void
F77_NAME(dtrsv)(const char *uplo, const char *trans,
const char *diag, const int *n,
const double *a, const int *lda,
double *x, const int *incx)
{
DTRSV(uplo, trans, diag, n, a, lda, x, incx);
}
void mexFunction(int nargout, mxArray *argout[], int nargin, const mxArray *argin[])
{
double tol;
double *A, *b, *L, *x, *u, *ut, *v, *vt, *d, *z;
double beta, alpha, normr;
double c, s, phibar, phi, nn;
double thet, rhot, rho;
double mbeta;
double *resvec, *xvec, *Atr, *r;
long m, n;
long maxit, it, i;
long int_zero = 0;
long int_one = 1;
double dbl_one = 1.0;
double dbl_mone = -1.0;
double dbl_zero = 0.0;
A = mxGetPr(argin[0]);
b = mxGetPr(argin[1]);
L = mxIsEmpty(argin[2]) ? NULL : mxGetPr(argin[2]);
m = mxGetM(argin[0]);
n = mxGetN(argin[0]);
tol = mxGetScalar(argin[3]) * DNRM2(&m, b, &int_one);
maxit = (int)mxGetScalar(argin[4]);
u = malloc(m * sizeof(double));
ut = malloc(m * sizeof(double));
v = malloc(n * sizeof(double));
vt = malloc(n * sizeof(double));
d = malloc(n * sizeof(double));
z = malloc(n * sizeof(double));
argout[0] = mxCreateDoubleMatrix(n, 1, mxREAL);
x = mxGetPr(argout[0]);
if (nargout > 2) {
argout[2] = mxCreateDoubleMatrix(maxit+1, 1, mxREAL);
resvec = mxGetPr(argout[2]);
argout[3] = mxCreateDoubleMatrix(maxit+1, 1, mxREAL);
xvec = mxGetPr(argout[3]);
r = malloc(m * sizeof(double));
memcpy(r, b, m * sizeof(double));
resvec[0] = DNRM2(&m, r, &int_one);
xvec[0] = DNRM2(&n, x, &int_one);
}
memset(x, 0, n * sizeof(double));
memset(d, 0, n * sizeof(double));
memcpy(u, b, m * sizeof(double));
if (L != NULL)
DTRSV("L", "N", "Not Unit", &m, L, &m, u, &int_one);
beta = DNRM2(&m, u, &int_one);
normr = beta;
scale(u, m, 1/beta);
c = 1; s = 0; phibar = beta;
memcpy(z, u, m * sizeof(double));
if (L != NULL)
DTRSV("L", "T", "Not Unit", &m, L, &m, z, &int_one);
DGEMV("T", &m, &n, &dbl_one, A, &m, z, &int_one, &dbl_zero, v, &int_one);
alpha = DNRM2(&n, v, &int_one);
scale(v, n, 1/alpha);
it = 0;
while (it < maxit) {
DGEMV("N", &m, &n, &dbl_one, A, &m, v, &int_one, &dbl_zero, ut, &int_one);
if (L != NULL)
DTRSV("L", "N", "Not Unit", &m, L, &m, ut, &int_one);
for (i = 0; i < m; i++)
u[i] = ut[i] - alpha * u[i];
beta = DNRM2(&m, u, &int_one);
scale(u, m, 1/beta);
thet = - s * alpha;
rhot = c * alpha;
rho = sqrt(rhot * rhot + beta * beta);
c = rhot / rho;
s = - beta / rho;
phi = c * phibar;
phibar = s * phibar;
for (i = 0; i < n; i++) {
d[i] = (v[i] - thet * d[i]) / rho;
x[i] = x[i] + phi * d[i];
}
it++;
if (nargout > 2) {
memcpy(r, b, m * sizeof(double));
DGEMV("N", &m, &n, &dbl_mone, A, &m, x, &int_one, &dbl_one, r, &int_one);
resvec[it] = DNRM2(&m, r, &int_one);
xvec[it] = DNRM2(&n, x, &int_one);
}
normr = fabs(s) * normr;
if (normr < tol)
break;
mbeta = -beta;
memcpy(z, u, m * sizeof(double));
if (L != NULL)
DTRSV("L", "T", "Not Unit", &m, L, &m, z, &int_one);
DGEMV("T", &m, &n, &dbl_one, A, &m, z, &int_one, &mbeta, v, &int_one);
alpha = DNRM2(&n, v, &int_one);
scale(v, n, 1/alpha);
}
if (nargout > 2){
mxSetM(argout[2] , it + 1);
mxSetM(argout[3] , it + 1);
}
if (nargout > 1)
argout[1] = mxCreateScalarDouble(it);
if (nn > tol)
mexPrintf("dense_lsqr: did not converge\n");
else
mexPrintf("dense_lsqr: converged at iteration %d\n", it);
free(u);
free(ut);
free(v);
free(d);
free(z);
if (nargout > 2)
free(r);
}
