*ipiv == NULL)
*ipiv = malloc(x->len*sizeof(int));
int one=1;
int info;
dgesv(&x->len,&one,A->data[0],&x->len,*ipiv,x->data,&x->len,&info);
}
void mexFunction( int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[] )
{
/* mex interface to LAPACK functions dsysvx and zhesvx */
int m, n, bnrhs, lda, *ipiv, ldb, info;
double *A,*b, *AT, *bT, *ret;
int i;
if (nrhs != 2) {
mexErrMsgTxt("Expect 2 input arguments and return 1 output argument");
}
A = mxGetPr(prhs[0]);
b = mxGetPr(prhs[1]);
m = mxGetM(prhs[0]);
n = mxGetN(prhs[0]);
bnrhs = mxGetN(prhs[1]);
AT = (double *)mxCalloc(m*n,sizeof(double));
bT = (double *)mxCalloc(m*bnrhs,sizeof(double));
ipiv = (int *)mxCalloc(m,sizeof(int));
for(i=0;i<m*bnrhs;i++) {
bT[i] = b[i];
}
for(i=0;i<m*n;i++) AT[i] = A[i];
lda = m;
ldb = m;
dgesv(&m, &bnrhs, AT, &lda, ipiv, bT, &ldb, &info);
plhs[0] = mxCreateDoubleMatrix(m,bnrhs,mxREAL);
ret = mxGetPr(plhs[0]);
for(i=0;i<m*bnrhs;i++) ret[i] = bT[i];
mxFree(AT);
mxFree(bT);
mxFree(ipiv);
}
// ================================
// solve linear equations C = A\B
// ================================
void solve(double* C, double* A, double* B,
const int rA, const int cA, const int rB, const int cB,
const char *mod, double *W, const int LW, ptrdiff_t *S) {
#ifdef USE_BLAS
int i, j, rank;
char uplo = 'U', side = 'L', trans = 'N', unit = 'N';
double one = 1.0, rcond = 0.000000001;
ptrdiff_t rA0 = rA, cA0 = cA, cB0 = cB, Lwork=LW, info;
ptrdiff_t rC0 = (rA>cA) ? rA : cA;
//ptrdiff_t ptr_S = S;
switch (mod[0]){
case 'L':
case 'U':
uplo = mod[0];
dtrsm(&side, &uplo, &trans, &unit, &rC0, &cB0, &one, A, &rA0, C, &rC0);
break;
case 'P':
dposv(&uplo, &rA0, &cB0, W, &rA0, C, &rA0, &info);// A has already been copied into W
break;
default:
if (rA == cA) {
//dgesv(&rA0, &cB0, W, &rA0, S, C, &rA0, &info);// A has already been copied into W
dgesv(&rA0, &cB0, W, &rA0, (ptrdiff_t*)S, C, &rA0, &info);// A has already been copied into W
}
else{
for( i=0; i<cB; i++ )
for( j=0; j<rB; j++ )
C[i*rC0+j] = B[i*rB+j];
//dgelsy(&rA0, &cA0, &cB0, A, &rA0, C, &rC0, S, &rcond, &rank, W, &Lwork, &info);
dgelsy(&rA0, &cA0, &cB0, A, &rA0, C, &rC0,
(ptrdiff_t*)S, &rcond, (ptrdiff_t*)&rank, W, &Lwork, &info);
}
}
#endif
}
int bundle_qp_solve_mask (bundle_t *bundle, uint64_t mask)
/*
* Attempts to solve the penalized bundle QP assuming the zero/nonzero constraint multiplier combination specified in 'mask' is correct:
* max z - 1/2t <x^T,x>
* s.c
* z - <A_i,x> <= b_i, i = 1,...,m : mul
* z scalar, x n-dimensional vector
*
* This QP is convex, therefore solving it is equivalent to solving the KKT conditions system.
*
* For all possible values of mask,
* if the i-th bit of mask is 1:
* => z* - <A_i,x*> = b_i.
* if the i-th bit of mask is 0:
* => mul*_i = 0.
*
* Also, supposing the KKT conditions are verified, we have, with k iterating over all 1-bits of mask,
* grad(z* - 1/2t <x^T,x*>) = sum over k of (mul*_k . grad(z* - <A_k,x*>))
* <=> [1 | -1/t x*] = sum over i of (mul*_k . [1 | -A_k])
* <=> t . sum over k of (mul*_k . A_k) = x*
* and sum over k of mul*_k = 1.
*
* Therefore by substituting x* we obtain the system:
* z* - <A_i, t . sum over k of (mul*_k . A_k)> = b_i, for all i with the i-th bit of 'mask' is 1
* <=> | -t(A'.A'^T) e | . | mul | = | b |, with e = (1, ..., 1) and dim(e) = number of bits of mask set to 1
* | e^T 0 | | z | | 1 |, and with A' = A with the rows corresponding to the bits set to 0 in mask removed.
*
* If the system is not linearly independent, then the optimal solution cannot be found with this mask.
* Otherwise, having mul* and z*, we verify dual feasibility, for all i set to 1 in mask:
* <=> mul_i* >= 0
* Also, we verify dual optimality:
* <=> z* is minimal for all dual-feasible z* found with other masks
* Finally, we verify primal feasibility, for all i set to 0 in mask:
* <=> z* - <A_i,x*> <= b_i, and substituting x*,
* <=> z* - t . sum over k of mul*_k <A_i, A_k^T> <= b_i
*
* If these hold then all KKT conditions are verified and z* is optimal.
*/
{
double z;
int info, isize;
uint64_t bit;
int i, j, k;
// get system size (in bundle->kkt_m) and active constraint indices (in bundle->kkt_i[])
// set system rhs (in bundle->kkt_mul[])
for (bundle->kkt_m = i = 0, bit = 1; i < bundle->m; i++, bit <<= 1)
if (mask & bit) {
bundle->kkt_i[bundle->kkt_m] = i;
bundle->kkt_mul[bundle->kkt_m] = bundle->b[i];
++bundle->kkt_m;
}
bundle->kkt_mul[bundle->kkt_m] = 1.0;
isize = 1 + bundle->kkt_m; // set matrix dimension size for LAPACK
// set system lhs (in bundle->kkt_a[][])
for (i = 0; i < bundle->kkt_m; i++) {
for (j = 0; j < bundle->kkt_m; j++)
bundle->kkt_a[i * isize + j] = bundle->kkt_a[j * isize + i] = - (bundle->aat[bundle->kkt_i[i] * bundle->max_m + bundle->kkt_i[j]] / bundle->scale);
bundle->kkt_a[i * isize + bundle->kkt_m] = 1.0;
bundle->kkt_a[bundle->kkt_m * isize + i] = 1.0;
}
bundle->kkt_a[bundle->kkt_m * isize + bundle->kkt_m] = 0.0;
// solve system using LAPACK, to retrieve mul* and z* (in bundle->kkt_mul[])
info = dgesv(isize, bundle->kkt_a, bundle->ipiv, bundle->kkt_mul);
// check if system has full rank
if (info > 0)
return 0;
// system is linearly independent and has a unique solution
z = bundle->kkt_mul[bundle->kkt_m];
// check dual feasibility
for (i = 0; i < bundle->kkt_m; i++)
if (bundle->kkt_mul[i] < 0.0)
return 0;
// check dual optimality
if (z > bundle->kkt_z * 1.01)
return 0;
else if (z < bundle->kkt_z)
bundle->kkt_z = z;
// check primal feasibility
for (k = i = 0, bit = 1; i < bundle->m; i++, bit <<= 1) {
if (mask & bit) {
bundle->next_b[i] = z;
}
else {
bundle->next_b[i] = 0.0;
for (j = 0; j < bundle->kkt_m; j++)
bundle->next_b[i] += bundle->kkt_mul[j] * bundle->aat[i * bundle->max_m + bundle->kkt_i[j]];
bundle->next_b[i] /= bundle->scale;
bundle->next_b[i] += bundle->b[i];
if (z > bundle->next_b[i] + bundle->epsilon)
return 0;
}
}
// the KKT conditions are all verified
return 1;
}
/* Return information if the solution was computed */
ptrdiff_t Basis_Solve(PT_Basis pB, double *q, double *x, T_Options options)
{
/* Basis B */
/* I = W union (Z+m) -> ordered */
/* X = M_/W,Z <- invertible */
/* G = M_W,Z */
/* Bx_B = q -> x = [w_W;z_Z] */
/* z_Z = iX*q_/W */
/* w_W = q_W - G*x_/W */
ptrdiff_t i, incx=1, nb, m, diml, info;
char T;
double alpha=-1.0, beta=1.0;
/* x(1:length(W)) = q(W) */
for(i=0;i<Index_Length(pB->pW);i++) x[i] = q[Index_Get(pB->pW, i)];
/* X = [] */
if(Index_Length(pB->pWc) == 0)
return 0;
/* z = q(B.Wc) */
for(i=0;i<Index_Length(pB->pWc);i++) pB->z[i] = q[Index_Get(pB->pWc, i)];
/* because the right hand side will be overwritten in dgesv, store it into
temporary vector r */
dcopy(&(Index_Length(pB->pWc)), pB->z, &incx, pB->r, &incx);
/* printf("x :\n"); */
/* Vector_Print_raw(pB->z,Index_Length(pB->pW)); */
/* printf("z :\n"); */
/* Vector_Print_raw(pB->z,Index_Length(pB->pWc)); */
/* x = [x1;x2] */
/* x2 = inv(X)*q(Wc) = inv(X)*z */
nb = 1; /* number of right hand side in A*x=b is 1 */
m = Matrix_Rows(pB->pF);
/* Find solution to general problem A*x=b using LAPACK
All the arguments have to be pointers. A and b will be altered on exit. */
switch (options.routine) {
case 1:
/* DGESV method implements LU factorization of A. */
dgesv(&m, &nb, pMAT(pB->pF), &((pB->pF)->rows_alloc),
pB->p, pB->r, &m, &info);
break;
case 2:
/* DGELS solves overdetermined or underdetermined real linear systems
involving an M-by-N matrix A, or its transpose, using a QR or LQ
factorization of A. It is assumed that A has full rank. */
T = 'n'; /* Not transposed */
diml = 2*m;
dgels(&T, &m, &m, &nb, pMAT(pB->pF), &((pB->pF)->rows_alloc),
pB->r, &m, pB->s, &diml, &info );
break;
default :
/* solve with factors F or U */
/* solve using LUMOD (no checks) */
/* LU_Solve0(pB->pLX, pB->pUX, pB->z, &(x[Index_Length(pB->pW)])); */
/* solve using LAPACK (contains also singularity checks) */
/* need to pass info as a pointer, otherwise weird numbers are assigned */
LU_Solve1(pB->pLX, pB->pUt, pB->z, &(x[Index_Length(pB->pW)]), &info);
/* if something went wrong, refactorize and solve again */
if (info!=0) {
/* printf("info=%ld, refactoring\n", info); */
/* Matrix_Print_row(pB->pLX); */
/* Matrix_Print_utril_row(pB->pUX); */
/* Matrix_Print_col(pB->pUt); */
LU_Refactorize(pB);
/* if this fails again, then no minimum ratio is found -> exit with
* numerical problems flag */
LU_Solve1(pB->pLX, pB->pUt, pB->z, &(x[Index_Length(pB->pW)]), &info);
}
}
/* x1 = -G*x2 + q(W) */
/* y = alpha*G*x + beta*y */
/* alpha = -1.0; */
/* beta = 1.0; */
T = 'n'; /* Not transposed */
if (options.routine>0) {
/* take LAPACK solution */
/* printf("lapack solution z:\n"); */
/* Vector_Print_raw(pB->r,Index_Length(pB->pWc)); */
/* matrix F after solution is factored in [L\U], we want the original format for the next call
to dgesv, thus create a copy F <- X */
Matrix_Copy(pB->pX, pB->pF, pB->w);
/* printf("x after lapack solution:\n"); */
/* Vector_Print_raw(x,Index_Length(pB->pW)+Index_Length(pB->pWc)); */
/* recompute the remaining variables according to basic solution */
dgemv(&T, &(Matrix_Rows(pB->pG)), &(Matrix_Cols(pB->pG)),
&alpha, pMAT(pB->pG), &((pB->pG)->rows_alloc),
pB->r, &incx, &beta, x, &incx);
/* append the basic solution at the end of x vector */
dcopy(&(Index_Length(pB->pWc)), pB->r, &incx, &(x[Index_Length(pB->pW)]), &incx);
} else {
/* take LUmod solution */
dgemv(&T, &(Matrix_Rows(pB->pG)), &(Matrix_Cols(pB->pG)),
&alpha, pMAT(pB->pG), &((pB->pG)->rows_alloc),
&(x[Index_Length(pB->pW)]), &incx,
&beta, x, &incx);
}
/* printf("y:\n"); */
/* Vector_Print_raw(x,Matrix_Rows(pB->pG)); */
return info;
}
void PolynomialInterp::InterpolateCoeffs(
int nPoints,
const double * dX,
const double * dY,
double * dA,
double dXmid,
double * dWorkspace,
int * iPivot
) {
// Check if an external workspace is specified
bool fExternalWorkspace = (dWorkspace == NULL)?(false):(true);
if (!fExternalWorkspace) {
dWorkspace = new double[nPoints*nPoints];
}
// Check if an external pivot vector is specified
bool fExternalPivot = (iPivot == NULL)?(false):(true);
if (!fExternalPivot) {
iPivot = new int[nPoints];
}
// Construct the Vandermonde matrix
int i;
int j;
int k = 0;
for (j = 0; j < nPoints; j++) {
dWorkspace[k] = 1.0;
k++;
}
for (i = 1; i < nPoints; i++) {
for (j = 0; j < nPoints; j++) {
dWorkspace[k] = (dX[j] - dXmid) * dWorkspace[k-nPoints];
k++;
}
}
// Initialize A
memcpy(dA, dY, nPoints * sizeof(double));
// Store CLAPACK parameters
int n = nPoints;
int nRHS = 1;
int nLDA = nPoints;
int nLDB = nPoints;
int nInfo;
#ifdef TEMPEST_LAPACK_ACML_INTERFACE
// Call the matrix solve
dgesv(n, nRHS, dWorkspace, nLDA, iPivot, dA, nLDB, &nInfo);
#endif
#ifdef TEMPEST_LAPACK_ESSL_INTERFACE
// Call the matrix solve
dgesv(n, nRHS, dWorkspace, nLDA, iPivot, dA, nLDB, nInfo);
#endif
#ifdef TEMPEST_LAPACK_FORTRAN_INTERFACE
// Call the matrix solve
dgesv_(&n, &nRHS, dWorkspace, &nLDA, iPivot, dA, &nLDB, &nInfo);
#endif
// Delete workspace
if (!fExternalWorkspace) {
delete[] dWorkspace;
}
if (!fExternalPivot) {
delete[] iPivot;
}
}
void dgWhat(Utype *What, Utype *Vhat, Utype *U, double beta){
extern void dgesv( int* n, int* nrhs, double* a, int* lda, int* ipiv,
double* b, int* ldb, int* info );
int i; //initialization for iteration
int j; //initialization for iteration
int k; //initialization for iteration
int po;
//--------------------------------------------------------------------------
//Initialization for Lapack function DGESV_
//--------------------------------------------------------------------------
//see http://www.netlib.no/netlib/lapack/double/dgesv_.f for more information
int n= 3*(What->basis.r+1); //Num of lin equ, order of the matrix A. N>=0
int nrhs = 1; //Num of rhs, i.e., num of columns of matrix B
int lda=3*(What->basis.r+1); //Leading dimen of A. LDA >= max(1,N)
int ldb = n; //Leading dimen of the array
int info = -1; //Parameter that tells if DGESV_ operation was succesful
int ipiv[3*(What->basis.r+1)]; //pivot indices define permutation matrix P
//Initialize Residual, Jacobian, and w arrays
double *R = (double* ) malloc ((What->basis.r+1)*3*sizeof(double));
double **dRkdU = (double **) malloc ((What->basis.r+1)*3*sizeof(double*));
double **dRdU = (double **) malloc ((What->basis.r+1)*3*sizeof(double*));
//Contains difference in states after the linear dG operation via DGESV_
double w[(What->basis.r+1)*3]; //Solution to the Raphson Newton system
// Next section continues to finish initializing dRkdU, dRdU such that
//the memory is all in one place and in a way that works for DGESV_ function
dRdU[0] = (double *) malloc
((What->basis.r+1)*3*(What->basis.r+1)*3*sizeof(double));
for (i=1; i<3*(What->basis.r+1); i++){
dRdU[i]=dRdU[i-1]+3*(What->basis.r+1);
}
dRkdU[0]= (double*)
malloc ((What->basis.r+1)*3*(What->basis.r+1)*3*sizeof(double));
for (i=1; i<3*(What->basis.r+1); i++){
dRkdU[i]=dRkdU[i-1]+3*(What->basis.r+1);
}
//==============================Implementation=--===========================
for (i=0; i<What->basis.r+1; i++){
//Make an initialial guess of x, y, z at r+1 points for t=0 window
What->solution.x.array[(What->tSpan.size-2)*(What->basis.r+1)+i]=1.1;
What->solution.y.array[(What->tSpan.size-2)*(What->basis.r+1)+i]=1.1;
What->solution.z.array[(What->tSpan.size-2)*(What->basis.r+1)+i]=1.1;
}
for (i=What->tSpan.size-1; i-->0;){ //Iterate through all the time intervals
//Starting from the last time interval, solving backwards
for ( j=0; j<What->basis.r+1; j++){
What->timett.array[(What->basis.r+1)*i+j]=
What->tSpan.array[i]-(xiL(What->basis.r, j)+1)/2.0*What->dt;
}
residualLgrng(U, Vhat, What, i, R, beta); //Calc residual 4 current t
jacobianLgrng(U, Vhat, What, i, dRdU, dRkdU);//Calc jacobian 4 current t
for (j=0; j<3*(What->basis.r+1); j++){ //Residual R to w and neg
w[j]=-R[j];
}
//Calculation of the update vectors; magic happens here
dgesv(&n,&nrhs, dRdU[0], &lda, ipiv, w, &ldb, &info ); //w = update
//Need to update the solution now
for (j=0; j<(What->basis.r+1); j++){ //Iterate and add w to the solution
What->solution.x.array[i*(What->basis.r+1)+j]+=w[j*3];
What->solution.y.array[i*(What->basis.r+1)+j]+=w[j*3+1];
What->solution.z.array[i*(What->basis.r+1)+j]+=w[j*3+2];
}
//Need to update the solution now
if (i>What->tSpan.size-2){
for (j=0; j<What->basis.r+1; j++){
What->solution.x.array[(i+1)*(What->basis.r+1)+j]=
What->solution.x.array[i*(What->basis.r+1)+j];
What->solution.y.array[(i+1)*(What->basis.r+1)+j]=
What->solution.y.array[i*(What->basis.r+1)+j];
What->solution.z.array[(i+1)*(What->basis.r+1)+j]=
What->solution.z.array[i*(What->basis.r+1)+j];
}
}
}
//Free everything!
free(R);
free(dRkdU[0]);
free(dRkdU);
free(dRdU[0]);
free(dRdU);
}
void dgVhat(Utype *Vhat, Utype *U){
//==============Initialization of Parameters and Variables==================
extern void dgesv( int* n, int* nrhs, double* a, int* lda, int* ipiv,
double* b, int* ldb, int* info );
int i; //initialization for iteration
int j; //initialization for iteration
int k; //initialization for iteration
//--------------------------------------------------------------------------
//Initialization for Lapack function DGESV
//--------------------------------------------------------------------------
//see http://www.netlib.no/netlib/lapack/double/dgesv.f for more information
int n= 3*(Vhat->basis.r+1); //Num of lin equ, order of the matrix A. N>=0
int nrhs = 1; //Num of rhs, i.e., num of columns of matrix B
int lda=3*(Vhat->basis.r+1); //Leading dimen of A. LDA >= max(1,N)
int ldb = n; //Leading dimen of the array
int info = -1; //Parameter that tells if DGESV operation was succesful
int ipiv[3*(Vhat->basis.r+1)]; //pivot indices define permutation matrix P
//Initialize Residual, Jacobian, and w arrays
double *R = (double* ) malloc ((Vhat->basis.r+1)*3*sizeof(double));
double **dRkdU = (double **) malloc ((Vhat->basis.r+1)*3*sizeof(double*));
double **dRdU = (double **) malloc ((Vhat->basis.r+1)*3*sizeof(double*));
//Contains difference in states after the linear dG operation via DGESV
double w[(Vhat->basis.r+1)*3]; //Solution to the Raphson Newton system
// Next section continues to finish initializing dRkdU, dRdU such that
//the memory is all in one place and in a way that works for DGESV function
dRdU[0] = (double *) malloc
((Vhat->basis.r+1)*3*(Vhat->basis.r+1)*3*sizeof(double));
for (i=1; i<3*(Vhat->basis.r+1); i++){
dRdU[i]=dRdU[i-1]+3*(Vhat->basis.r+1);
}
dRkdU[0]= (double*)
malloc ((Vhat->basis.r+1)*3*(Vhat->basis.r+1)*3*sizeof(double));
for (i=1; i<3*(Vhat->basis.r+1); i++){
dRkdU[i]=dRkdU[i-1]+3*(Vhat->basis.r+1);
}
//============================Implementation================================
for (i=0; i<Vhat->basis.r+1; i++){
Vhat->solution.x.array[i]=1.1; //Initial guess x at r+1 pts 4 1st window
Vhat->solution.y.array[i]=1.1; //Initial guess y at r+1 pts 4 1st window
Vhat->solution.z.array[i]=1.1; //Initial guess z at r+1 pts 4 1st window
}
for (i=0; i<Vhat->tSpan.size-1; i++){ //Iterate through all time intervals
//find the time array that is associate with r+1 points
for (j = 0; j<Vhat->basis.r+1; j++){
Vhat->timett.array[(Vhat->basis.r+1)*i+j]=
Vhat->tSpan.array[i]+(xiL(Vhat->basis.r, j)+1)/2.0*Vhat->dt;
}
residualTan(U, Vhat, i, R); //Calculate residual for current time
jacobianTan(U, Vhat, i, dRdU, dRkdU); //Calc jacobian for current t
for (j=0; j<3*(Vhat->basis.r+1); j++){ //Residual R to w and neg
w[j]=-R[j];
}
//Calculation of the update vectors; magic happens here
dgesv(&n,&nrhs, dRdU[0], &lda, ipiv, w, &ldb, &info );// w = update
//Need to update the solution now
for (j=0; j<(Vhat->basis.r+1); j++){ //Update initial guesses
Vhat->solution.x.array[i*(Vhat->basis.r+1)+j]+=w[j*3];
Vhat->solution.y.array[i*(Vhat->basis.r+1)+j]+=w[j*3+1];
Vhat->solution.z.array[i*(Vhat->basis.r+1)+j]+=w[j*3+2];
}
residualTan(U, Vhat, i, R); //Calculate residual for current time//This will be the guess for the next element
// for (j=0; j<3*(Vhat->basis.r+1); j++){ //Residual R to w and neg
// printf("%g\n", R[j]);
// }
if (i<Vhat->tSpan.size-2){
for (j=0; j<(Vhat->basis.r+1); j++){
Vhat->solution.x.array[(i+1)*(Vhat->basis.r+1)+j]=
Vhat->solution.x.array[i*(Vhat->basis.r+1)+j];
Vhat->solution.y.array[(i+1)*(Vhat->basis.r+1)+j]=
Vhat->solution.y.array[i*(Vhat->basis.r+1)+j];
Vhat->solution.z.array[(i+1)*(Vhat->basis.r+1)+j]=
Vhat->solution.z.array[i*(Vhat->basis.r+1)+j];
}
}
}
//Free everything!
free(R);
free(dRkdU[0]);
free(dRkdU);
free(dRdU[0]);
free(dRdU);
}
double nmf_neals(double * a, double * w0, double * h0, int * pm, int * pn, \
int * pk, int * maxiter, const double * pTolX, const double * pTolFun)
{
// code added to be able to call from R
int m = * pm;
int n = * pn;
int k = * pk;
const double TolX = * pTolX;
const double TolFun = * pTolFun;
// also: changed w0, h0 to simple pointer (instead of double)
// // end code added
#ifdef PROFILE_NMF_NEALS
struct timeval start, end;
gettimeofday(&start, 0);
#endif
#if DEBUG_LEVEL >= 2
printf("Entering nmf_neals\n");
#endif
#ifdef ERROR_CHECKING
errno = 0;
#endif
double * help1 = (double*) malloc(sizeof(double)*k*k);
double * help2 = (double*) malloc(sizeof(double)*k*n);
double * help3 = (double*) malloc(sizeof(double)*k*m);
//-----------------------------------------
// definition of necessary dynamic data structures
//...for calculating matrix h
double* h = (double*) malloc(sizeof(double)*k*n);
int* jpvt_h = (int*) malloc(sizeof(int)*k);
int info;
//...for calculating matrix w
double* w = (double*) malloc(sizeof(double)*m*k);
//----------------
//...for calculating the norm of A-W*H
double* d = (double*) malloc(sizeof(double)*m*n); //d = a - w*h
double dnorm0 = 0;
double dnorm = 0;
const double eps = dlamch('E'); //machine precision epsilon
const double sqrteps = sqrt(eps); //squareroot of epsilon
//-------------------
#ifdef ERROR_CHECKING
if (errno) {
perror("Error allocating memory in nmf_neals");
free(help1);
free(help2);
free(help3);
free(h);
free(jpvt_h);
free(w);
free(d);
return -1;
}
#endif
// declaration of data structures for switch to als algorithm
// ----------------------------------------------------------
int als_data_allocated = 0; // indicates wheter data structures were already allocated
// factor matrices for factorizing matrix w
double * q;
double * r;
// factor matrices for factorizing matrix h
double * q_h;
double * r_h;
double* tau_h; //stores elementary reflectors of factor matrix Q
double* work_w; //work array for factorization of matrix w
int lwork_w;
double* work_h; //work array for factorization of matrix h
int lwork_h;
double * work_qta; //work array for dorgqr
int lwork_qta;
double * work_qth; //work array for dorgqr
int lwork_qth;
//query for optimal workspace size for routine dgeqp3...
double querysize;
//Loop-Indices
int iter, i;
//variable for storing if fallback happened in current iteration
int fallback;
// factorisation step in a loop from 1 to maxiter
for (iter = 1; iter <= *maxiter; ++iter) {
//no fallback in this iteration so far
fallback = 0;
// calculating matrix h
//----------------
//help1 = w0'*w0
dgemm('T', 'N', k, k, m, 1.0, w0, m, w0, m, 0., help1, k);
//help2 = w0'*a
dgemm('T', 'N', k, n, m, 1.0, w0, m, a, m, 0., help2, k);
//LU-Factorisation of help1 to solve equation help1 * x = help2
dgesv(k, n, help1, k, jpvt_h, help2, k, &info);
// if factor matrix U is singular -> switch back to als algorithm to compute h
if( info > 0) {
//set fallback to 1 to indicate that fallback happened
fallback = 1;
// do dynamic data structures need to be allocated?
if (!als_data_allocated) {
als_data_allocated = 1;
// factor matrices for factorizing matrix w
q = (double*) malloc(sizeof(double)*m*k);
r = (double*) malloc(sizeof(double)*m*k);
// factor matrices for factorizing matrix h
q_h = (double*) malloc(sizeof(double)*n*k);
r_h = (double*) malloc(sizeof(double)*n*k);
tau_h = (double*) malloc(sizeof(double)*k); //stores elementary reflectors of factor matrix Q
//query for optimal workspace size for routine dgeqp3...
//for matrix w
dgeqp3(m, k, q, m, jpvt_h, tau_h, &querysize, -1, &info);
lwork_w = (int) querysize;
work_w = (double*) malloc(sizeof(double)*lwork_w); //work array for factorization of matrix help1 (dgeqp3)
//for matrix h
dgeqp3(n, k, q_h, n, jpvt_h, tau_h, &querysize, -1, &info);
lwork_h = (int) querysize;
work_h = (double*) malloc(sizeof(double)*lwork_h); //work array for factorization of matrix h
//query for optimal workspace size for routine dorgqr...
//for matrix w
dorgqr(m, k, k, q, m, tau_h, &querysize, -1, &info);
lwork_qta = (int)querysize;
work_qta = (double*) malloc(sizeof(double)*lwork_qta); //work array for dorgqr
//for matrix h
dorgqr(n, k, k, q_h, n, tau_h, &querysize, -1, &info);
lwork_qth = (int)querysize;
work_qth = (double*) malloc(sizeof(double)*lwork_qth);
}
// calculating matrix h
//----------------
//re-initialization
//copy *w0 to q
dlacpy('A', m, k, w0, m, q, m);
//initialise jpvt_h to 0 -> every column free
for (i = 0; i<k; ++i)
jpvt_h[i] = 0;
// Q-R factorization with column pivoting
dgeqp3(m, k, q, m, jpvt_h, tau_h, work_w, lwork_w, &info);
//copying upper triangular factor-matrix r out of q into r
dlacpy('U', m, k, q, m, r, k);
//Begin of least-squares-solution to w0 * x = a
//generate explicit matrix q (m times k) and calculate q' * a
dorgqr(m, k, k, q, m, tau_h, work_qta, lwork_qta, &info);
dgemm('T', 'N', k, n, m, 1.0, q, m, a, m, 0.0, q_h, k);
//solve R * x = (Q'*A)
dtrtrs('U','N','N',k,n,r,k,q_h,k,&info);
//copy matrix q to h, but permutated according to jpvt_h
for (i=0; i<k; ++i) {
dcopy(n, q_h + i, k, h + jpvt_h[i] - 1, k);
}
//transform negative and very small positive values to zero for performance reasons and to keep the non-negativity constraint
for (i=0; i<k*n; ++i) {
if (h[i] < ZERO_THRESHOLD)
h[i] = 0.;
}
}
else {
//h = max(ZERO_THRESHOLD, help1\help2)
for (i=0; i < k*n; ++i)
h[i] = (help2[i] > ZERO_THRESHOLD ? help2[i] : 0.);
}
// calculating matrix w = max(0, help1\help3)'
//----------------------------
//help1 = h*h'
dgemm('N', 'T', k, k, n, 1.0, h, k, h, k, 0., help1, k);
//help3 = h*a'
dgemm('N', 'T', k, m, n, 1.0, h, k, a, m, 0., help3, k);
//LU-Factorisation of help1
dgesv(k, m, help1, k, jpvt_h, help3, k, &info);
//
if( info > 0) {
// do dynamic data structures need to be allocated?
if (!als_data_allocated) {
als_data_allocated = 1;
// factor matrices for factorizing matrix w
q = (double*) malloc(sizeof(double)*m*k);
r = (double*) malloc(sizeof(double)*m*k);
// factor matrices for factorizing matrix h
q_h = (double*) malloc(sizeof(double)*n*k);
r_h = (double*) malloc(sizeof(double)*n*k);
tau_h = (double*) malloc(sizeof(double)*k); //stores elementary reflectors of factor matrix Q
//query for optimal workspace size for routine dgeqp3...
//for matrix w
dgeqp3(m, k, q, m, jpvt_h, tau_h, &querysize, -1, &info);
lwork_w = (int) querysize;
work_w = (double*) malloc(sizeof(double)*lwork_w); //work array for factorization of matrix help1 (dgeqp3)
//..for matrix h
dgeqp3(n, k, q_h, n, jpvt_h, tau_h, &querysize, -1, &info);
lwork_h = (int) querysize;
work_h = (double*) malloc(sizeof(double)*lwork_h); //work array for factorization of matrix h
//query for optimal workspace size for routine dorgqr...
//for matrix w
dorgqr(m, k, k, q, m, tau_h, &querysize, -1, &info);
lwork_qta = (int)querysize;
work_qta = (double*) malloc(sizeof(double)*lwork_qta); //work array for dorgqr
// ... for matrix h
dorgqr(n, k, k, q_h, n, tau_h, &querysize, -1, &info);
lwork_qth = (int)querysize;
work_qth = (double*) malloc(sizeof(double)*lwork_qth);
}
//calculating matrix w
//copy original matrix h to q_h, but transposed
for (i=0; i<k; ++i) {
dcopy(n, h + i, k, q_h + i*n, 1);
}
//initialise jpvt_a to 0 -> every column free
for (i = 0; i<k; ++i)
jpvt_h[i] = 0;
//Q-R factorization
dgeqp3(n, k, q_h, n, jpvt_h, tau_h, work_h, lwork_h, &info);
//copying upper triangular factor-matrix r_h out of q into r_h
dlacpy('U', n, k, q_h, n, r_h, k);
//Begin of least-squares-solution to w0 * x = a
//generate explicit matrix q (n times k) and calculate *a = q' * a'
dorgqr(n, k, k, q_h, n, tau_h, work_qth, lwork_qth, &info);
dgemm('T', 'T', k, m, n, 1.0, q_h, n, a, m, 0.0, q, k);
//solve R_h * x = (Q'*A')
dtrtrs('U', 'N', 'N', k, m, r_h, k, q, k, &info);
//jpvt_h*(R\(Q'*A')) permutation and transposed copy to w
for (i=0; i<k; ++i) {
dcopy(m, q + i, k, w + m * (jpvt_h[i] - 1), 1);
}
//transform negative and very small positive values to zero for performance reasons and to keep the non-negativity constraint
for (i=0; i<k*m; ++i) {
if (w[i] < ZERO_THRESHOLD)
w[i] = 0.;
}
}
else {
//w = max(0, help3)'
for (i=0; i<k; ++i) {
dcopy(m, help3 + i, k, w + i*m, 1);
}
for (i=0; i<m*k; ++i) {
if (w[i] < ZERO_THRESHOLD)
w[i] = 0.;
}
}
// calculating the norm of D = A-W*H
dnorm = calculateNorm(a, w, h, d, m, n, k);
// calculating change in w -> dw
//----------------------------------
double dw;
dw = calculateMaxchange(w, w0, m, k, sqrteps);
// calculating change in h -> dh
//-----------------------------------
double dh;
dh = calculateMaxchange(h, h0, k, n, sqrteps);
//Max-Change = max(dh, dw) = delta
double delta;
delta = (dh > dw) ? dh : dw;
// storing the matrix results of the current iteration
swap(&w0, &w);
swap(&h0, &h);
// storing the norm results of the current iteration
dnorm0 = dnorm;
#if DEBUG_LEVEL >= 1
printf("iter: %.6d\t dnorm: %.16f\t delta: %.16f\n", iter, dnorm, delta);
#endif
//Check for Convergence
if (iter > 1) {
if (delta < TolX) {
*maxiter = iter;
break;
}
else
if (dnorm <= TolFun*dnorm0) {
*maxiter = iter;
break;
}
}
} //end of loop from 1 to maxiter
#if DEBUG_LEVEL >= 2
printf("Exiting nmf_neals\n");
#endif
#ifdef PROFILE_NMF_NEALS
gettimeofday(&end, 0);
outputTiming("", start, end);
#endif
// freeing memory if used
free(help1);
free(help2);
free(help3);
free(h);
free(jpvt_h);
free(w);
free(d);
if(als_data_allocated) {
free(q);
free(r);
free(q_h);
free(r_h);
free(work_h);
free(work_w);
free(tau_h);
free(work_qta);
free(work_qth);
}
// returning calculated norm
return dnorm;
}
