CAMLprim value sunml_spils_qr_fact(value vn, value vh, value vq, value vnewjob)
{
CAMLparam4(vn, vh, vq, vnewjob);
int r;
int n = Int_val(vn);
#if SUNDIALS_ML_SAFE == 1
struct caml_ba_array *bh = ARRAY2_DATA(vh);
intnat hn = bh->dim[0];
intnat hm = bh->dim[1];
if (hn < n + 1)
caml_invalid_argument("qr_fact: h is too small (< n + 1).");
if (hm < n)
caml_invalid_argument("qr_fact: h is too small (< n).");
if (ARRAY1_LEN(vq) < 2 * n)
caml_invalid_argument("qr_fact: q is too small (< 2n).");
#endif
r = QRfact(n, ARRAY2_ACOLS(vh), REAL_ARRAY(vq), Bool_val(vnewjob));
if (r != 0) {
caml_raise_with_arg(MATRIX_EXN_TAG(ZeroDiagonalElement),
Val_long(r));
}
CAMLreturn (Val_unit);
}
int SpgmrSolve(SpgmrMem mem, void *A_data, N_Vector x, N_Vector b,
int pretype, int gstype, real delta, int max_restarts,
void *P_data, N_Vector sx, N_Vector sb, ATimesFn atimes,
PSolveFn psolve, real *res_norm, int *nli, int *nps)
{
N_Vector *V, xcor, vtemp;
real **Hes, *givens, *yg;
real s_r0_norm, beta, rotation_product, r_norm, s_product, rho;
boole preOnLeft, preOnRight, scale_x, scale_b, converged;
int i, j, k, l, l_plus_1, l_max, krydim, ier, ntries;
if (mem == NULL) return(SPGMR_MEM_NULL);
/* Make local copies of mem variables */
l_max = mem->l_max;
V = mem->V;
Hes = mem->Hes;
givens = mem->givens;
xcor = mem->xcor;
yg = mem->yg;
vtemp = mem->vtemp;
*nli = *nps = 0; /* Initialize counters */
converged = FALSE; /* Initialize converged flag */
if (max_restarts < 0) max_restarts = 0;
if ((pretype != LEFT) && (pretype != RIGHT) && (pretype != BOTH))
pretype = NONE;
preOnLeft = ((pretype == LEFT) || (pretype == BOTH));
preOnRight = ((pretype == RIGHT) || (pretype == BOTH));
scale_x = (sx != NULL);
scale_b = (sb != NULL);
/* Set vtemp and V[0] to initial (unscaled) residual r_0 = b - A*x_0 */
if (N_VDotProd(x, x) == ZERO) {
N_VScale(ONE, b, vtemp);
} else {
if (atimes(A_data, x, vtemp) != 0)
return(SPGMR_ATIMES_FAIL);
N_VLinearSum(ONE, b, -ONE, vtemp, vtemp);
}
N_VScale(ONE, vtemp, V[0]);
/* Apply b-scaling to vtemp, get L2 norm of sb r_0, and return if small */
/*
if (scale_b) N_VProd(sb, vtemp, vtemp);
s_r0_norm = RSqrt(N_VDotProd(vtemp, vtemp));
if (s_r0_norm <= delta) return(SPGMR_SUCCESS);
*/
/* Apply left preconditioner and b-scaling to V[0] = r_0 */
if (preOnLeft) {
ier = psolve(P_data, V[0], vtemp, LEFT);
(*nps)++;
if (ier != 0)
return((ier < 0) ? SPGMR_PSOLVE_FAIL_UNREC : SPGMR_PSOLVE_FAIL_REC);
} else {
N_VScale(ONE, V[0], vtemp);
}
if (scale_b) {
N_VProd(sb, vtemp, V[0]);
} else {
N_VScale(ONE, vtemp, V[0]);
}
/* Set r_norm = beta to L2 norm of V[0] = sb P1_inv r_0, and
return if small */
*res_norm = r_norm = beta = RSqrt(N_VDotProd(V[0], V[0]));
if (r_norm <= delta)
return(SPGMR_SUCCESS);
/* Set xcor = 0 */
N_VConst(ZERO, xcor);
/* Begin outer iterations: up to (max_restarts + 1) attempts */
for (ntries = 0; ntries <= max_restarts; ntries++) {
/* Initialize the Hessenberg matrix Hes and Givens rotation
product. Normalize the initial vector V[0]. */
for (i=0; i <= l_max; i++)
for (j=0; j < l_max; j++)
Hes[i][j] = ZERO;
rotation_product = ONE;
N_VScale(ONE/r_norm, V[0], V[0]);
/* Inner loop: generate Krylov sequence and Arnoldi basis */
for(l=0; l < l_max; l++) {
(*nli)++;
krydim = l_plus_1 = l + 1;
/* Generate A-tilde V[l], where A-tilde = sb P1_inv A P2_inv sx_inv */
/* Apply x-scaling: vtemp = sx_inv V[l] */
if (scale_x) {
N_VDiv(V[l], sx, vtemp);
} else {
N_VScale(ONE, V[l], vtemp);
}
/* Apply right precoditioner: vtemp = P2_inv sx_inv V[l] */
N_VScale(ONE, vtemp, V[l_plus_1]);
if (preOnRight) {
ier = psolve(P_data, V[l_plus_1], vtemp, RIGHT);
(*nps)++;
if (ier != 0)
return((ier < 0) ? SPGMR_PSOLVE_FAIL_UNREC : SPGMR_PSOLVE_FAIL_REC);
}
/* Apply A: V[l+1] = A P2_inv sx_inv V[l] */
if (atimes(A_data, vtemp, V[l_plus_1] ) != 0)
return(SPGMR_ATIMES_FAIL);
/* Apply left preconditioning: vtemp = P1_inv A P2_inv sx_inv V[l] */
if (preOnLeft) {
ier = psolve(P_data, V[l_plus_1], vtemp, LEFT);
(*nps)++;
if (ier != 0)
return((ier < 0) ? SPGMR_PSOLVE_FAIL_UNREC : SPGMR_PSOLVE_FAIL_REC);
} else {
N_VScale(ONE, V[l_plus_1], vtemp);
}
/* Apply b-scaling: V[l+1] = sb P1_inv A P2_inv sx_inv V[l] */
if (scale_b) {
N_VProd(sb, vtemp, V[l_plus_1]);
} else {
N_VScale(ONE, vtemp, V[l_plus_1]);
}
/* Orthogonalize V[l+1] against previous V[i]: V[l+1] = w_tilde. */
if (gstype == CLASSICAL_GS) {
if (ClassicalGS(V, Hes, l_plus_1, l_max, &(Hes[l_plus_1][l]),
vtemp, yg) != 0)
return(SPGMR_GS_FAIL);
} else {
if (ModifiedGS(V, Hes, l_plus_1, l_max, &(Hes[l_plus_1][l])) != 0)
return(SPGMR_GS_FAIL);
}
/* Update the QR factorization of Hes */
if(QRfact(krydim, Hes, givens, l) != 0 )
return(SPGMR_QRFACT_FAIL);
/* Update residual norm estimate; break if convergence test passes */
rotation_product *= givens[2*l+1];
if ((*res_norm = rho = ABS(rotation_product*r_norm)) <= delta) {
converged = TRUE;
break;
}
/* Normalize V[l+1] with norm value from the Gram-Schmidt */
N_VScale(ONE/Hes[l_plus_1][l], V[l_plus_1], V[l_plus_1]);
}
/* Inner loop is done. Compute the new correction vector xcor */
/* Construct g, then solve for y */
yg[0] = r_norm;
for (i=1; i <= krydim; i++) yg[i]=ZERO;
if (QRsol(krydim, Hes, givens, yg) != 0)
return(SPGMR_QRSOL_FAIL);
/* Add correction vector V_l y to xcor */
for (k=0; k < krydim; k++)
N_VLinearSum(yg[k], V[k], ONE, xcor, xcor);
/* If converged, construct the final solution vector x */
if (converged) {
/* Apply x-scaling and right precond.: vtemp = P2_inv sx_inv xcor */
if (scale_x) N_VDiv(xcor, sx, xcor);
if (preOnRight) {
ier = psolve(P_data, xcor, vtemp, RIGHT);
(*nps)++;
if (ier != 0)
return((ier < 0) ? SPGMR_PSOLVE_FAIL_UNREC : SPGMR_PSOLVE_FAIL_REC);
} else {
N_VScale(ONE, xcor, vtemp);
}
/* Add correction to initial x to get final solution x, and return */
N_VLinearSum(ONE, x, ONE, vtemp, x);
return(SPGMR_SUCCESS);
}
/* Not yet converged; if allowed, prepare for restart */
if (ntries == max_restarts) break;
/* Construct last column of Q in yg */
s_product = ONE;
for (i=krydim; i > 0; i--) {
yg[i] = s_product*givens[2*i-2];
s_product *= givens[2*i-1];
}
yg[0] = s_product;
/* Scale r_norm and yg */
r_norm *= s_product;
for (i=0; i <= krydim; i++)
yg[i] *= r_norm;
r_norm = ABS(r_norm);
/* Multiply yg by V_(krydim+1) to get last residual vector; restart */
N_VScale(yg[0], V[0], V[0]);
for( k=1; k <= krydim; k++)
N_VLinearSum(yg[k], V[k], ONE, V[0], V[0]);
}
/* Failed to converge, even after allowed restarts.
If the residual norm was reduced below its initial value, compute
and return x anyway. Otherwise return failure flag. */
if (rho < beta) {
/* Apply the x-scaling and right precond.: vtemp = P2_inv sx_inv xcor */
if (scale_x) N_VDiv(xcor, sx, xcor);
if (preOnRight) {
ier = psolve(P_data, xcor, vtemp, RIGHT);
(*nps)++;
if (ier != 0)
return((ier < 0) ? SPGMR_PSOLVE_FAIL_UNREC : SPGMR_PSOLVE_FAIL_REC);
} else {
N_VScale(ONE, xcor, vtemp);
}
/* Add vtemp to initial x to get final solution x, and return */
N_VLinearSum(ONE, x, ONE, vtemp, x);
return(SPGMR_RES_REDUCED);
}
return(SPGMR_CONV_FAIL);
}
/*----------------------------------------------------------------
Function : SpfgmrSolve
---------------------------------------------------------------*/
int SpfgmrSolve(SpfgmrMem mem, void *A_data, N_Vector x,
N_Vector b, int pretype, int gstype, realtype delta,
int max_restarts, int maxit, void *P_data,
N_Vector s1, N_Vector s2, ATimesFn atimes,
PSolveFn psolve, realtype *res_norm, int *nli, int *nps)
{
N_Vector *V, *Z, xcor, vtemp;
realtype **Hes, *givens, *yg;
realtype beta, rotation_product, r_norm, s_product, rho;
booleantype preOnRight, scale1, scale2, converged;
int i, j, k, l, l_max, krydim, ier, ntries;
if (mem == NULL) return(SPFGMR_MEM_NULL);
/* Initialize some variables */
krydim = 0;
/* Make local copies of mem variables. */
l_max = mem->l_max;
V = mem->V;
Z = mem->Z;
Hes = mem->Hes;
givens = mem->givens;
xcor = mem->xcor;
yg = mem->yg;
vtemp = mem->vtemp;
*nli = *nps = 0; /* Initialize counters */
converged = SUNFALSE; /* Initialize converged flag */
/* If maxit is greater than l_max, then set maxit=l_max */
if (maxit > l_max) maxit = l_max;
/* Check for legal value of max_restarts */
if (max_restarts < 0) max_restarts = 0;
/* Set preconditioning flag (enabling any preconditioner implies right
preconditioning, since FGMRES does not support left preconditioning) */
preOnRight = ((pretype == PREC_RIGHT) || (pretype == PREC_BOTH) || (pretype == PREC_LEFT));
/* Set scaling flags */
scale1 = (s1 != NULL);
scale2 = (s2 != NULL);
/* Set vtemp to initial (unscaled) residual r_0 = b - A*x_0. */
if (N_VDotProd(x, x) == ZERO) {
N_VScale(ONE, b, vtemp);
} else {
ier = atimes(A_data, x, vtemp);
if (ier != 0)
return((ier < 0) ? SPFGMR_ATIMES_FAIL_UNREC : SPFGMR_ATIMES_FAIL_REC);
N_VLinearSum(ONE, b, -ONE, vtemp, vtemp);
}
/* Apply left scaling to vtemp = r_0 to fill V[0]. */
if (scale1) {
N_VProd(s1, vtemp, V[0]);
} else {
N_VScale(ONE, vtemp, V[0]);
}
/* Set r_norm = beta to L2 norm of V[0] = s1 r_0, and return if small */
*res_norm = r_norm = beta = SUNRsqrt(N_VDotProd(V[0], V[0]));
if (r_norm <= delta)
return(SPFGMR_SUCCESS);
/* Initialize rho to avoid compiler warning message */
rho = beta;
/* Set xcor = 0. */
N_VConst(ZERO, xcor);
/* Begin outer iterations: up to (max_restarts + 1) attempts. */
for (ntries=0; ntries<=max_restarts; ntries++) {
/* Initialize the Hessenberg matrix Hes and Givens rotation
product. Normalize the initial vector V[0]. */
for (i=0; i<=l_max; i++)
for (j=0; j<l_max; j++)
Hes[i][j] = ZERO;
rotation_product = ONE;
N_VScale(ONE/r_norm, V[0], V[0]);
/* Inner loop: generate Krylov sequence and Arnoldi basis. */
for (l=0; l<maxit; l++) {
(*nli)++;
krydim = l + 1;
/* Generate A-tilde V[l], where A-tilde = s1 A P_inv s2_inv. */
/* Apply right scaling: vtemp = s2_inv V[l]. */
if (scale2) N_VDiv(V[l], s2, vtemp);
else N_VScale(ONE, V[l], vtemp);
/* Apply right preconditioner: vtemp = Z[l] = P_inv s2_inv V[l]. */
if (preOnRight) {
N_VScale(ONE, vtemp, V[l+1]);
ier = psolve(P_data, V[l+1], vtemp, delta, PREC_RIGHT);
(*nps)++;
if (ier != 0)
return((ier < 0) ? SPFGMR_PSOLVE_FAIL_UNREC : SPFGMR_PSOLVE_FAIL_REC);
}
N_VScale(ONE, vtemp, Z[l]);
/* Apply A: V[l+1] = A P_inv s2_inv V[l]. */
ier = atimes(A_data, vtemp, V[l+1]);
if (ier != 0)
return((ier < 0) ? SPFGMR_ATIMES_FAIL_UNREC : SPFGMR_ATIMES_FAIL_REC);
/* Apply left scaling: V[l+1] = s1 A P_inv s2_inv V[l]. */
if (scale1) N_VProd(s1, V[l+1], V[l+1]);
/* Orthogonalize V[l+1] against previous V[i]: V[l+1] = w_tilde. */
if (gstype == CLASSICAL_GS) {
if (ClassicalGS(V, Hes, l+1, l_max, &(Hes[l+1][l]),
vtemp, yg) != 0)
return(SPFGMR_GS_FAIL);
} else {
if (ModifiedGS(V, Hes, l+1, l_max, &(Hes[l+1][l])) != 0)
return(SPFGMR_GS_FAIL);
}
/* Update the QR factorization of Hes. */
if(QRfact(krydim, Hes, givens, l) != 0 )
return(SPFGMR_QRFACT_FAIL);
/* Update residual norm estimate; break if convergence test passes. */
rotation_product *= givens[2*l+1];
*res_norm = rho = SUNRabs(rotation_product*r_norm);
if (rho <= delta) { converged = SUNTRUE; break; }
/* Normalize V[l+1] with norm value from the Gram-Schmidt routine. */
N_VScale(ONE/Hes[l+1][l], V[l+1], V[l+1]);
}
/* Inner loop is done. Compute the new correction vector xcor. */
/* Construct g, then solve for y. */
yg[0] = r_norm;
for (i=1; i<=krydim; i++) yg[i]=ZERO;
if (QRsol(krydim, Hes, givens, yg) != 0)
return(SPFGMR_QRSOL_FAIL);
/* Add correction vector Z_l y to xcor. */
for (k=0; k<krydim; k++)
N_VLinearSum(yg[k], Z[k], ONE, xcor, xcor);
/* If converged, construct the final solution vector x and return. */
if (converged) {
N_VLinearSum(ONE, x, ONE, xcor, x);
return(SPFGMR_SUCCESS);
}
/* Not yet converged; if allowed, prepare for restart. */
if (ntries == max_restarts) break;
/* Construct last column of Q in yg. */
s_product = ONE;
for (i=krydim; i>0; i--) {
yg[i] = s_product*givens[2*i-2];
s_product *= givens[2*i-1];
}
yg[0] = s_product;
/* Scale r_norm and yg. */
r_norm *= s_product;
for (i=0; i<=krydim; i++)
yg[i] *= r_norm;
r_norm = SUNRabs(r_norm);
/* Multiply yg by V_(krydim+1) to get last residual vector; restart. */
N_VScale(yg[0], V[0], V[0]);
for (k=1; k<=krydim; k++)
N_VLinearSum(yg[k], V[k], ONE, V[0], V[0]);
}
/* Failed to converge, even after allowed restarts.
If the residual norm was reduced below its initial value, compute
and return x anyway. Otherwise return failure flag. */
if (rho < beta) {
N_VLinearSum(ONE, x, ONE, xcor, x);
return(SPFGMR_RES_REDUCED);
}
return(SPFGMR_CONV_FAIL);
}
