void dd (header *hd)
{ header *st=hd,*hd1,*result;
int c1,c2,i,j,r;
double *m1,*m2,*mr;
complex *mc1,*mc2,*mcr,hc1,hc2;
interval *mi1,*mi2,*mir,hi1,hi2;
hd1=next_param(st);
equal_params_2(&hd,&hd1); if (error) return;
getmatrix(hd,&r,&c1,&m1); if (r!=1) wrong_arg();
getmatrix(hd1,&r,&c2,&m2); if (r!=1) wrong_arg();
if (c1!=c2) wrong_arg();
if (iscomplex(hd)) /* complex values */
{ mc1=(complex *)m1; mc2=(complex *)m2;
result=new_cmatrix(1,c1,""); if (error) return;
mcr=(complex *)matrixof(result);
memmove((char *)mcr,(char *)mc2,c1*sizeof(complex));
for (i=1; i<c1; i++)
{ for (j=c1-1; j>=i; j--)
{ if (mc1[j][0]==mc1[j-i][0] &&
mc1[j][1]==mc1[j-i][1]) wrong_arg();
c_sub(mcr[j],mcr[j-1],hc1);
c_sub(mc1[j],mc1[j-i],hc2);
c_div(hc1,hc2,mcr[j]);
}
}
}
else if (isinterval(hd)) /* complex values */
{ mi1=(complex *)m1; mi2=(complex *)m2;
result=new_imatrix(1,c1,""); if (error) return;
mir=(interval *)matrixof(result);
memmove((char *)mir,(char *)mi2,c1*sizeof(interval));
for (i=1; i<c1; i++)
{ for (j=c1-1; j>=i; j--)
{ i_sub(mir[j],mir[j-1],hi1);
if (hi1[0]<=0 && hi1[1]>=0)
{ output("Interval points coincide\n");
error=1; return;
}
i_sub(mi1[j],mi1[j-i],hi2);
i_div(hi1,hi2,mir[j]);
}
}
}
else if (isreal(hd))
{ result=new_matrix(1,c1,""); if (error) return;
mr=matrixof(result);
memmove((char *)mr,(char *)m2,c1*sizeof(double));
for (i=1; i<c1; i++)
{ for (j=c1-1; j>=i; j--)
{ if (m1[j]==m1[j-i]) wrong_arg();
mr[j]=(mr[j]-mr[j-1])/(m1[j]-m1[j-i]);
}
}
}
else wrong_arg();
moveresult(st,result);
}
/**
* \brief Expand pole product
* \param c resulting filter coefficients
* \param poles pole locations
* \param K number of poles
* \ingroup vyv_gaussian
*
* This routine expands the product to obtain the filter coefficients:
* \f[ \prod_{k=0}^{K-1}\frac{\mathrm{poles}[k]-1}{\mathrm{poles}[k]-z^{-1}}
= \frac{c[0]}{1+\sum_{k=1}^K c[k] z^{-k}}. \f]
*/
static void expand_pole_product(double *c, const complex4c *poles, int K)
{
complex4c denom[VYV_MAX_K + 1];
int k, j;
assert(K <= VYV_MAX_K);
denom[0] = poles[0];
denom[1] = make_complex(-1, 0);
for (k = 1; k < K; ++k)
{
denom[k + 1] = c_neg(denom[k]);
for (j = k; j > 0; --j)
denom[j] = c_sub(c_mul(denom[j], poles[k]), denom[j - 1]);
denom[0] = c_mul(denom[0], poles[k]);
}
for (k = 1; k <= K; ++k)
c[k] = c_div(denom[k], denom[0]).real;
for (c[0] = 1, k = 1; k <= K; ++k)
c[0] += c[k];
return;
}
static struct polynom *pol_div(struct polynom *p,struct polynom *q,struct polynom *p1,struct polynom *p2)
{
int i,j;
struct complex z,z1;
z.x=0; z.y=0; // RS 7.2.2013
p->n=p1->n-p2->n;
if (p->n<0)
{
sur_print("\nDegree of dividend < Degree of divisor");
WAIT; return(p);
}
for (i=0; i<=p->n; ++i)
p->a[i].x=p->a[i].y=0.0;
for (i=0; i<=p1->n; ++i)
{ q->a[i].x=p1->a[i].x; q->a[i].y=p1->a[i].y; }
for (i=p1->n; i>=p2->n; --i)
{
if (c_zero(&(q->a[i]))) continue;
c_div(&z,&(q->a[i]),&(p2->a[p2->n]));
p->a[i-p2->n].x=z.x; p->a[i-p2->n].y=z.y;
q->a[i].x=q->a[i].y=0.0;
for (j=i-1; j>=i-p2->n; --j)
c_sub(&(q->a[j]),&(q->a[j]),
c_mult(&z1,&z,&(p2->a[p2->n-i+j])));
}
i=p2->n-1;
while (c_zero(&(q->a[i])) && i>0) --i;
q->n=i;
return(p);
}
void Dn_up(struct c_complex z,long nstop,struct c_complex*D)
/*:16*/
#line 216 "./mie.w"
{
struct c_complex zinv,k_over_z;
long k;
D[0]= c_inv(c_tan(z));
zinv= c_inv(z);
for(k= 1;k<nstop;k++){
k_over_z= c_smul((double)k,zinv);
D[k]= c_sub(c_inv(c_sub(k_over_z,D[k-1])),k_over_z);
}
}
void CholeskySolver<TYPE>::CholeskyDecomposition(const BaseMatrix<TYPE> &bm)
{
assert(bm.Nrows() == bm.Ncols());
int n = lm.Nrows();
const TYPE &e = SimpleSolver<TYPE>::epsilon;
TYPE temp;
for (int i = 1; i <= n; ++i)
{
if (i == 1)
{
temp = bm(i, i);
}
else
{
temp = bm(i, i) - (c_sub(lm, i, i, 1, i - 1) * t(c_sub(lm, i, i, 1, i - 1)))(1, 1);
}
if (temp <= e)
{
LinearEquationSolver<TYPE>::fail = true;
return;
}
else
{
lm(i, i) = std::sqrt(temp);
for (int j = i + 1; j <= n; ++j)
{
if (i == 1)
{
lm(j, i) = bm(j, i) / lm(i, i);
}
else
{
lm(j, i) = (bm(j, i) - (c_sub(lm, i, i, 1, i - 1) * t(c_sub(lm, j, j, 1, i - 1)))(1, 1)) / lm(i, i);
}
}
}
}
}
void polydd (header *hd)
{ header *st=hd,*hd1,*result;
int c1,c2,i,j,r;
double *m1,*m2,*mr,x;
complex *mc1,*mc2,*mcr,hc,xc;
hd1=next_param(st);
equal_params_2(&hd,&hd1); if (error) return;
getmatrix(hd,&r,&c1,&m1); if (r!=1) wrong_arg();
getmatrix(hd1,&r,&c2,&m2); if (r!=1) wrong_arg();
if (c1!=c2) wrong_arg();
if (iscomplex(hd)) /* complex values */
{ mc1=(complex *)m1; mc2=(complex *)m2;
result=new_cmatrix(1,c1,""); if (error) return;
mcr=(complex *)matrixof(result);
c_copy(mcr[c1-1],mc2[c1-1]);
for (i=c1-2; i>=0; i--)
{ c_copy(xc,mc1[i]);
c_mult(xc,mcr[i+1],hc);
c_sub(mc2[i],hc,mcr[i]);
for (j=i+1; j<c1-1; j++)
{ c_mult(xc,mcr[j+1],hc);
c_sub(mcr[j],hc,mcr[j]);
}
}
}
else
{ result=new_matrix(1,c1,""); if (error) return;
mr=matrixof(result);
mr[c1-1]=m2[c1-1];
for (i=c1-2; i>=0; i--)
{ x=m1[i];
mr[i]=m2[i]-x*mr[i+1];
for (j=i+1; j<c1-1; j++) mr[j]=mr[j]-x*mr[j+1];
}
}
moveresult(st,result);
}
void Dn_down(struct c_complex z,long nstop,struct c_complex*D)
/*:19*/
#line 247 "./mie.w"
{
long k;
struct c_complex zinv,k_over_z;
D[nstop-1]= Lentz_Dn(z,nstop);
zinv= c_inv(z);
for(k= nstop-1;k>=1;k--){
k_over_z= c_smul((double)k,zinv);
D[k-1]= c_sub(k_over_z,c_inv(c_add(D[k],k_over_z)));
}
}
//傅里叶变化
void fft(int N,complex f[])
{
complex t,wn;//中间变量
int i,j,k,m,n,l,r,M;
int la,lb,lc;
/*----计算分解的级数M=log2(N)----*/
for(i=N,M=1;(i=i/2)!=1;M++);
/*----按照倒位序重新排列原信号----*/
for(i=1,j=N/2;i<=N-2;i++)
{
if(i<j)
{
t=f[j];
f[j]=f[i];
f[i]=t;
}
k=N/2;
while(k<=j)
{
j=j-k;
k=k/2;
}
j=j+k;
}
/*----FFT算法----*/
for(m=1;m<=M;m++)
{
la=pow(2,m); //la=2^m代表第m级每个分组所含节点数
lb=la/2; //lb代表第m级每个分组所含碟形单元数
//同时它也表示每个碟形单元上下节点之间的距离
/*----碟形运算----*/
for(l=1;l<=lb;l++)
{
r=(l-1)*pow(2,M-m);
for(n=l-1;n<N-1;n=n+la) //遍历每个分组，分组总数为N/la
{
lc=n+lb; //n,lc分别代表一个碟形单元的上、下节点编号
Wn_i(N,r,&wn,1);//wn=Wnr
c_mul(f[lc],wn,&t);//t = f[lc] * wn复数运算
c_sub(f[n],t,&(f[lc]));//f[lc] = f[n] - f[lc] * Wnr
c_plus(f[n],t,&(f[n]));//f[n] = f[n] + f[lc] * Wnr
}
}
}
}
/*! \brief Check the inf-norm of the error vector
*/
void cinf_norm_error(int nrhs, SuperMatrix *X, complex *xtrue)
{
DNformat *Xstore;
float err, xnorm;
complex *Xmat, *soln_work;
complex temp;
int i, j;
Xstore = X->Store;
Xmat = Xstore->nzval;
for (j = 0; j < nrhs; j++) {
soln_work = &Xmat[j*Xstore->lda];
err = xnorm = 0.0;
for (i = 0; i < X->nrow; i++) {
c_sub(&temp, &soln_work[i], &xtrue[i]);
err = SUPERLU_MAX(err, c_abs(&temp));
xnorm = SUPERLU_MAX(xnorm, c_abs(&soln_work[i]));
}
err = err / xnorm;
printf("||X - Xtrue||/||X|| = %e\n", err);
}
}
static struct polynom *pol_sub(struct polynom *p,struct polynom *p1,struct polynom *p2)
{
int i;
// RS REM struct complex tulo;
p->n=(p1->n>p2->n)? (p1->n):(p2->n);
for (i=0; i<=p->n; ++i)
{
if (i<=p1->n)
{
if (i<=p2->n)
c_sub(&(p->a[i]),&(p1->a[i]),&(p2->a[i]));
else
{ p->a[i].x=p1->a[i].x; p->a[i].y=p1->a[i].y; }
}
else
{ p->a[i].x=-(p2->a[i].x); p->a[i].y=-(p2->a[i].y); }
}
i=p->n;
while (c_zero(&(p->a[i])) && i>0) --i;
p->n=i;
return(p);
}
/*! \brief Performs numeric block updates within the relaxed snode.
*/
int
csnode_bmod (
const int jcol, /* in */
const int jsupno, /* in */
const int fsupc, /* in */
complex *dense, /* in */
complex *tempv, /* working array */
GlobalLU_t *Glu, /* modified */
SuperLUStat_t *stat /* output */
)
{
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
_fcd ftcs1 = _cptofcd("L", strlen("L")),
ftcs2 = _cptofcd("N", strlen("N")),
ftcs3 = _cptofcd("U", strlen("U"));
#endif
int incx = 1, incy = 1;
complex alpha = {-1.0, 0.0}, beta = {1.0, 0.0};
#endif
complex comp_zero = {0.0, 0.0};
int luptr, nsupc, nsupr, nrow;
int isub, irow, i, iptr;
register int ufirst, nextlu;
int *lsub, *xlsub;
complex *lusup;
int *xlusup;
flops_t *ops = stat->ops;
lsub = Glu->lsub;
xlsub = Glu->xlsub;
lusup = (complex *) Glu->lusup;
xlusup = Glu->xlusup;
nextlu = xlusup[jcol];
/*
* Process the supernodal portion of L\U[*,j]
*/
for (isub = xlsub[fsupc]; isub < xlsub[fsupc+1]; isub++) {
irow = lsub[isub];
lusup[nextlu] = dense[irow];
dense[irow] = comp_zero;
++nextlu;
}
xlusup[jcol + 1] = nextlu; /* Initialize xlusup for next column */
if ( fsupc < jcol ) {
luptr = xlusup[fsupc];
nsupr = xlsub[fsupc+1] - xlsub[fsupc];
nsupc = jcol - fsupc; /* Excluding jcol */
ufirst = xlusup[jcol]; /* Points to the beginning of column
jcol in supernode L\U(jsupno). */
nrow = nsupr - nsupc;
ops[TRSV] += 4 * nsupc * (nsupc - 1);
ops[GEMV] += 8 * nrow * nsupc;
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
CTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &lusup[luptr], &nsupr,
&lusup[ufirst], &incx );
CGEMV( ftcs2, &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr,
&lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#else
#if SCIPY_FIX
if (nsupr < nsupc) {
/* Fail early rather than passing in invalid parameters to TRSV. */
ABORT("failed to factorize matrix");
}
#endif
ctrsv_( "L", "N", "U", &nsupc, &lusup[luptr], &nsupr,
&lusup[ufirst], &incx );
cgemv_( "N", &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr,
&lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#endif
#else
clsolve ( nsupr, nsupc, &lusup[luptr], &lusup[ufirst] );
cmatvec ( nsupr, nrow, nsupc, &lusup[luptr+nsupc],
&lusup[ufirst], &tempv[0] );
/* Scatter tempv[*] into lusup[*] */
iptr = ufirst + nsupc;
for (i = 0; i < nrow; i++) {
c_sub(&lusup[iptr], &lusup[iptr], &tempv[i]);
++iptr;
tempv[i] = comp_zero;
}
#endif
}
return 0;
}
void LUdecomposition(long n, complex **A, complex *b, complex *x)
{
long i,j,k,*p;
complex akk, bk, z, sum;
complex *Ak;
/* Allocate auxiliary variables */
p = (long *)Mem(MEM_ALLOC, n, sizeof(long));
/* Gaussian elimination with partial pivoting */
for (k=0; k<n-1; k++){ /* columns of A */
/* --- Pivoting --- */
akk.re = 0.0;
akk.im = 0.0;
j = k;
for (i=k; i<n; i++){
if ( c_norm(A[i][k]) > c_norm(akk)){
akk = A[i][k];
CheckValue(FUNCTION_NAME, "A[i][k].re","", A[i][k].re, -INFTY, INFTY);
CheckValue(FUNCTION_NAME, "A[i][k].im","", A[i][k].im, -INFTY, INFTY);
j = i;
}
}
if (j != k){ /* swap rows j and k*/
Ak = A[k];
A[k] = A[j]; /* swap pointers*/
A[j] = Ak;
bk = b[k];
b[k] = b[j];
b[j] = bk;
}
p[k] = j; /* Keep list of permutations */
/* Sanity check */
if (akk.re != A[k][k].re && akk.im != A[k][k].im){
Die(FUNCTION_NAME, "Something went wrong with pivoting?");
return;
}
if (akk.re == 0.0 && akk.im == 0.0){
Die(FUNCTION_NAME, "Matrix singular?");
return;
}
/* Store L part */
for (i=k+1;i<n; i++){
A[i][k] = c_div(A[i][k],A[k][k]);
CheckValue(FUNCTION_NAME, "A[i][k].re","", A[i][k].re, -INFTY, INFTY);
CheckValue(FUNCTION_NAME, "A[i][k].im","", A[i][k].im, -INFTY, INFTY);
}
/* Update */
for (i=k+1; i<n; i++){
/* update b */
z = c_mul(A[i][k], b[k]);
b[i] = c_sub(b[i], z);
CheckValue(FUNCTION_NAME, "b[i].re","", b[i].re, -INFTY, INFTY);
CheckValue(FUNCTION_NAME, "b[i].im","", b[i].im, -INFTY, INFTY);
for (j=k+1; j<n; j++){
/* Update U part of A */
z = c_mul( A[i][k], A[k][j]);
A[i][j] = c_sub(A[i][j],z);
CheckValue(FUNCTION_NAME, "A[i][j].re","", A[i][j].re, -INFTY, INFTY);
CheckValue(FUNCTION_NAME, "A[i][j].im","", A[i][j].im, -INFTY, INFTY);
}
}
}
/* Solve x */
x[n-1] = c_div(b[n-1],A[n-1][n-1]);
for (i=n-2; i>=0; i--){
sum.re = 0.0;
sum.im = 0.0;
for (j=i+1; j<n; j++){
z = c_mul(A[i][j], x[j]);
sum = c_add(sum, z);
}
z = c_sub(b[i], sum);
x[i] = c_div(z, A[i][i]);
}
Mem(MEM_FREE, p);
/* Return */
return;
}
int
sp_ctrsv(char *uplo, char *trans, char *diag, SuperMatrix *L,
SuperMatrix *U, complex *x, int *info)
{
/*
* Purpose
* =======
*
* sp_ctrsv() solves one of the systems of equations
* A*x = b, or A'*x = b,
* where b and x are n element vectors and A is a sparse unit , or
* non-unit, upper or lower triangular matrix.
* No test for singularity or near-singularity is included in this
* routine. Such tests must be performed before calling this routine.
*
* Parameters
* ==========
*
* uplo - (input) char*
* On entry, uplo specifies whether the matrix is an upper or
* lower triangular matrix as follows:
* uplo = 'U' or 'u' A is an upper triangular matrix.
* uplo = 'L' or 'l' A is a lower triangular matrix.
*
* trans - (input) char*
* On entry, trans specifies the equations to be solved as
* follows:
* trans = 'N' or 'n' A*x = b.
* trans = 'T' or 't' A'*x = b.
* trans = 'C' or 'c' A'*x = b.
*
* diag - (input) char*
* On entry, diag specifies whether or not A is unit
* triangular as follows:
* diag = 'U' or 'u' A is assumed to be unit triangular.
* diag = 'N' or 'n' A is not assumed to be unit
* triangular.
*
* L - (input) SuperMatrix*
* The factor L from the factorization Pr*A*Pc=L*U. Use
* compressed row subscripts storage for supernodes,
* i.e., L has types: Stype = SC, Dtype = SLU_C, Mtype = TRLU.
*
* U - (input) SuperMatrix*
* The factor U from the factorization Pr*A*Pc=L*U.
* U has types: Stype = NC, Dtype = SLU_C, Mtype = TRU.
*
* x - (input/output) complex*
* Before entry, the incremented array X must contain the n
* element right-hand side vector b. On exit, X is overwritten
* with the solution vector x.
*
* info - (output) int*
* If *info = -i, the i-th argument had an illegal value.
*
*/
#ifdef _CRAY
_fcd ftcs1 = _cptofcd("L", strlen("L")),
ftcs2 = _cptofcd("N", strlen("N")),
ftcs3 = _cptofcd("U", strlen("U"));
#endif
SCformat *Lstore;
NCformat *Ustore;
complex *Lval, *Uval;
int incx = 1, incy = 1;
complex alpha = {1.0, 0.0}, beta = {1.0, 0.0};
complex comp_zero = {0.0, 0.0};
int nrow;
int fsupc, nsupr, nsupc, luptr, istart, irow;
int i, k, iptr, jcol;
complex *work;
flops_t solve_ops;
extern SuperLUStat_t SuperLUStat;
/* Test the input parameters */
*info = 0;
if ( !lsame_(uplo,"L") && !lsame_(uplo, "U") ) *info = -1;
else if ( !lsame_(trans, "N") && !lsame_(trans, "T") ) *info = -2;
else if ( !lsame_(diag, "U") && !lsame_(diag, "N") ) *info = -3;
else if ( L->nrow != L->ncol || L->nrow < 0 ) *info = -4;
else if ( U->nrow != U->ncol || U->nrow < 0 ) *info = -5;
if ( *info ) {
i = -(*info);
xerbla_("sp_ctrsv", &i);
return 0;
}
Lstore = L->Store;
Lval = Lstore->nzval;
Ustore = U->Store;
Uval = Ustore->nzval;
solve_ops = 0;
if ( !(work = complexCalloc(L->nrow)) )
ABORT("Malloc fails for work in sp_ctrsv().");
if ( lsame_(trans, "N") ) { /* Form x := inv(A)*x. */
if ( lsame_(uplo, "L") ) {
/* Form x := inv(L)*x */
if ( L->nrow == 0 ) return 0; /* Quick return */
for (k = 0; k <= Lstore->nsuper; k++) {
fsupc = L_FST_SUPC(k);
istart = L_SUB_START(fsupc);
nsupr = L_SUB_START(fsupc+1) - istart;
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
nrow = nsupr - nsupc;
solve_ops += 4 * nsupc * (nsupc - 1);
solve_ops += 8 * nrow * nsupc;
if ( nsupc == 1 ) {
for (iptr=istart+1; iptr < L_SUB_START(fsupc+1); ++iptr) {
irow = L_SUB(iptr);
++luptr;
cc_mult(&comp_zero, &x[fsupc], &Lval[luptr]);
c_sub(&x[irow], &x[irow], &comp_zero);
}
} else {
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
CTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
CGEMV(ftcs2, &nrow, &nsupc, &alpha, &Lval[luptr+nsupc],
&nsupr, &x[fsupc], &incx, &beta, &work[0], &incy);
#else
ctrsv_("L", "N", "U", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
cgemv_("N", &nrow, &nsupc, &alpha, &Lval[luptr+nsupc],
&nsupr, &x[fsupc], &incx, &beta, &work[0], &incy);
#endif
#else
clsolve ( nsupr, nsupc, &Lval[luptr], &x[fsupc]);
cmatvec ( nsupr, nsupr-nsupc, nsupc, &Lval[luptr+nsupc],
&x[fsupc], &work[0] );
#endif
iptr = istart + nsupc;
for (i = 0; i < nrow; ++i, ++iptr) {
irow = L_SUB(iptr);
c_sub(&x[irow], &x[irow], &work[i]); /* Scatter */
work[i] = comp_zero;
}
}
} /* for k ... */
} else {
/* Form x := inv(U)*x */
if ( U->nrow == 0 ) return 0; /* Quick return */
for (k = Lstore->nsuper; k >= 0; k--) {
fsupc = L_FST_SUPC(k);
nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
solve_ops += 4 * nsupc * (nsupc + 1);
if ( nsupc == 1 ) {
c_div(&x[fsupc], &x[fsupc], &Lval[luptr]);
for (i = U_NZ_START(fsupc); i < U_NZ_START(fsupc+1); ++i) {
irow = U_SUB(i);
cc_mult(&comp_zero, &x[fsupc], &Uval[i]);
c_sub(&x[irow], &x[irow], &comp_zero);
}
} else {
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
CTRSV(ftcs3, ftcs2, ftcs2, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
ctrsv_("U", "N", "N", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
#else
cusolve ( nsupr, nsupc, &Lval[luptr], &x[fsupc] );
#endif
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1);
i++) {
irow = U_SUB(i);
cc_mult(&comp_zero, &x[jcol], &Uval[i]);
c_sub(&x[irow], &x[irow], &comp_zero);
}
}
}
} /* for k ... */
}
} else { /* Form x := inv(A')*x */
if ( lsame_(uplo, "L") ) {
/* Form x := inv(L')*x */
if ( L->nrow == 0 ) return 0; /* Quick return */
for (k = Lstore->nsuper; k >= 0; --k) {
fsupc = L_FST_SUPC(k);
istart = L_SUB_START(fsupc);
nsupr = L_SUB_START(fsupc+1) - istart;
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
solve_ops += 8 * (nsupr - nsupc) * nsupc;
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
iptr = istart + nsupc;
for (i = L_NZ_START(jcol) + nsupc;
i < L_NZ_START(jcol+1); i++) {
irow = L_SUB(iptr);
cc_mult(&comp_zero, &x[irow], &Lval[i]);
c_sub(&x[jcol], &x[jcol], &comp_zero);
iptr++;
}
}
if ( nsupc > 1 ) {
solve_ops += 4 * nsupc * (nsupc - 1);
#ifdef _CRAY
ftcs1 = _cptofcd("L", strlen("L"));
ftcs2 = _cptofcd("T", strlen("T"));
ftcs3 = _cptofcd("U", strlen("U"));
CTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
ctrsv_("L", "T", "U", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
}
}
} else {
/* Form x := inv(U')*x */
if ( U->nrow == 0 ) return 0; /* Quick return */
for (k = 0; k <= Lstore->nsuper; k++) {
fsupc = L_FST_SUPC(k);
nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); i++) {
irow = U_SUB(i);
cc_mult(&comp_zero, &x[irow], &Uval[i]);
c_sub(&x[jcol], &x[jcol], &comp_zero);
}
}
solve_ops += 4 * nsupc * (nsupc + 1);
if ( nsupc == 1 ) {
c_div(&x[fsupc], &x[fsupc], &Lval[luptr]);
} else {
#ifdef _CRAY
ftcs1 = _cptofcd("U", strlen("U"));
ftcs2 = _cptofcd("T", strlen("T"));
ftcs3 = _cptofcd("N", strlen("N"));
CTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
ctrsv_("U", "T", "N", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
}
} /* for k ... */
}
}
SuperLUStat.ops[SOLVE] += solve_ops;
SUPERLU_FREE(work);
return 0;
}
/*! \brief Solves one of the systems of equations A*x = b, or A'*x = b
*
* <pre>
* Purpose
* =======
*
* sp_ctrsv() solves one of the systems of equations
* A*x = b, or A'*x = b,
* where b and x are n element vectors and A is a sparse unit , or
* non-unit, upper or lower triangular matrix.
* No test for singularity or near-singularity is included in this
* routine. Such tests must be performed before calling this routine.
*
* Parameters
* ==========
*
* uplo - (input) char*
* On entry, uplo specifies whether the matrix is an upper or
* lower triangular matrix as follows:
* uplo = 'U' or 'u' A is an upper triangular matrix.
* uplo = 'L' or 'l' A is a lower triangular matrix.
*
* trans - (input) char*
* On entry, trans specifies the equations to be solved as
* follows:
* trans = 'N' or 'n' A*x = b.
* trans = 'T' or 't' A'*x = b.
* trans = 'C' or 'c' A^H*x = b.
*
* diag - (input) char*
* On entry, diag specifies whether or not A is unit
* triangular as follows:
* diag = 'U' or 'u' A is assumed to be unit triangular.
* diag = 'N' or 'n' A is not assumed to be unit
* triangular.
*
* L - (input) SuperMatrix*
* The factor L from the factorization Pr*A*Pc=L*U. Use
* compressed row subscripts storage for supernodes,
* i.e., L has types: Stype = SC, Dtype = SLU_C, Mtype = TRLU.
*
* U - (input) SuperMatrix*
* The factor U from the factorization Pr*A*Pc=L*U.
* U has types: Stype = NC, Dtype = SLU_C, Mtype = TRU.
*
* x - (input/output) complex*
* Before entry, the incremented array X must contain the n
* element right-hand side vector b. On exit, X is overwritten
* with the solution vector x.
*
* info - (output) int*
* If *info = -i, the i-th argument had an illegal value.
* </pre>
*/
int
sp_ctrsv(char *uplo, char *trans, char *diag, SuperMatrix *L,
SuperMatrix *U, complex *x, SuperLUStat_t *stat, int *info)
{
#ifdef _CRAY
_fcd ftcs1 = _cptofcd("L", strlen("L")),
ftcs2 = _cptofcd("N", strlen("N")),
ftcs3 = _cptofcd("U", strlen("U"));
#endif
SCformat *Lstore;
NCformat *Ustore;
complex *Lval, *Uval;
int incx = 1, incy = 1;
complex temp;
complex alpha = {1.0, 0.0}, beta = {1.0, 0.0};
complex comp_zero = {0.0, 0.0};
int nrow;
int fsupc, nsupr, nsupc, luptr, istart, irow;
int i, k, iptr, jcol;
complex *work;
flops_t solve_ops;
/* Test the input parameters */
*info = 0;
if ( strncmp(uplo,"L", 1)!=0 && strncmp(uplo, "U", 1)!=0 ) *info = -1;
else if ( strncmp(trans, "N", 1)!=0 && strncmp(trans, "T", 1)!=0 &&
strncmp(trans, "C", 1)!=0) *info = -2;
else if ( strncmp(diag, "U", 1)!=0 && strncmp(diag, "N", 1)!=0 )
*info = -3;
else if ( L->nrow != L->ncol || L->nrow < 0 ) *info = -4;
else if ( U->nrow != U->ncol || U->nrow < 0 ) *info = -5;
if ( *info ) {
i = -(*info);
input_error("sp_ctrsv", &i);
return 0;
}
Lstore = L->Store;
Lval = Lstore->nzval;
Ustore = U->Store;
Uval = Ustore->nzval;
solve_ops = 0;
if ( !(work = complexCalloc(L->nrow)) )
ABORT("Malloc fails for work in sp_ctrsv().");
if ( strncmp(trans, "N", 1)==0 ) { /* Form x := inv(A)*x. */
if ( strncmp(uplo, "L", 1)==0 ) {
/* Form x := inv(L)*x */
if ( L->nrow == 0 ) return 0; /* Quick return */
for (k = 0; k <= Lstore->nsuper; k++) {
fsupc = L_FST_SUPC(k);
istart = L_SUB_START(fsupc);
nsupr = L_SUB_START(fsupc+1) - istart;
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
nrow = nsupr - nsupc;
/* 1 c_div costs 10 flops */
solve_ops += 4 * nsupc * (nsupc - 1) + 10 * nsupc;
solve_ops += 8 * nrow * nsupc;
if ( nsupc == 1 ) {
for (iptr=istart+1; iptr < L_SUB_START(fsupc+1); ++iptr) {
irow = L_SUB(iptr);
++luptr;
cc_mult(&comp_zero, &x[fsupc], &Lval[luptr]);
c_sub(&x[irow], &x[irow], &comp_zero);
}
} else {
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
CTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
CGEMV(ftcs2, &nrow, &nsupc, &alpha, &Lval[luptr+nsupc],
&nsupr, &x[fsupc], &incx, &beta, &work[0], &incy);
#else
ctrsv_("L", "N", "U", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
cgemv_("N", &nrow, &nsupc, &alpha, &Lval[luptr+nsupc],
&nsupr, &x[fsupc], &incx, &beta, &work[0], &incy);
#endif
#else
clsolve ( nsupr, nsupc, &Lval[luptr], &x[fsupc]);
cmatvec ( nsupr, nsupr-nsupc, nsupc, &Lval[luptr+nsupc],
&x[fsupc], &work[0] );
#endif
iptr = istart + nsupc;
for (i = 0; i < nrow; ++i, ++iptr) {
irow = L_SUB(iptr);
c_sub(&x[irow], &x[irow], &work[i]); /* Scatter */
work[i] = comp_zero;
}
}
} /* for k ... */
} else {
/* Form x := inv(U)*x */
if ( U->nrow == 0 ) return 0; /* Quick return */
for (k = Lstore->nsuper; k >= 0; k--) {
fsupc = L_FST_SUPC(k);
nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
/* 1 c_div costs 10 flops */
solve_ops += 4 * nsupc * (nsupc + 1) + 10 * nsupc;
if ( nsupc == 1 ) {
c_div(&x[fsupc], &x[fsupc], &Lval[luptr]);
for (i = U_NZ_START(fsupc); i < U_NZ_START(fsupc+1); ++i) {
irow = U_SUB(i);
cc_mult(&comp_zero, &x[fsupc], &Uval[i]);
c_sub(&x[irow], &x[irow], &comp_zero);
}
} else {
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
CTRSV(ftcs3, ftcs2, ftcs2, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
ctrsv_("U", "N", "N", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
#else
cusolve ( nsupr, nsupc, &Lval[luptr], &x[fsupc] );
#endif
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1);
i++) {
irow = U_SUB(i);
cc_mult(&comp_zero, &x[jcol], &Uval[i]);
c_sub(&x[irow], &x[irow], &comp_zero);
}
}
}
} /* for k ... */
}
} else if ( strncmp(trans, "T", 1)==0 ) { /* Form x := inv(A')*x */
if ( strncmp(uplo, "L", 1)==0 ) {
/* Form x := inv(L')*x */
if ( L->nrow == 0 ) return 0; /* Quick return */
for (k = Lstore->nsuper; k >= 0; --k) {
fsupc = L_FST_SUPC(k);
istart = L_SUB_START(fsupc);
nsupr = L_SUB_START(fsupc+1) - istart;
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
solve_ops += 8 * (nsupr - nsupc) * nsupc;
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
iptr = istart + nsupc;
for (i = L_NZ_START(jcol) + nsupc;
i < L_NZ_START(jcol+1); i++) {
irow = L_SUB(iptr);
cc_mult(&comp_zero, &x[irow], &Lval[i]);
c_sub(&x[jcol], &x[jcol], &comp_zero);
iptr++;
}
}
if ( nsupc > 1 ) {
solve_ops += 4 * nsupc * (nsupc - 1);
#ifdef _CRAY
ftcs1 = _cptofcd("L", strlen("L"));
ftcs2 = _cptofcd("T", strlen("T"));
ftcs3 = _cptofcd("U", strlen("U"));
CTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
ctrsv_("L", "T", "U", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
}
}
} else {
/* Form x := inv(U')*x */
if ( U->nrow == 0 ) return 0; /* Quick return */
for (k = 0; k <= Lstore->nsuper; k++) {
fsupc = L_FST_SUPC(k);
nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); i++) {
irow = U_SUB(i);
cc_mult(&comp_zero, &x[irow], &Uval[i]);
c_sub(&x[jcol], &x[jcol], &comp_zero);
}
}
/* 1 c_div costs 10 flops */
solve_ops += 4 * nsupc * (nsupc + 1) + 10 * nsupc;
if ( nsupc == 1 ) {
c_div(&x[fsupc], &x[fsupc], &Lval[luptr]);
} else {
#ifdef _CRAY
ftcs1 = _cptofcd("U", strlen("U"));
ftcs2 = _cptofcd("T", strlen("T"));
ftcs3 = _cptofcd("N", strlen("N"));
CTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
ctrsv_("U", "T", "N", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
}
} /* for k ... */
}
} else { /* Form x := conj(inv(A'))*x */
if ( strncmp(uplo, "L", 1)==0 ) {
/* Form x := conj(inv(L'))*x */
if ( L->nrow == 0 ) return 0; /* Quick return */
for (k = Lstore->nsuper; k >= 0; --k) {
fsupc = L_FST_SUPC(k);
istart = L_SUB_START(fsupc);
nsupr = L_SUB_START(fsupc+1) - istart;
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
solve_ops += 8 * (nsupr - nsupc) * nsupc;
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
iptr = istart + nsupc;
for (i = L_NZ_START(jcol) + nsupc;
i < L_NZ_START(jcol+1); i++) {
irow = L_SUB(iptr);
cc_conj(&temp, &Lval[i]);
cc_mult(&comp_zero, &x[irow], &temp);
c_sub(&x[jcol], &x[jcol], &comp_zero);
iptr++;
}
}
if ( nsupc > 1 ) {
solve_ops += 4 * nsupc * (nsupc - 1);
#ifdef _CRAY
ftcs1 = _cptofcd("L", strlen("L"));
ftcs2 = _cptofcd(trans, strlen("T"));
ftcs3 = _cptofcd("U", strlen("U"));
CTRSV(ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
ctrsv_("L", trans, "U", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
}
}
} else {
/* Form x := conj(inv(U'))*x */
if ( U->nrow == 0 ) return 0; /* Quick return */
for (k = 0; k <= Lstore->nsuper; k++) {
fsupc = L_FST_SUPC(k);
nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
for (jcol = fsupc; jcol < L_FST_SUPC(k+1); jcol++) {
solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); i++) {
irow = U_SUB(i);
cc_conj(&temp, &Uval[i]);
cc_mult(&comp_zero, &x[irow], &temp);
c_sub(&x[jcol], &x[jcol], &comp_zero);
}
}
/* 1 c_div costs 10 flops */
solve_ops += 4 * nsupc * (nsupc + 1) + 10 * nsupc;
if ( nsupc == 1 ) {
cc_conj(&temp, &Lval[luptr]);
c_div(&x[fsupc], &x[fsupc], &temp);
} else {
#ifdef _CRAY
ftcs1 = _cptofcd("U", strlen("U"));
ftcs2 = _cptofcd(trans, strlen("T"));
ftcs3 = _cptofcd("N", strlen("N"));
CTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#else
ctrsv_("U", trans, "N", &nsupc, &Lval[luptr], &nsupr,
&x[fsupc], &incx);
#endif
}
} /* for k ... */
}
}
stat->ops[SOLVE] += solve_ops;
SUPERLU_FREE(work);
return 0;
}
void
cgstrs (trans_t trans, SuperMatrix *L, SuperMatrix *U,
int *perm_c, int *perm_r, SuperMatrix *B,
SuperLUStat_t *stat, int *info)
{
#ifdef _CRAY
_fcd ftcs1, ftcs2, ftcs3, ftcs4;
#endif
int incx = 1, incy = 1;
#ifdef USE_VENDOR_BLAS
complex alpha = {1.0, 0.0}, beta = {1.0, 0.0};
complex *work_col;
#endif
complex temp_comp;
DNformat *Bstore;
complex *Bmat;
SCformat *Lstore;
NCformat *Ustore;
complex *Lval, *Uval;
int fsupc, nrow, nsupr, nsupc, luptr, istart, irow;
int i, j, k, iptr, jcol, n, ldb, nrhs;
complex *work, *rhs_work, *soln;
flops_t solve_ops;
void cprint_soln();
/* Test input parameters ... */
*info = 0;
Bstore = B->Store;
ldb = Bstore->lda;
nrhs = B->ncol;
if ( trans != NOTRANS && trans != TRANS && trans != CONJ ) *info = -1;
else if ( L->nrow != L->ncol || L->nrow < 0 ||
L->Stype != SLU_SC || L->Dtype != SLU_C || L->Mtype != SLU_TRLU )
*info = -2;
else if ( U->nrow != U->ncol || U->nrow < 0 ||
U->Stype != SLU_NC || U->Dtype != SLU_C || U->Mtype != SLU_TRU )
*info = -3;
else if ( ldb < SUPERLU_MAX(0, L->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_C || B->Mtype != SLU_GE )
*info = -6;
if ( *info ) {
i = -(*info);
xerbla_("cgstrs", &i);
return;
}
n = L->nrow;
work = complexCalloc(n * nrhs);
if ( !work ) ABORT("Malloc fails for local work[].");
soln = complexMalloc(n);
if ( !soln ) ABORT("Malloc fails for local soln[].");
Bmat = Bstore->nzval;
Lstore = L->Store;
Lval = Lstore->nzval;
Ustore = U->Store;
Uval = Ustore->nzval;
solve_ops = 0;
if ( trans == NOTRANS ) {
/* Permute right hand sides to form Pr*B */
for (i = 0; i < nrhs; i++) {
rhs_work = &Bmat[i*ldb];
for (k = 0; k < n; k++) soln[perm_r[k]] = rhs_work[k];
for (k = 0; k < n; k++) rhs_work[k] = soln[k];
}
/* Forward solve PLy=Pb. */
for (k = 0; k <= Lstore->nsuper; k++) {
fsupc = L_FST_SUPC(k);
istart = L_SUB_START(fsupc);
nsupr = L_SUB_START(fsupc+1) - istart;
nsupc = L_FST_SUPC(k+1) - fsupc;
nrow = nsupr - nsupc;
solve_ops += 4 * nsupc * (nsupc - 1) * nrhs;
solve_ops += 8 * nrow * nsupc * nrhs;
if ( nsupc == 1 ) {
for (j = 0; j < nrhs; j++) {
rhs_work = &Bmat[j*ldb];
luptr = L_NZ_START(fsupc);
for (iptr=istart+1; iptr < L_SUB_START(fsupc+1); iptr++){
irow = L_SUB(iptr);
++luptr;
cc_mult(&temp_comp, &rhs_work[fsupc], &Lval[luptr]);
c_sub(&rhs_work[irow], &rhs_work[irow], &temp_comp);
}
}
} else {
luptr = L_NZ_START(fsupc);
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
ftcs1 = _cptofcd("L", strlen("L"));
ftcs2 = _cptofcd("N", strlen("N"));
ftcs3 = _cptofcd("U", strlen("U"));
CTRSM( ftcs1, ftcs1, ftcs2, ftcs3, &nsupc, &nrhs, &alpha,
&Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
CGEMM( ftcs2, ftcs2, &nrow, &nrhs, &nsupc, &alpha,
&Lval[luptr+nsupc], &nsupr, &Bmat[fsupc], &ldb,
&beta, &work[0], &n );
#else
ctrsm_("L", "L", "N", "U", &nsupc, &nrhs, &alpha,
&Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
cgemm_( "N", "N", &nrow, &nrhs, &nsupc, &alpha,
&Lval[luptr+nsupc], &nsupr, &Bmat[fsupc], &ldb,
&beta, &work[0], &n );
#endif
for (j = 0; j < nrhs; j++) {
rhs_work = &Bmat[j*ldb];
work_col = &work[j*n];
iptr = istart + nsupc;
for (i = 0; i < nrow; i++) {
irow = L_SUB(iptr);
c_sub(&rhs_work[irow], &rhs_work[irow], &work_col[i]);
work_col[i].r = 0.0;
work_col[i].i = 0.0;
iptr++;
}
}
#else
for (j = 0; j < nrhs; j++) {
rhs_work = &Bmat[j*ldb];
clsolve (nsupr, nsupc, &Lval[luptr], &rhs_work[fsupc]);
cmatvec (nsupr, nrow, nsupc, &Lval[luptr+nsupc],
&rhs_work[fsupc], &work[0] );
iptr = istart + nsupc;
for (i = 0; i < nrow; i++) {
irow = L_SUB(iptr);
c_sub(&rhs_work[irow], &rhs_work[irow], &work[i]);
work[i].r = 0.;
work[i].i = 0.;
iptr++;
}
}
#endif
} /* else ... */
} /* for L-solve */
#ifdef DEBUG
printf("After L-solve: y=\n");
cprint_soln(n, nrhs, Bmat);
#endif
/*
* Back solve Ux=y.
*/
for (k = Lstore->nsuper; k >= 0; k--) {
fsupc = L_FST_SUPC(k);
istart = L_SUB_START(fsupc);
nsupr = L_SUB_START(fsupc+1) - istart;
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
solve_ops += 4 * nsupc * (nsupc + 1) * nrhs;
if ( nsupc == 1 ) {
rhs_work = &Bmat[0];
for (j = 0; j < nrhs; j++) {
c_div(&rhs_work[fsupc], &rhs_work[fsupc], &Lval[luptr]);
rhs_work += ldb;
}
} else {
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
ftcs1 = _cptofcd("L", strlen("L"));
ftcs2 = _cptofcd("U", strlen("U"));
ftcs3 = _cptofcd("N", strlen("N"));
CTRSM( ftcs1, ftcs2, ftcs3, ftcs3, &nsupc, &nrhs, &alpha,
&Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
#else
ctrsm_("L", "U", "N", "N", &nsupc, &nrhs, &alpha,
&Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
#endif
#else
for (j = 0; j < nrhs; j++)
cusolve ( nsupr, nsupc, &Lval[luptr], &Bmat[fsupc+j*ldb] );
#endif
}
for (j = 0; j < nrhs; ++j) {
rhs_work = &Bmat[j*ldb];
for (jcol = fsupc; jcol < fsupc + nsupc; jcol++) {
solve_ops += 8*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); i++ ){
irow = U_SUB(i);
cc_mult(&temp_comp, &rhs_work[jcol], &Uval[i]);
c_sub(&rhs_work[irow], &rhs_work[irow], &temp_comp);
}
}
}
} /* for U-solve */
#ifdef DEBUG
printf("After U-solve: x=\n");
cprint_soln(n, nrhs, Bmat);
#endif
/* Compute the final solution X := Pc*X. */
for (i = 0; i < nrhs; i++) {
rhs_work = &Bmat[i*ldb];
for (k = 0; k < n; k++) soln[k] = rhs_work[perm_c[k]];
for (k = 0; k < n; k++) rhs_work[k] = soln[k];
}
stat->ops[SOLVE] = solve_ops;
} else { /* Solve A'*X=B or CONJ(A)*X=B */
/* Permute right hand sides to form Pc'*B. */
for (i = 0; i < nrhs; i++) {
rhs_work = &Bmat[i*ldb];
for (k = 0; k < n; k++) soln[perm_c[k]] = rhs_work[k];
for (k = 0; k < n; k++) rhs_work[k] = soln[k];
}
stat->ops[SOLVE] = 0;
if (trans == TRANS) {
for (k = 0; k < nrhs; ++k) {
/* Multiply by inv(U'). */
sp_ctrsv("U", "T", "N", L, U, &Bmat[k*ldb], stat, info);
/* Multiply by inv(L'). */
sp_ctrsv("L", "T", "U", L, U, &Bmat[k*ldb], stat, info);
}
} else { /* trans == CONJ */
for (k = 0; k < nrhs; ++k) {
/* Multiply by conj(inv(U')). */
sp_ctrsv("U", "C", "N", L, U, &Bmat[k*ldb], stat, info);
/* Multiply by conj(inv(L')). */
sp_ctrsv("L", "C", "U", L, U, &Bmat[k*ldb], stat, info);
}
}
/* Compute the final solution X := Pr'*X (=inv(Pr)*X) */
for (i = 0; i < nrhs; i++) {
rhs_work = &Bmat[i*ldb];
for (k = 0; k < n; k++) soln[k] = rhs_work[perm_r[k]];
for (k = 0; k < n; k++) rhs_work[k] = soln[k];
}
}
SUPERLU_FREE(work);
SUPERLU_FREE(soln);
}
void Mie(double x,struct c_complex m,double*mu,long nangles,struct c_complex*s1,
struct c_complex*s2,double*qext,double*qsca,double*qback,double*g)
/*:34*/
#line 519 "./mie.w"
{
/*36:*/
#line 546 "./mie.w"
struct c_complex*D;
struct c_complex z1,an,bn,bnm1,anm1,qbcalc;
double*pi0,*pi1,*tau;
struct c_complex xi,xi0,xi1;
double psi,psi0,psi1;
double alpha,beta,factor;
long n,k,nstop,sign;
*qext= -1;
*qsca= -1;
*qback= -1;
*g= -1;
/*:36*/
#line 522 "./mie.w"
/*37:*/
#line 559 "./mie.w"
if(m.im> 0.0){
mie_error("This program requires m.im>=0",1);
return;
}
if(x<=0.0){
mie_error("This program requires positive sphere sizes",2);
return;
}
if(nangles<0){
mie_error("This program requires non-negative angle sizes",3);
return;
}
if(nangles<0){
mie_error("This program requires non-negative angle sizes",4);
return;
}
if((nangles> 0)&&(s1==NULL)){
mie_error("Space must be allocated for s1 if nangles!=0",5);
return;
}
if((nangles> 0)&&(s2==NULL)){
mie_error("Space must be allocated for s2if nangles!=0",6);
return;
}
if(x> 20000){
mie_error("Program not validated for spheres with x>20000",7);
return;
}
/*:37*/
#line 524 "./mie.w"
/*38:*/
#line 589 "./mie.w"
if((m.re==0)&&(x<0.1)){
small_conducting_Mie(x,m,mu,nangles,s1,s2,qext,qsca,qback,g);
return;
}
if((m.re> 0.0)&&(c_abs(m)*x<0.1)){
small_Mie(x,m,mu,nangles,s1,s2,qext,qsca,qback,g);
return;
}
/*:38*/
#line 525 "./mie.w"
/*40:*/
#line 616 "./mie.w"
nstop= floor(x+4.05*pow(x,0.33333)+2.0);
/*:40*/
#line 527 "./mie.w"
/*39:*/
#line 600 "./mie.w"
if(nangles> 0){
set_carray(s1,nangles,c_set(0.0,0.0));
set_carray(s2,nangles,c_set(0.0,0.0));
pi0= new_darray(nangles);
pi1= new_darray(nangles);
tau= new_darray(nangles);
set_darray(pi0,nangles,0.0);
set_darray(tau,nangles,0.0);
set_darray(pi1,nangles,1.0);
}
/*:39*/
#line 529 "./mie.w"
if(m.re> 0)
/*41:*/
#line 634 "./mie.w"
{
struct c_complex z;
z= c_smul(x,m);
D= new_carray(nstop+1);
if(D==NULL){
mie_error("Cannot allocate log array",8);
return;
}
if(fabs(m.im*x)<((13.78*m.re-10.8)*m.re+3.9))
Dn_up(z,nstop,D);
else
Dn_down(z,nstop,D);
}
/*:41*/
#line 531 "./mie.w"
/*42:*/
#line 671 "./mie.w"
psi0= sin(x);
psi1= psi0/x-cos(x);
xi0= c_set(psi0,cos(x));
xi1= c_set(psi1,cos(x)/x+sin(x));
*qsca= 0.0;
*g= 0.0;
*qext= 0.0;
sign= 1;
qbcalc= c_set(0.0,0.0);
anm1= c_set(0.0,0.0);
bnm1= c_set(0.0,0.0);
/*:42*/
#line 533 "./mie.w"
for(n= 1;n<=nstop;n++){
/*43:*/
#line 696 "./mie.w"
if(m.re==0.0){
an= c_sdiv(n*psi1/x-psi0,c_sub(c_smul(n/x,xi1),xi0));
bn= c_sdiv(psi1,xi1);
}else if(m.im==0.0){
z1.re= D[n].re/m.re+n/x;
an= c_sdiv(z1.re*psi1-psi0,c_sub(c_smul(z1.re,xi1),xi0));
z1.re= D[n].re*m.re+n/x;
bn= c_sdiv(z1.re*psi1-psi0,c_sub(c_smul(z1.re,xi1),xi0));
}else{
z1= c_div(D[n],m);
z1.re+= n/x;
an= c_div(c_set(z1.re*psi1-psi0,z1.im*psi1),c_sub(c_mul(z1,xi1),xi0));
z1= c_mul(D[n],m);
z1.re+= n/x;
bn= c_div(c_set(z1.re*psi1-psi0,z1.im*psi1),c_sub(c_mul(z1,xi1),xi0));
}
/*:43*/
#line 536 "./mie.w"
/*44:*/
#line 734 "./mie.w"
for(k= 0;k<nangles;k++){
factor= (2.0*n+1.0)/(n+1.0)/n;
tau[k]= n*mu[k]*pi1[k]-(n+1)*pi0[k];
alpha= factor*pi1[k];
beta= factor*tau[k];
s1[k].re+= alpha*an.re+beta*bn.re;
s1[k].im+= alpha*an.im+beta*bn.im;
s2[k].re+= alpha*bn.re+beta*an.re;
s2[k].im+= alpha*bn.im+beta*an.im;
}
for(k= 0;k<nangles;k++){
factor= pi1[k];
pi1[k]= ((2.0*n+1.0)*mu[k]*pi1[k]-(n+1.0)*pi0[k])/n;
pi0[k]= factor;
}
/*:44*/
#line 537 "./mie.w"
/*45:*/
#line 780 "./mie.w"
factor= 2.0*n+1.0;
*g+= (n-1.0/n)*(anm1.re*an.re+anm1.im*an.im+bnm1.re*bn.re+bnm1.im*bn.im);
*g+= factor/n/(n+1.0)*(an.re*bn.re+an.im*bn.im);
*qsca+= factor*(c_norm(an)+c_norm(bn));
*qext+= factor*(an.re+bn.re);
sign*= -1;
qbcalc.re+= sign*factor*(an.re-bn.re);
qbcalc.im+= sign*factor*(an.im-bn.im);
/*:45*/
#line 538 "./mie.w"
/*46:*/
#line 804 "./mie.w"
factor= (2.0*n+1.0)/x;
xi= c_sub(c_smul(factor,xi1),xi0);
xi0= xi1;
xi1= xi;
psi= factor*psi1-psi0;
psi0= psi1;
psi1= xi1.re;
anm1= an;
bnm1= bn;
/*:46*/
#line 539 "./mie.w"
}
/*47:*/
#line 817 "./mie.w"
*qsca*= 2/(x*x);
*qext*= 2/(x*x);
*g*= 4/(*qsca)/(x*x);
*qback= c_norm(qbcalc)/(x*x);
/*:47*/
#line 542 "./mie.w"
/*48:*/
#line 823 "./mie.w"
if(m.re> 0)free_carray(D);
if(nangles> 0){
free_darray(pi0);
free_darray(pi1);
free_darray(tau);
}
/*:48*/
#line 543 "./mie.w"
}
/* Return value: 0 - successful return
* > 0 - number of bytes allocated when run out of space
*/
int
ccolumn_bmod (
const int jcol, /* in */
const int nseg, /* in */
complex *dense, /* in */
complex *tempv, /* working array */
int *segrep, /* in */
int *repfnz, /* in */
int fpanelc, /* in -- first column in the current panel */
GlobalLU_t *Glu, /* modified */
SuperLUStat_t *stat /* output */
)
{
/*
* Purpose:
* ========
* Performs numeric block updates (sup-col) in topological order.
* It features: col-col, 2cols-col, 3cols-col, and sup-col updates.
* Special processing on the supernodal portion of L\U[*,j]
*
*/
#ifdef _CRAY
_fcd ftcs1 = _cptofcd("L", strlen("L")),
ftcs2 = _cptofcd("N", strlen("N")),
ftcs3 = _cptofcd("U", strlen("U"));
#endif
int incx = 1, incy = 1;
complex alpha, beta;
/* krep = representative of current k-th supernode
* fsupc = first supernodal column
* nsupc = no of columns in supernode
* nsupr = no of rows in supernode (used as leading dimension)
* luptr = location of supernodal LU-block in storage
* kfnz = first nonz in the k-th supernodal segment
* no_zeros = no of leading zeros in a supernodal U-segment
*/
complex ukj, ukj1, ukj2;
int luptr, luptr1, luptr2;
int fsupc, nsupc, nsupr, segsze;
int nrow; /* No of rows in the matrix of matrix-vector */
int jcolp1, jsupno, k, ksub, krep, krep_ind, ksupno;
register int lptr, kfnz, isub, irow, i;
register int no_zeros, new_next;
int ufirst, nextlu;
int fst_col; /* First column within small LU update */
int d_fsupc; /* Distance between the first column of the current
panel and the first column of the current snode. */
int *xsup, *supno;
int *lsub, *xlsub;
complex *lusup;
int *xlusup;
int nzlumax;
complex *tempv1;
complex zero = {0.0, 0.0};
complex one = {1.0, 0.0};
complex none = {-1.0, 0.0};
complex comp_temp, comp_temp1;
int mem_error;
flops_t *ops = stat->ops;
xsup = Glu->xsup;
supno = Glu->supno;
lsub = Glu->lsub;
xlsub = Glu->xlsub;
lusup = Glu->lusup;
xlusup = Glu->xlusup;
nzlumax = Glu->nzlumax;
jcolp1 = jcol + 1;
jsupno = supno[jcol];
/*
* For each nonz supernode segment of U[*,j] in topological order
*/
k = nseg - 1;
for (ksub = 0; ksub < nseg; ksub++) {
krep = segrep[k];
k--;
ksupno = supno[krep];
if ( jsupno != ksupno ) { /* Outside the rectangular supernode */
fsupc = xsup[ksupno];
fst_col = SUPERLU_MAX ( fsupc, fpanelc );
/* Distance from the current supernode to the current panel;
d_fsupc=0 if fsupc > fpanelc. */
d_fsupc = fst_col - fsupc;
luptr = xlusup[fst_col] + d_fsupc;
lptr = xlsub[fsupc] + d_fsupc;
kfnz = repfnz[krep];
kfnz = SUPERLU_MAX ( kfnz, fpanelc );
segsze = krep - kfnz + 1;
nsupc = krep - fst_col + 1;
nsupr = xlsub[fsupc+1] - xlsub[fsupc]; /* Leading dimension */
nrow = nsupr - d_fsupc - nsupc;
krep_ind = lptr + nsupc - 1;
/*
* Case 1: Update U-segment of size 1 -- col-col update
*/
if ( segsze == 1 ) {
ukj = dense[lsub[krep_ind]];
luptr += nsupr*(nsupc-1) + nsupc;
for (i = lptr + nsupc; i < xlsub[fsupc+1]; ++i) {
irow = lsub[i];
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
c_sub(&dense[irow], &dense[irow], &comp_temp);
luptr++;
}
} else if ( segsze <= 3 ) {
ukj = dense[lsub[krep_ind]];
luptr += nsupr*(nsupc-1) + nsupc-1;
ukj1 = dense[lsub[krep_ind - 1]];
luptr1 = luptr - nsupr;
if ( segsze == 2 ) { /* Case 2: 2cols-col update */
cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
c_sub(&ukj, &ukj, &comp_temp);
dense[lsub[krep_ind]] = ukj;
for (i = lptr + nsupc; i < xlsub[fsupc+1]; ++i) {
irow = lsub[i];
luptr++;
luptr1++;
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&dense[irow], &dense[irow], &comp_temp);
}
} else { /* Case 3: 3cols-col update */
ukj2 = dense[lsub[krep_ind - 2]];
luptr2 = luptr1 - nsupr;
cc_mult(&comp_temp, &ukj2, &lusup[luptr2-1]);
c_sub(&ukj1, &ukj1, &comp_temp);
cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&ukj, &ukj, &comp_temp);
dense[lsub[krep_ind]] = ukj;
dense[lsub[krep_ind-1]] = ukj1;
for (i = lptr + nsupc; i < xlsub[fsupc+1]; ++i) {
irow = lsub[i];
luptr++;
luptr1++;
luptr2++;
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&dense[irow], &dense[irow], &comp_temp);
}
}
} else {
/*
* Case: sup-col update
* Perform a triangular solve and block update,
* then scatter the result of sup-col update to dense
*/
no_zeros = kfnz - fst_col;
/* Copy U[*,j] segment from dense[*] to tempv[*] */
isub = lptr + no_zeros;
for (i = 0; i < segsze; i++) {
irow = lsub[isub];
tempv[i] = dense[irow];
++isub;
}
/* Dense triangular solve -- start effective triangle */
luptr += nsupr * no_zeros + no_zeros;
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
CTRSV( ftcs1, ftcs2, ftcs3, &segsze, &lusup[luptr],
&nsupr, tempv, &incx );
#else
ctrsv_( "L", "N", "U", &segsze, &lusup[luptr],
&nsupr, tempv, &incx );
#endif
luptr += segsze; /* Dense matrix-vector */
tempv1 = &tempv[segsze];
alpha = one;
beta = zero;
#ifdef _CRAY
CGEMV( ftcs2, &nrow, &segsze, &alpha, &lusup[luptr],
&nsupr, tempv, &incx, &beta, tempv1, &incy );
#else
cgemv_( "N", &nrow, &segsze, &alpha, &lusup[luptr],
&nsupr, tempv, &incx, &beta, tempv1, &incy );
#endif
#else
clsolve ( nsupr, segsze, &lusup[luptr], tempv );
luptr += segsze; /* Dense matrix-vector */
tempv1 = &tempv[segsze];
cmatvec (nsupr, nrow , segsze, &lusup[luptr], tempv, tempv1);
#endif
/* Scatter tempv[] into SPA dense[] as a temporary storage */
isub = lptr + no_zeros;
for (i = 0; i < segsze; i++) {
irow = lsub[isub];
dense[irow] = tempv[i];
tempv[i] = zero;
++isub;
}
/* Scatter tempv1[] into SPA dense[] */
for (i = 0; i < nrow; i++) {
irow = lsub[isub];
c_sub(&dense[irow], &dense[irow], &tempv1[i]);
tempv1[i] = zero;
++isub;
}
}
} /* if jsupno ... */
} /* for each segment... */
/*
* Process the supernodal portion of L\U[*,j]
*/
nextlu = xlusup[jcol];
fsupc = xsup[jsupno];
/* Copy the SPA dense into L\U[*,j] */
new_next = nextlu + xlsub[fsupc+1] - xlsub[fsupc];
while ( new_next > nzlumax ) {
if (mem_error = cLUMemXpand(jcol, nextlu, LUSUP, &nzlumax, Glu))
return (mem_error);
lusup = Glu->lusup;
lsub = Glu->lsub;
}
for (isub = xlsub[fsupc]; isub < xlsub[fsupc+1]; isub++) {
irow = lsub[isub];
lusup[nextlu] = dense[irow];
dense[irow] = zero;
++nextlu;
}
xlusup[jcolp1] = nextlu; /* Close L\U[*,jcol] */
/* For more updates within the panel (also within the current supernode),
* should start from the first column of the panel, or the first column
* of the supernode, whichever is bigger. There are 2 cases:
* 1) fsupc < fpanelc, then fst_col := fpanelc
* 2) fsupc >= fpanelc, then fst_col := fsupc
*/
fst_col = SUPERLU_MAX ( fsupc, fpanelc );
if ( fst_col < jcol ) {
/* Distance between the current supernode and the current panel.
d_fsupc=0 if fsupc >= fpanelc. */
d_fsupc = fst_col - fsupc;
lptr = xlsub[fsupc] + d_fsupc;
luptr = xlusup[fst_col] + d_fsupc;
nsupr = xlsub[fsupc+1] - xlsub[fsupc]; /* Leading dimension */
nsupc = jcol - fst_col; /* Excluding jcol */
nrow = nsupr - d_fsupc - nsupc;
/* Points to the beginning of jcol in snode L\U(jsupno) */
ufirst = xlusup[jcol] + d_fsupc;
ops[TRSV] += 4 * nsupc * (nsupc - 1);
ops[GEMV] += 8 * nrow * nsupc;
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
CTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &lusup[luptr],
&nsupr, &lusup[ufirst], &incx );
#else
ctrsv_( "L", "N", "U", &nsupc, &lusup[luptr],
&nsupr, &lusup[ufirst], &incx );
#endif
alpha = none; beta = one; /* y := beta*y + alpha*A*x */
#ifdef _CRAY
CGEMV( ftcs2, &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr,
&lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#else
cgemv_( "N", &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr,
&lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#endif
#else
clsolve ( nsupr, nsupc, &lusup[luptr], &lusup[ufirst] );
cmatvec ( nsupr, nrow, nsupc, &lusup[luptr+nsupc],
&lusup[ufirst], tempv );
/* Copy updates from tempv[*] into lusup[*] */
isub = ufirst + nsupc;
for (i = 0; i < nrow; i++) {
c_sub(&lusup[isub], &lusup[isub], &tempv[i]);
tempv[i] = zero;
++isub;
}
#endif
} /* if fst_col < jcol ... */
return 0;
}
void
cpanel_bmod (
const int m, /* in - number of rows in the matrix */
const int w, /* in */
const int jcol, /* in */
const int nseg, /* in */
complex *dense, /* out, of size n by w */
complex *tempv, /* working array */
int *segrep, /* in */
int *repfnz, /* in, of size n by w */
GlobalLU_t *Glu, /* modified */
SuperLUStat_t *stat /* output */
)
{
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
_fcd ftcs1 = _cptofcd("L", strlen("L")),
ftcs2 = _cptofcd("N", strlen("N")),
ftcs3 = _cptofcd("U", strlen("U"));
#endif
int incx = 1, incy = 1;
complex alpha, beta;
#endif
register int k, ksub;
int fsupc, nsupc, nsupr, nrow;
int krep, krep_ind;
complex ukj, ukj1, ukj2;
int luptr, luptr1, luptr2;
int segsze;
int block_nrow; /* no of rows in a block row */
register int lptr; /* Points to the row subscripts of a supernode */
int kfnz, irow, no_zeros;
register int isub, isub1, i;
register int jj; /* Index through each column in the panel */
int *xsup, *supno;
int *lsub, *xlsub;
complex *lusup;
int *xlusup;
int *repfnz_col; /* repfnz[] for a column in the panel */
complex *dense_col; /* dense[] for a column in the panel */
complex *tempv1; /* Used in 1-D update */
complex *TriTmp, *MatvecTmp; /* used in 2-D update */
complex zero = {0.0, 0.0};
complex one = {1.0, 0.0};
complex comp_temp, comp_temp1;
register int ldaTmp;
register int r_ind, r_hi;
static int first = 1, maxsuper, rowblk, colblk;
flops_t *ops = stat->ops;
xsup = Glu->xsup;
supno = Glu->supno;
lsub = Glu->lsub;
xlsub = Glu->xlsub;
lusup = Glu->lusup;
xlusup = Glu->xlusup;
if ( first ) {
maxsuper = SUPERLU_MAX( sp_ienv(3), sp_ienv(7) );
rowblk = sp_ienv(4);
colblk = sp_ienv(5);
first = 0;
}
ldaTmp = maxsuper + rowblk;
/*
* For each nonz supernode segment of U[*,j] in topological order
*/
k = nseg - 1;
for (ksub = 0; ksub < nseg; ksub++) { /* for each updating supernode */
/* krep = representative of current k-th supernode
* fsupc = first supernodal column
* nsupc = no of columns in a supernode
* nsupr = no of rows in a supernode
*/
krep = segrep[k--];
fsupc = xsup[supno[krep]];
nsupc = krep - fsupc + 1;
nsupr = xlsub[fsupc+1] - xlsub[fsupc];
nrow = nsupr - nsupc;
lptr = xlsub[fsupc];
krep_ind = lptr + nsupc - 1;
repfnz_col = repfnz;
dense_col = dense;
if ( nsupc >= colblk && nrow > rowblk ) { /* 2-D block update */
TriTmp = tempv;
/* Sequence through each column in panel -- triangular solves */
for (jj = jcol; jj < jcol + w; jj++,
repfnz_col += m, dense_col += m, TriTmp += ldaTmp ) {
kfnz = repfnz_col[krep];
if ( kfnz == EMPTY ) continue; /* Skip any zero segment */
segsze = krep - kfnz + 1;
luptr = xlusup[fsupc];
ops[TRSV] += 4 * segsze * (segsze - 1);
ops[GEMV] += 8 * nrow * segsze;
/* Case 1: Update U-segment of size 1 -- col-col update */
if ( segsze == 1 ) {
ukj = dense_col[lsub[krep_ind]];
luptr += nsupr*(nsupc-1) + nsupc;
for (i = lptr + nsupc; i < xlsub[fsupc+1]; i++) {
irow = lsub[i];
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
c_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
++luptr;
}
} else if ( segsze <= 3 ) {
ukj = dense_col[lsub[krep_ind]];
ukj1 = dense_col[lsub[krep_ind - 1]];
luptr += nsupr*(nsupc-1) + nsupc-1;
luptr1 = luptr - nsupr;
if ( segsze == 2 ) {
cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
c_sub(&ukj, &ukj, &comp_temp);
dense_col[lsub[krep_ind]] = ukj;
for (i = lptr + nsupc; i < xlsub[fsupc+1]; ++i) {
irow = lsub[i];
luptr++; luptr1++;
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
}
} else {
ukj2 = dense_col[lsub[krep_ind - 2]];
luptr2 = luptr1 - nsupr;
cc_mult(&comp_temp, &ukj2, &lusup[luptr2-1]);
c_sub(&ukj1, &ukj1, &comp_temp);
cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&ukj, &ukj, &comp_temp);
dense_col[lsub[krep_ind]] = ukj;
dense_col[lsub[krep_ind-1]] = ukj1;
for (i = lptr + nsupc; i < xlsub[fsupc+1]; ++i) {
irow = lsub[i];
luptr++; luptr1++; luptr2++;
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
}
}
} else { /* segsze >= 4 */
/* Copy U[*,j] segment from dense[*] to TriTmp[*], which
holds the result of triangular solves. */
no_zeros = kfnz - fsupc;
isub = lptr + no_zeros;
for (i = 0; i < segsze; ++i) {
irow = lsub[isub];
TriTmp[i] = dense_col[irow]; /* Gather */
++isub;
}
/* start effective triangle */
luptr += nsupr * no_zeros + no_zeros;
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
CTRSV( ftcs1, ftcs2, ftcs3, &segsze, &lusup[luptr],
&nsupr, TriTmp, &incx );
#else
ctrsv_( "L", "N", "U", &segsze, &lusup[luptr],
&nsupr, TriTmp, &incx );
#endif
#else
clsolve ( nsupr, segsze, &lusup[luptr], TriTmp );
#endif
} /* else ... */
} /* for jj ... end tri-solves */
/* Block row updates; push all the way into dense[*] block */
for ( r_ind = 0; r_ind < nrow; r_ind += rowblk ) {
r_hi = SUPERLU_MIN(nrow, r_ind + rowblk);
block_nrow = SUPERLU_MIN(rowblk, r_hi - r_ind);
luptr = xlusup[fsupc] + nsupc + r_ind;
isub1 = lptr + nsupc + r_ind;
repfnz_col = repfnz;
TriTmp = tempv;
dense_col = dense;
/* Sequence through each column in panel -- matrix-vector */
for (jj = jcol; jj < jcol + w; jj++,
repfnz_col += m, dense_col += m, TriTmp += ldaTmp) {
kfnz = repfnz_col[krep];
if ( kfnz == EMPTY ) continue; /* Skip any zero segment */
segsze = krep - kfnz + 1;
if ( segsze <= 3 ) continue; /* skip unrolled cases */
/* Perform a block update, and scatter the result of
matrix-vector to dense[]. */
no_zeros = kfnz - fsupc;
luptr1 = luptr + nsupr * no_zeros;
MatvecTmp = &TriTmp[maxsuper];
#ifdef USE_VENDOR_BLAS
alpha = one;
beta = zero;
#ifdef _CRAY
CGEMV(ftcs2, &block_nrow, &segsze, &alpha, &lusup[luptr1],
&nsupr, TriTmp, &incx, &beta, MatvecTmp, &incy);
#else
cgemv_("N", &block_nrow, &segsze, &alpha, &lusup[luptr1],
&nsupr, TriTmp, &incx, &beta, MatvecTmp, &incy);
#endif
#else
cmatvec(nsupr, block_nrow, segsze, &lusup[luptr1],
TriTmp, MatvecTmp);
#endif
/* Scatter MatvecTmp[*] into SPA dense[*] temporarily
* such that MatvecTmp[*] can be re-used for the
* the next blok row update. dense[] will be copied into
* global store after the whole panel has been finished.
*/
isub = isub1;
for (i = 0; i < block_nrow; i++) {
irow = lsub[isub];
c_sub(&dense_col[irow], &dense_col[irow],
&MatvecTmp[i]);
MatvecTmp[i] = zero;
++isub;
}
} /* for jj ... */
} /* for each block row ... */
/* Scatter the triangular solves into SPA dense[*] */
repfnz_col = repfnz;
TriTmp = tempv;
dense_col = dense;
for (jj = jcol; jj < jcol + w; jj++,
repfnz_col += m, dense_col += m, TriTmp += ldaTmp) {
kfnz = repfnz_col[krep];
if ( kfnz == EMPTY ) continue; /* Skip any zero segment */
segsze = krep - kfnz + 1;
if ( segsze <= 3 ) continue; /* skip unrolled cases */
no_zeros = kfnz - fsupc;
isub = lptr + no_zeros;
for (i = 0; i < segsze; i++) {
irow = lsub[isub];
dense_col[irow] = TriTmp[i];
TriTmp[i] = zero;
++isub;
}
} /* for jj ... */
} else { /* 1-D block modification */
/* Sequence through each column in the panel */
for (jj = jcol; jj < jcol + w; jj++,
repfnz_col += m, dense_col += m) {
kfnz = repfnz_col[krep];
if ( kfnz == EMPTY ) continue; /* Skip any zero segment */
segsze = krep - kfnz + 1;
luptr = xlusup[fsupc];
ops[TRSV] += 4 * segsze * (segsze - 1);
ops[GEMV] += 8 * nrow * segsze;
/* Case 1: Update U-segment of size 1 -- col-col update */
if ( segsze == 1 ) {
ukj = dense_col[lsub[krep_ind]];
luptr += nsupr*(nsupc-1) + nsupc;
for (i = lptr + nsupc; i < xlsub[fsupc+1]; i++) {
irow = lsub[i];
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
c_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
++luptr;
}
} else if ( segsze <= 3 ) {
ukj = dense_col[lsub[krep_ind]];
luptr += nsupr*(nsupc-1) + nsupc-1;
ukj1 = dense_col[lsub[krep_ind - 1]];
luptr1 = luptr - nsupr;
if ( segsze == 2 ) {
cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
c_sub(&ukj, &ukj, &comp_temp);
dense_col[lsub[krep_ind]] = ukj;
for (i = lptr + nsupc; i < xlsub[fsupc+1]; ++i) {
irow = lsub[i];
++luptr; ++luptr1;
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
}
} else {
ukj2 = dense_col[lsub[krep_ind - 2]];
luptr2 = luptr1 - nsupr;
cc_mult(&comp_temp, &ukj2, &lusup[luptr2-1]);
c_sub(&ukj1, &ukj1, &comp_temp);
cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&ukj, &ukj, &comp_temp);
dense_col[lsub[krep_ind]] = ukj;
dense_col[lsub[krep_ind-1]] = ukj1;
for (i = lptr + nsupc; i < xlsub[fsupc+1]; ++i) {
irow = lsub[i];
++luptr; ++luptr1; ++luptr2;
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
}
}
} else { /* segsze >= 4 */
/*
* Perform a triangular solve and block update,
* then scatter the result of sup-col update to dense[].
*/
no_zeros = kfnz - fsupc;
/* Copy U[*,j] segment from dense[*] to tempv[*]:
* The result of triangular solve is in tempv[*];
* The result of matrix vector update is in dense_col[*]
*/
isub = lptr + no_zeros;
for (i = 0; i < segsze; ++i) {
irow = lsub[isub];
tempv[i] = dense_col[irow]; /* Gather */
++isub;
}
/* start effective triangle */
luptr += nsupr * no_zeros + no_zeros;
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
CTRSV( ftcs1, ftcs2, ftcs3, &segsze, &lusup[luptr],
&nsupr, tempv, &incx );
#else
ctrsv_( "L", "N", "U", &segsze, &lusup[luptr],
&nsupr, tempv, &incx );
#endif
luptr += segsze; /* Dense matrix-vector */
tempv1 = &tempv[segsze];
alpha = one;
beta = zero;
#ifdef _CRAY
CGEMV( ftcs2, &nrow, &segsze, &alpha, &lusup[luptr],
&nsupr, tempv, &incx, &beta, tempv1, &incy );
#else
cgemv_( "N", &nrow, &segsze, &alpha, &lusup[luptr],
&nsupr, tempv, &incx, &beta, tempv1, &incy );
#endif
#else
clsolve ( nsupr, segsze, &lusup[luptr], tempv );
luptr += segsze; /* Dense matrix-vector */
tempv1 = &tempv[segsze];
cmatvec (nsupr, nrow, segsze, &lusup[luptr], tempv, tempv1);
#endif
/* Scatter tempv[*] into SPA dense[*] temporarily, such
* that tempv[*] can be used for the triangular solve of
* the next column of the panel. They will be copied into
* ucol[*] after the whole panel has been finished.
*/
isub = lptr + no_zeros;
for (i = 0; i < segsze; i++) {
irow = lsub[isub];
dense_col[irow] = tempv[i];
tempv[i] = zero;
isub++;
}
/* Scatter the update from tempv1[*] into SPA dense[*] */
/* Start dense rectangular L */
for (i = 0; i < nrow; i++) {
irow = lsub[isub];
c_sub(&dense_col[irow], &dense_col[irow], &tempv1[i]);
tempv1[i] = zero;
++isub;
}
} /* else segsze>=4 ... */
} /* for each column in the panel... */
} /* else 1-D update ... */
} /* for each updating supernode ... */
}
int cgst01(int m, int n, SuperMatrix *A, SuperMatrix *L,
SuperMatrix *U, int *perm_c, int *perm_r, float *resid)
{
/*
Purpose
=======
CGST01 reconstructs a matrix A from its L*U factorization and
computes the residual
norm(L*U - A) / ( N * norm(A) * EPS ),
where EPS is the machine epsilon.
Arguments
==========
M (input) INT
The number of rows of the matrix A. M >= 0.
N (input) INT
The number of columns of the matrix A. N >= 0.
A (input) SuperMatrix *, dimension (A->nrow, A->ncol)
The original M x N matrix A.
L (input) SuperMatrix *, dimension (L->nrow, L->ncol)
The factor matrix L.
U (input) SuperMatrix *, dimension (U->nrow, U->ncol)
The factor matrix U.
perm_c (input) INT array, dimension (N)
The column permutation from CGSTRF.
perm_r (input) INT array, dimension (M)
The pivot indices from CGSTRF.
RESID (output) FLOAT*
norm(L*U - A) / ( N * norm(A) * EPS )
=====================================================================
*/
/* Local variables */
complex zero = {0.0, 0.0};
int i, j, k, arow, lptr,isub, urow, superno, fsupc, u_part;
complex utemp, comp_temp;
float anorm, tnorm, cnorm;
float eps;
complex *work;
SCformat *Lstore;
NCformat *Astore, *Ustore;
complex *Aval, *Lval, *Uval;
int *colbeg, *colend;
/* Function prototypes */
extern float clangs(char *, SuperMatrix *);
/* Quick exit if M = 0 or N = 0. */
if (m <= 0 || n <= 0) {
*resid = 0.f;
return 0;
}
work = (complex *)complexCalloc(m);
Astore = A->Store;
Aval = Astore->nzval;
Lstore = L->Store;
Lval = Lstore->nzval;
Ustore = U->Store;
Uval = Ustore->nzval;
colbeg = intMalloc(n);
colend = intMalloc(n);
for (i = 0; i < n; i++) {
colbeg[perm_c[i]] = Astore->colptr[i];
colend[perm_c[i]] = Astore->colptr[i+1];
}
/* Determine EPS and the norm of A. */
eps = smach("Epsilon");
anorm = clangs("1", A);
cnorm = 0.;
/* Compute the product L*U, one column at a time */
for (k = 0; k < n; ++k) {
/* The U part outside the rectangular supernode */
for (i = U_NZ_START(k); i < U_NZ_START(k+1); ++i) {
urow = U_SUB(i);
utemp = Uval[i];
superno = Lstore->col_to_sup[urow];
fsupc = L_FST_SUPC(superno);
u_part = urow - fsupc + 1;
lptr = L_SUB_START(fsupc) + u_part;
work[L_SUB(lptr-1)].r -= utemp.r;
work[L_SUB(lptr-1)].i -= utemp.i;
for (j = L_NZ_START(urow) + u_part; j < L_NZ_START(urow+1); ++j) {
isub = L_SUB(lptr);
cc_mult(&comp_temp, &utemp, &Lval[j]);
c_sub(&work[isub], &work[isub], &comp_temp);
++lptr;
}
}
/* The U part inside the rectangular supernode */
superno = Lstore->col_to_sup[k];
fsupc = L_FST_SUPC(superno);
urow = L_NZ_START(k);
for (i = fsupc; i <= k; ++i) {
utemp = Lval[urow++];
u_part = i - fsupc + 1;
lptr = L_SUB_START(fsupc) + u_part;
work[L_SUB(lptr-1)].r -= utemp.r;
work[L_SUB(lptr-1)].i -= utemp.i;
for (j = L_NZ_START(i)+u_part; j < L_NZ_START(i+1); ++j) {
isub = L_SUB(lptr);
cc_mult(&comp_temp, &utemp, &Lval[j]);
c_sub(&work[isub], &work[isub], &comp_temp);
++lptr;
}
}
/* Now compute A[k] - (L*U)[k] (Both matrices may be permuted.) */
for (i = colbeg[k]; i < colend[k]; ++i) {
arow = Astore->rowind[i];
work[perm_r[arow]].r += Aval[i].r;
work[perm_r[arow]].i += Aval[i].i;
}
/* Now compute the 1-norm of the column vector work */
tnorm = 0.;
for (i = 0; i < m; ++i) {
tnorm += fabs(work[i].r) + fabs(work[i].i);
work[i] = zero;
}
cnorm = SUPERLU_MAX(tnorm, cnorm);
}
*resid = cnorm;
if (anorm <= 0.f) {
if (*resid != 0.f) {
*resid = 1.f / eps;
}
} else {
*resid = *resid / (float) n / anorm / eps;
}
SUPERLU_FREE(work);
SUPERLU_FREE(colbeg);
SUPERLU_FREE(colend);
return 0;
/* End of CGST01 */
} /* cgst01_ */
void
pcgstrf_bmod1D(
const int pnum, /* process number */
const int m, /* number of rows in the matrix */
const int w, /* current panel width */
const int jcol, /* leading column of the current panel */
const int fsupc, /* leading column of the updating supernode */
const int krep, /* last column of the updating supernode */
const int nsupc, /* number of columns in the updating s-node */
int nsupr, /* number of rows in the updating supernode */
int nrow, /* number of rows below the diagonal block of
the updating supernode */
int *repfnz, /* in */
int *panel_lsub, /* modified */
int *w_lsub_end, /* modified */
int *spa_marker, /* modified; size n-by-w */
complex *dense, /* modified */
complex *tempv, /* working array - zeros on entry/exit */
GlobalLU_t *Glu, /* modified */
Gstat_t *Gstat /* modified */
)
{
/*
* -- SuperLU MT routine (version 2.0) --
* Lawrence Berkeley National Lab, Univ. of California Berkeley,
* and Xerox Palo Alto Research Center.
* September 10, 2007
*
* Purpose
* =======
*
* Performs numeric block updates (sup-panel) in topological order.
* It features: col-col, 2cols-col, 3cols-col, and sup-col updates.
* Results are returned in SPA dense[*,w].
*
*/
#if ( MACH==CRAY_PVP )
_fcd ftcs1 = _cptofcd("L", strlen("L")),
ftcs2 = _cptofcd("N", strlen("N")),
ftcs3 = _cptofcd("U", strlen("U"));
#endif
#ifdef USE_VENDOR_BLAS
int incx = 1, incy = 1;
complex alpha, beta;
#endif
complex ukj, ukj1, ukj2;
int luptr, luptr1, luptr2;
int segsze;
register int lptr; /* start of row subscripts of the updating supernode */
register int i, krep_ind, kfnz, isub, irow, no_zeros;
register int jj; /* index through each column in the panel */
int *repfnz_col; /* repfnz[] for a column in the panel */
complex *dense_col; /* dense[] for a column in the panel */
complex *tempv1; /* used to store matrix-vector result */
int *col_marker; /* each column of the spa_marker[*,w] */
int *col_lsub; /* each column of the panel_lsub[*,w] */
int *lsub, *xlsub_end;
complex *lusup;
int *xlusup;
register float flopcnt;
complex zero = {0.0, 0.0};
complex one = {1.0, 0.0};
complex comp_temp, comp_temp1;
#ifdef TIMING
double *utime = Gstat->utime;
double f_time;
#endif
lsub = Glu->lsub;
xlsub_end = Glu->xlsub_end;
lusup = Glu->lusup;
xlusup = Glu->xlusup;
lptr = Glu->xlsub[fsupc];
krep_ind = lptr + nsupc - 1;
/* Pointers to each column of the w-wide arrays. */
repfnz_col= repfnz;
dense_col = dense;
col_marker= spa_marker;
col_lsub = panel_lsub;
#if ( DEBUGlevel>=2 )
if (jcol == BADPAN && krep == BADREP) {
printf("(%d) pcgstrf_bmod1D[1] jcol %d, fsupc %d, krep %d, nsupc %d, nsupr %d, nrow %d\n",
pnum, jcol, fsupc, krep, nsupc, nsupr, nrow);
PrintInt10("lsub[xlsub[2774]]", nsupr, &lsub[lptr]);
}
#endif
/*
* Sequence through each column in the panel ...
*/
for (jj = jcol; jj < jcol + w; ++jj, col_marker += m, col_lsub += m,
repfnz_col += m, dense_col += m) {
kfnz = repfnz_col[krep];
if ( kfnz == EMPTY ) continue; /* Skip any zero segment */
segsze = krep - kfnz + 1;
luptr = xlusup[fsupc];
/* Calculate flops: tri-solve + mat-vector */
Gstat->procstat[pnum].fcops += flopcnt;
/* Case 1: Update U-segment of size 1 -- col-col update */
if ( segsze == 1 ) {
#ifdef TIMING
f_time = SuperLU_timer_();
#endif
ukj = dense_col[lsub[krep_ind]];
luptr += nsupr*(nsupc-1) + nsupc;
#if ( DEBUGlevel>=2 )
if (krep == BADCOL && jj == -1) {
printf("(%d) pcgstrf_bmod1D[segsze=1]: k %d, j %d, ukj %.10e\n",
pnum, lsub[krep_ind], jj, ukj);
PrintInt10("segsze=1", nsupr, &lsub[lptr]);
}
#endif
for (i = lptr + nsupc; i < xlsub_end[fsupc]; i++) {
irow = lsub[i];
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
c_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
++luptr;
#ifdef SCATTER_FOUND
if ( col_marker[irow] != jj ) {
col_marker[irow] = jj;
col_lsub[w_lsub_end[jj-jcol]++] = irow;
}
#endif
}
#ifdef TIMING
utime[FLOAT] += SuperLU_timer_() - f_time;
#endif
} else if ( segsze <= 3 ) {
#ifdef TIMING
f_time = SuperLU_timer_();
#endif
ukj = dense_col[lsub[krep_ind]];
luptr += nsupr*(nsupc-1) + nsupc-1;
ukj1 = dense_col[lsub[krep_ind - 1]];
luptr1 = luptr - nsupr;
if ( segsze == 2 ) {
cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
c_sub(&ukj, &ukj, &comp_temp);
dense_col[lsub[krep_ind]] = ukj;
for (i = lptr + nsupc; i < xlsub_end[fsupc]; ++i) {
irow = lsub[i];
++luptr; ++luptr1;
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
#ifdef SCATTER_FOUND
if ( col_marker[irow] != jj ) {
col_marker[irow] = jj;
col_lsub[w_lsub_end[jj-jcol]++] = irow;
}
#endif
}
} else {
ukj2 = dense_col[lsub[krep_ind - 2]];
luptr2 = luptr1 - nsupr;
cc_mult(&comp_temp, &ukj2, &lusup[luptr2-1]);
c_sub(&ukj1, &ukj1, &comp_temp);
cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&ukj, &ukj, &comp_temp);
dense_col[lsub[krep_ind]] = ukj;
dense_col[lsub[krep_ind-1]] = ukj1;
for (i = lptr + nsupc; i < xlsub_end[fsupc]; ++i) {
irow = lsub[i];
++luptr; ++luptr1; ++luptr2;
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
#ifdef SCATTER_FOUND
if ( col_marker[irow] != jj ) {
col_marker[irow] = jj;
col_lsub[w_lsub_end[jj-jcol]++] = irow;
}
#endif
}
}
#ifdef TIMING
utime[FLOAT] += SuperLU_timer_() - f_time;
#endif
} else { /* segsze >= 4 */
/*
* Perform a triangular solve and matrix-vector update,
* then scatter the result of sup-col update to dense[*].
*/
no_zeros = kfnz - fsupc;
/* Gather U[*,j] segment from dense[*] to tempv[*]:
* The result of triangular solve is in tempv[*];
* The result of matrix vector update is in dense_col[*]
*/
isub = lptr + no_zeros;
/*#pragma ivdep*/
for (i = 0; i < segsze; ++i) {
irow = lsub[isub];
tempv[i] = dense_col[irow]; /* Gather */
++isub;
}
/* start effective triangle */
luptr += nsupr * no_zeros + no_zeros;
#ifdef TIMING
f_time = SuperLU_timer_();
#endif
#ifdef USE_VENDOR_BLAS
#if ( MACH==CRAY_PVP )
CTRSV( ftcs1, ftcs2, ftcs3, &segsze, &lusup[luptr],
&nsupr, tempv, &incx );
#else
ctrsv_( "L", "N", "U", &segsze, &lusup[luptr],
&nsupr, tempv, &incx );
#endif
luptr += segsze; /* Dense matrix-vector */
tempv1 = &tempv[segsze];
alpha = one;
beta = zero;
#if ( MACH==CRAY_PVP )
CGEMV( ftcs2, &nrow, &segsze, &alpha, &lusup[luptr],
&nsupr, tempv, &incx, &beta, tempv1, &incy );
#else
cgemv_( "N", &nrow, &segsze, &alpha, &lusup[luptr],
&nsupr, tempv, &incx, &beta, tempv1, &incy );
#endif /* _CRAY_PVP */
#else
clsolve ( nsupr, segsze, &lusup[luptr], tempv );
luptr += segsze; /* Dense matrix-vector */
tempv1 = &tempv[segsze];
cmatvec (nsupr, nrow, segsze, &lusup[luptr], tempv, tempv1);
#endif
#ifdef TIMING
utime[FLOAT] += SuperLU_timer_() - f_time;
#endif
/* Scatter tempv[*] into SPA dense[*] temporarily,
* such that tempv[*] can be used for the triangular solve of
* the next column of the panel. They will be copied into
* ucol[*] after the whole panel has been finished.
*/
isub = lptr + no_zeros;
/*#pragma ivdep*/
for (i = 0; i < segsze; i++) {
irow = lsub[isub];
dense_col[irow] = tempv[i]; /* Scatter */
tempv[i] = zero;
isub++;
#if ( DEBUGlevel>=2 )
if (jj == -1 && krep == 3423)
printf("(%d) pcgstrf_bmod1D[scatter] jj %d, dense_col[%d] %e\n",
pnum, jj, irow, dense_col[irow]);
#endif
}
/* Scatter the update from tempv1[*] into SPA dense[*] */
/*#pragma ivdep*/
for (i = 0; i < nrow; i++) {
irow = lsub[isub];
c_sub(&dense_col[irow], &dense_col[irow],
&tempv1[i]); /* Scatter-add */
#ifdef SCATTER_FOUND
if ( col_marker[irow] != jj ) {
col_marker[irow] = jj;
col_lsub[w_lsub_end[jj-jcol]++] = irow;
}
#endif
tempv1[i] = zero;
isub++;
}
} /* else segsze >= 4 ... */
} /* for jj ... */
}
static int polroot(
struct polynom *p,
struct complex *pz, /* pointer to root */
struct complex *pz0 /* pointer to initial value */
)
{
int i;
int n_iter;
struct polynom d;
struct complex v,v0,vd,delta,zmin;
double y,ymin;
// extern struct polynom *pol_der();
// extern struct complex *pol_value();
delta.x=0; delta.y=0; // RS 7.2.2013
//printf("\np->n=%d",p->n); getch();
if (p->n==1)
{
c_div(pz,&(p->a[0]),&(p->a[1]));
pz->x=-(pz->x); pz->y=-(pz->y);
return(1);
}
//printf("\nr2");
pol_value(p,pz0,&v0);
//printf("\nr3");
if (c_zero(&v0))
{
pz->x=pz0->x;
pz->y=pz0->y;
return(1);
}
//printf("\nr4");
zmin.x=pz0->x; zmin.y=pz0->y;
ymin=v0.x*v0.x+v0.y*v0.y;
pol_der(&d,p);
//printf("\nr5");
n_iter=0;
while (1)
{
pol_value(&d,pz0,&vd);
c_div(&delta,&v0,&vd);
c_sub(pz,pz0,&delta);
pol_value(p,pz,&v);
v0.x=v.x; v0.y=v.y;
pz0->x=pz->x; pz0->y=pz->y;
++n_iter;
PR_UP;
sprintf(sbuf,"\npolroot: N=%d Re=%e Im=%e",n_iter,pz->x,pz->y); sur_print(sbuf); // RS CHA Rprintf
/* Rprintf("zero: %d\n",c_zero(pz)); getch(); */
/* if (c_zero(&pz)) break; */
if (c_zero(pz)) break;
y=v.x*v.x+v.y*v.y;
if (y<ymin)
{ ymin=y; zmin.x=pz->x; zmin.y=pz->y; }
if (fabs(delta.x)<roots_eps && fabs(delta.y)<roots_eps) break;
if (n_iter>roots_max_iter)
{
pz->x=zmin.x; pz->y=zmin.y;
break;
}
if (sur_kbhit())
{
pz->x=zmin.x; pz->y=zmin.y;
i=sur_getch(); if (i=='.') break;
}
}
return (n_iter);
}
int
pcgstrf_snode_bmod(
const int pnum, /* process number */
const int jcol, /* in - current column in the s-node */
const int jsupno, /* in */
const int fsupc, /* in - first column in the s-node */
complex *dense, /* in */
complex *tempv, /* working array */
GlobalLU_t *Glu, /* modified */
Gstat_t *Gstat /* modified */
)
{
/*
* -- SuperLU MT routine (version 2.0) --
* Lawrence Berkeley National Lab, Univ. of California Berkeley,
* and Xerox Palo Alto Research Center.
* September 10, 2007
*
* Performs numeric block updates within the relaxed supernode.
*/
complex zero = {0.0, 0.0};
complex one = {1.0, 0.0};
complex none = {-1.0, 0.0};
#if ( MACH==CRAY_PVP )
_fcd ftcs1, ftcs2, ftcs3;
#endif
#ifdef USE_VENDOR_BLAS
int incx = 1, incy = 1;
complex alpha = none, beta = one;
#endif
int luptr, nsupc, nsupr, nrow;
int isub, irow, i, iptr;
register int ufirst, nextlu;
complex *lusup;
int *lsub, *xlsub, *xlsub_end, *xlusup, *xlusup_end;
register float flopcnt;
lsub = Glu->lsub;
xlsub = Glu->xlsub;
xlsub_end = Glu->xlsub_end;
lusup = Glu->lusup;
xlusup = Glu->xlusup;
xlusup_end = Glu->xlusup_end;
nextlu = xlusup[jcol];
/*
* Process the supernodal portion of L\U[*,j]
*/
for (isub = xlsub[fsupc]; isub < xlsub_end[fsupc]; isub++) {
irow = lsub[isub];
lusup[nextlu] = dense[irow];
dense[irow] = zero;
++nextlu;
}
xlusup_end[jcol] = nextlu;
if ( fsupc < jcol ) {
luptr = xlusup[fsupc];
nsupr = xlsub_end[fsupc] - xlsub[fsupc];
nsupc = jcol - fsupc; /* Excluding jcol */
ufirst = xlusup[jcol]; /* Points to the beginning of column
jcol in supernode L\U(jsupno). */
nrow = nsupr - nsupc;
flopcnt = nsupc * (nsupc - 1) + 2 * nrow * nsupc; //sj
Gstat->procstat[pnum].fcops += flopcnt;
/* ops[TRSV] += nsupc * (nsupc - 1);
ops[GEMV] += 2 * nrow * nsupc; */
#ifdef USE_VENDOR_BLAS
#if ( MACH==CRAY_PVP )
ftcs1 = _cptofcd("L", strlen("L"));
ftcs2 = _cptofcd("N", strlen("N"));
ftcs3 = _cptofcd("U", strlen("U"));
CTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &lusup[luptr], &nsupr,
&lusup[ufirst], &incx );
CGEMV( ftcs2, &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr,
&lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#else
ctrsv_( "L", "N", "U", &nsupc, &lusup[luptr], &nsupr,
&lusup[ufirst], &incx );
cgemv_( "N", &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr,
&lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#endif
#else
clsolve ( nsupr, nsupc, &lusup[luptr], &lusup[ufirst] );
cmatvec ( nsupr, nrow, nsupc, &lusup[luptr+nsupc],
&lusup[ufirst], &tempv[0] );
/* Scatter tempv[*] into lusup[*] */
iptr = ufirst + nsupc;
for (i = 0; i < nrow; i++) {
c_sub(&lusup[iptr], &lusup[iptr], &tempv[i]);
++iptr;
tempv[i] = zero;
}
#endif
}
return 0;
}
void simulation_solve(simulation_t *simulation)
{
int m,s;
int i,j,k, i_max, x;
m = simulation->n_vars;
int n = m+1;
s = simulation_context_get_n_samples(simulation->nodelist->netlist->sc);
for ( k = 0 ; k < m ; ++k )
{
//pivot is col k
//find a line with the maximum k
i_max = simulation_max(simulation, k,m);
if ( cell_is_zero(simulation, &simulation->cells[i_max][k]) )
{
fprintf(stderr,"singular matrix, zero found @ row %d col %d (mean = %.1f)\n", i_max, k,
(double)cell_mean(simulation,&simulation->cells[i_max][k]));
simulation_dump(simulation);
assert(0);
}
assert(i_max >= k);
if ( i_max != k )
{
cell_t *tmp;
tmp = simulation->cells[k];
simulation->cells[k] = simulation->cells[i_max];
simulation->cells[i_max] = tmp;
}
for ( i = k + 1 ; i < m ; i ++ )
{
if ( simulation->cells[i][k].state == CELL_ZERO )
{
//fprintf(stderr,"continue\n");
continue;
}
assert( i != k);
#ifdef USE_OMP
#pragma omp parallel for
#endif
for ( j = n - 1 ; j > k ; --j )
{
// Fij = Fij - Fkj * Fik/Fkk
assert( j != k );
cell_t *line_i = simulation->cells[i];
cell_t *line_k = simulation->cells[k];
line_i[j].state = CELL_SET;
for ( x = 0 ; x < s ; ++x )
{
//assert( line_k[k].state != CELL_ZERO && !cell_is_zero(simulation,&line_k[k]));
line_i[j].values[x] = c_let(
c_sub(line_i[j].values[x],
c_mul(line_k[j].values[x],
c_div( line_i[k].values[x], line_k[k].values[x] ))));
/*
line_i[j].values[x] =
line_i[j].values[x] - line_k[j].values[x]
* ( line_i[k].values[x] / line_k[k].values[x] );
*/
/*
assert( i != k );
line_i[j].values[x] =
line_i[j].values[x] * line_k[k].values[x]
- line_k[j].values[x] * line_i[k].values[x];
*/
}
}
simulation->cells[i][k].state = CELL_ZERO;
#ifdef USE_OMP
#pragma omp parallel for
#endif
for ( x = 0 ; x < s ; ++x )
{
simulation->cells[i][k].values[x]=0.L;
}
}
}
//simulation_dump(simulation);
//backward elimination
//simulation_dump(simulation);
if (1)
for ( k = m - 1 ; k >= 0 ; --k )
{
//set pivot to 1
// Lk = Lk / Fk,k
#ifdef USE_OMP
#pragma omp parallel for
#endif
for ( j = k+1 ; j < n ; ++j )
{
assert( j != k );
simulation->cells[k][j].state = CELL_SET;
for ( x = 0 ; x < s ; ++x )
{
//assert( simulation->cells[k][k].state != CELL_ZERO && !cell_is_zero(simulation, &simulation->cells[k][k]));
simulation->cells[k][j].values[x] =
c_let(
c_div(simulation->cells[k][j].values[x], simulation->cells[k][k].values[x] ));
/*
simulation->cells[k][j].values[x] =
simulation->cells[k][j].values[x] / simulation->cells[k][k].values[x];
*/
}
}
simulation->cells[k][k].state = CELL_POSITIVE_UNITY;
#ifdef USE_OMP
#pragma omp parallel for
#endif
for ( x = 0 ; x < s ; ++x )
{
simulation->cells[k][k].values[x] = 1.L + I * 0.L;
}
}
//zeroes pivot col
for ( k = m - 1 ; k >= 0 ; --k ) // vertical pivot Fk,k
{
assert( simulation->cells[k][k].state == CELL_POSITIVE_UNITY );
// Li = Li - Lk * Fik
#ifdef USE_OMP
#pragma omp parallel for
#endif
for ( i = 0 ; i < k ; ++i) // vertical
{
assert( i != k );
for ( j = k + 1 ; j < m ; ++ j )
assert( simulation->cells[i][j].state == CELL_ZERO );
// => Fir = Fir - Fik x Fkr
// => Fi,k = 0
int result_col = n - 1;
simulation->cells[i][result_col].state = CELL_SET;
for ( x = 0 ; x < s ; ++x )
{
simulation->cells[i][result_col].values[x] = c_let(
c_sub(simulation->cells[i][result_col].values[x],
c_mul(simulation->cells[i][k].values[x], simulation->cells[k][result_col].values[x])));
/*
simulation->cells[i][j].values[x] =
simulation->cells[i][j].values[x]
- simulation->cells[i][k].values[x] * simulation->cells[k][j].values[x];
*/
}
simulation->cells[i][k].state = CELL_ZERO;
for ( x = 0 ; x < s ; ++x )
{
simulation->cells[i][k].values[x] = 0.L;
}
}
}
//sanity check
assert( m == simulation->n_vars );
assert( n == simulation->n_vars+1 );
for ( i = 0 ; i < m ; ++ i )
for ( j = 0 ; j < m ; ++ j )
if ( i==j )
assert(simulation->cells[i][j].state == CELL_POSITIVE_UNITY );
else
assert(simulation->cells[i][j].state == CELL_ZERO );
}
void schurFactorization(long n, complex **A, complex **T, complex **U)
{
/* Schur factorization: A = U*T*U', T = upper triangular, U = unitary */
long i,j,iter,maxIter;
double tol, diff1,diff2;
complex T11, T12, T21, T22;
complex sigma1, sigma2, sigma;
complex z, z1, z2;
complex **P, **Q, **R;
/* Allocate auxiliary matrices */
P = (complex **)Mem(MEM_ALLOC,n, sizeof(complex *));
Q = (complex **)Mem(MEM_ALLOC,n, sizeof(complex *));
R = (complex **)Mem(MEM_ALLOC,n, sizeof(complex *));
for (i=0; i<n; i++){
P[i] = (complex *)Mem(MEM_ALLOC,n, sizeof(complex));
Q[i] = (complex *)Mem(MEM_ALLOC,n, sizeof(complex));
R[i] = (complex *)Mem(MEM_ALLOC,n, sizeof(complex));
}
/* ------------------------------------------------------------*/
/* Parameters for iteration */
maxIter = 500;
tol = 1E-30;
/* ------------------------------------------------------------*/
/* Init U = eye(n) (identity matrix) */
for (i=0; i<n; i++){
U[i][i].re = 1.0;
U[i][i].im = 0.0;
}
/* ------------------------------------------------------------*/
/* Reduce A to Hessenberg form */
hessFactorization(n,A,P,T);
/* ------------------------------------------------------------*/
/* Compute Schur factorization of Hessenberg matrix T */
for (j=n-1; j>0; j--){ /* Main loop */
for (iter=0; iter<maxIter; iter++){ /* Iteration loop */
sigma.re = T[j][j].re;
sigma.im = T[j][j].im;
/* -- Use Wilkinson shift -- */
/* submatrix considered in the shift */
T11 = T[j-1][j-1];
T12 = T[j-1][j];
T21 = T[j][j-1];
T22 = T[j][j];
/* Compute eigenvalues of submatrix */
z.re = 0.0;
z.im = 0.0;
z2.re = 0.0;
z2.im = 0.0;
/* z = T11*T11 + T22*T22 - 2*T11*T22 + 4*T12*T21 */
z1 = c_mul(T11,T11);
z = c_add(z ,z1);
z2 = c_add(z2,z1);
z1 = c_mul(T22,T22);
z = c_add(z ,z1);
z2 = c_add(z2,z1);
z1 = c_mul(T11,T22);
z1.re = -2.0 * z1.re;
z1.im = -2.0 * z1.im;
z = c_add(z,z1);
z1 = c_mul(T12,T21);
z1.re = 4.0 * z1.re;
z1.im = 4.0 * z1.im;
z = c_add(z,z1);
/* Square root*/
z = c_sqrt(z);
/* Eigenvalues */
sigma1 = c_add(z2,z);
sigma2 = c_sub(z2,z);
/* printf("sigma1 = %e %e\n", sigma1.re, sigma1.im); */
/* printf("sigma2 = %e %e\n", sigma2.re, sigma2.im); */
/* Select eigenvalue for shift*/
diff1 = c_norm( c_sub(T[j][j], sigma1) );
diff2 = c_norm( c_sub(T[j][j], sigma2) );
if (diff1 < diff2){
sigma.re = sigma1.re;
sigma.im = sigma1.im;
}else{
sigma.re = sigma2.re;
sigma.im = sigma2.im;
}
/* --- QR step with Wilkinson shift --- */
/* Shift: T(1:j,1:j) = T(1:j,1:j) - sigma * eye(j) */
for (i=0; i<j+1; i++){
CheckValue(FUNCTION_NAME, "T[i][i].re","", T[i][i].re, -INFTY, INFTY);
CheckValue(FUNCTION_NAME, "T[i][i].im","", T[i][i].im, -INFTY, INFTY);
T[i][i].re = T[i][i].re - sigma.re;
T[i][i].im = T[i][i].im - sigma.im;
}
/* Compute QR factorization of shifted Hessenberg matrix */
for (i=0; i<n; i++){
memset(Q[i], 0, n*sizeof(complex));
memset(R[i], 0, n*sizeof(complex));
}
QRfactorization(n,T,Q,R);
/* T = T_new = R * Q */
for (i=0; i<n; i++){
memset(T[i], 0, n*sizeof(complex));
}
matProduct(n, n, n, R, Q, T);
/* T(1:j,1:j) = T(1:j,1:j) + sigma * eye(j) */
for (i=0; i<j+1; i++){
T[i][i].re = T[i][i].re + sigma.re;
T[i][i].im = T[i][i].im + sigma.im;
}
/* R = U_new = U * Q */
for (i=0; i<n; i++){
memset(R[i], 0, n*sizeof(complex));
}
matProduct(n,n,n,U,Q,R);
/* U = R */
for (i=0; i<n; i++){
memcpy(U[i],R[i], n*sizeof(complex));
}
/* Check convergence */
if (c_norm( T[j][j-1] ) <= tol * (c_norm(T[j-1][j-1]) + c_norm(T[j][j]))){
T[j][j-1].re = 0.0;
T[j][j-1].im = 0.0;
break;
}
} /* end of iter loop */
} /* end of main loop */
/* -------------------------------------------------------------*/
/* U = P*U */
for (i=0; i<n; i++){
memset(U[i], 0, n*sizeof(complex));
}
matProduct(n,n,n,P,R,U);
/* -------------------------------------------------------------*/
/* Free auxiliary variables */
for (i=0; i<n; i++){
Mem(MEM_FREE,P[i]);
Mem(MEM_FREE,Q[i]);
Mem(MEM_FREE,R[i]);
}
Mem(MEM_FREE,P);
Mem(MEM_FREE,Q);
Mem(MEM_FREE,R);
/* Return */
return;
}
int main()
{
//initialize testing array
float testVector[] = {0.1f,0.2f,0.3f,0.4f,0.5f};
/*COMMENTED OUT LENGTH PARAM AS IT IS INCLUDED IN HEADER FILE*/
//get the size of the array
//int length = sizeof(testVector)/sizeof(float);
//initiate empty output array of size length
float outputArrayC[length];
//initialize the struct at p=r=q 0.1 and x=k=0
kalman_state currentState = {0.1f, 0.1f, 0.0f , 0.1f, 0.0f};
//call function Kalmanfilter_C
Kalmanfilter_C(measurements, outputArrayC, ¤tState, length);
//initiate empty output array of size length
float outputArrayASM[length];
//reinitialize the struct at p=r=q 0.1 and x=k=0
currentState.p = DEF_p;
currentState.r = DEF_r;
currentState.k = DEF_k;
currentState.q = DEF_q;
currentState.x = DEF_x;
//call subroutine Kalmanfilter_asm
Kalmanfilter_asm(measurements, outputArrayASM, ¤tState, length );
//Check for correctness with a error tolerance of 0.000001
float errorTolerance = 0.000001f;
float errorPercentage = 0.01;
//is_valid(outputArrayC, outputArrayASM, length, errorTolerance, "c vs asm");
//is_valid_relative(outputArrayC, outputArrayASM, length, errorTolerance, errorPercentage,"c vs asm");
int p;
//print KalmanFilter output
for ( p = 0; p < length; p++ )
{
printf("OutputASM: %f & OutputC %f\n", outputArrayASM[p], outputArrayC[p]);
}
float differenceC[length];
float differenceCMSIS[length];
//Difference
arm_sub_f32 (measurements, outputArrayC, differenceCMSIS, length);
c_sub(measurements, outputArrayC, differenceC, length);
//is_valid(differenceC, differenceCMSIS, length, errorTolerance, "Difference");
//is_valid_relative(differenceC, differenceCMSIS, length, errorTolerance, errorPercentage,"Difference");
//Print difference vector
for ( p = 0; p < length; p++ )
{
printf("DifferenceC: %f & DifferenceCMSIS %f \n", differenceC[p], differenceCMSIS[p]);
}
//Mean
float meanCMSIS;
float meanC;
arm_mean_f32 (differenceCMSIS, length , &meanCMSIS);
c_mean(differenceC,length, &meanC);
//is_valid(&meanC, &meanCMSIS, 1, errorTolerance, "mean");
//is_valid_relative(&meanC, &meanCMSIS, 1, errorTolerance, errorPercentage, "mean");
//Print mean values
printf("MeanC: %f & MeanCMSIS %f \n", meanC, meanCMSIS);
//STD
float stdC;
float stdCMSIS;
arm_std_f32 (differenceCMSIS, length, &stdCMSIS);
c_std(differenceC, length, &stdC);
//is_valid(&stdC, &stdCMSIS, 1, errorTolerance, "STD");
//is_valid_relative(&stdC, &stdCMSIS, 1, errorTolerance, errorPercentage,"STD");
//Print std values
printf("StandardDevC: %f & StandardDevCMSIS %f \n", stdC, stdCMSIS);
//correlation
float corC[2*length-1];
float corCMSIS[2*length-1];
arm_correlate_f32 (measurements, length, outputArrayC, length, corCMSIS);
c_correlate(measurements, outputArrayC, corC, length);
//is_valid(corC, corCMSIS, 2*length-1, errorTolerance, "correlation");
//is_valid_relative(corC, corCMSIS, 2*length-1, errorTolerance, errorPercentage, "correlation");
//convolution
float convC[2*length-1];
float convCMSIS[2*length-1];
arm_conv_f32 (measurements, length, outputArrayC, length, convCMSIS);
c_conv(measurements, outputArrayC, convC, length);
//is_valid(convC, convCMSIS, 2*length-1, errorTolerance, "convolution");
//is_valid_relative(convC, convCMSIS, 2*length-1, errorTolerance, errorPercentage, "convolution");
//Print correlation and convolution values
for ( p = 0; p < (2*length-1); p++ )
{
printf("ConvC: %f & ConvCMSIS: %f \n", convC[p], convCMSIS[p]);
}
for ( p = 0; p < (2*length-1); p++ )
{
printf("CorrelateC: %f & CorrelatCMSIS: %f \n", corC[p], corCMSIS[p]);
}
return 0;
}
int
pcgstrf_column_bmod(
const int pnum, /* process number */
const int jcol, /* current column in the panel */
const int fpanelc,/* first column in the panel */
const int nseg, /* number of s-nodes to update jcol */
int *segrep,/* in */
int *repfnz,/* in */
complex *dense, /* modified */
complex *tempv, /* working array */
pxgstrf_shared_t *pxgstrf_shared, /* modified */
Gstat_t *Gstat /* modified */
)
{
/*
* -- SuperLU MT routine (version 2.0) --
* Lawrence Berkeley National Lab, Univ. of California Berkeley,
* and Xerox Palo Alto Research Center.
* September 10, 2007
*
* Purpose:
* ========
* Performs numeric block updates (sup-col) in topological order.
* It features: col-col, 2cols-col, 3cols-col, and sup-col updates.
* Special processing on the supernodal portion of L\U[*,j].
*
* Return value:
* =============
* 0 - successful return
* > 0 - number of bytes allocated when run out of space
*
*/
#if ( MACH==CRAY_PVP )
_fcd ftcs1 = _cptofcd("L", strlen("L")),
ftcs2 = _cptofcd("N", strlen("N")),
ftcs3 = _cptofcd("U", strlen("U"));
#endif
#ifdef USE_VENDOR_BLAS
int incx = 1, incy = 1;
complex alpha, beta;
#endif
GlobalLU_t *Glu = pxgstrf_shared->Glu; /* modified */
/* krep = representative of current k-th supernode
* fsupc = first supernodal column
* nsupc = no of columns in supernode
* nsupr = no of rows in supernode (used as leading dimension)
* luptr = location of supernodal LU-block in storage
* kfnz = first nonz in the k-th supernodal segment
* no_zeros = no of leading zeros in a supernodal U-segment
*/
complex ukj, ukj1, ukj2;
register int lptr, kfnz, isub, irow, i, no_zeros;
register int luptr, luptr1, luptr2;
int fsupc, nsupc, nsupr, segsze;
int nrow; /* No of rows in the matrix of matrix-vector */
int jsupno, k, ksub, krep, krep_ind, ksupno;
int ufirst, nextlu;
int fst_col; /* First column within small LU update */
int d_fsupc; /* Distance between the first column of the current
panel and the first column of the current snode.*/
int *xsup, *supno;
int *lsub, *xlsub, *xlsub_end;
complex *lusup;
int *xlusup, *xlusup_end;
complex *tempv1;
int mem_error;
register float flopcnt;
complex zero = {0.0, 0.0};
complex one = {1.0, 0.0};
complex none = {-1.0, 0.0};
complex comp_temp, comp_temp1;
xsup = Glu->xsup;
supno = Glu->supno;
lsub = Glu->lsub;
xlsub = Glu->xlsub;
xlsub_end = Glu->xlsub_end;
lusup = Glu->lusup;
xlusup = Glu->xlusup;
xlusup_end = Glu->xlusup_end;
jsupno = supno[jcol];
/*
* For each nonz supernode segment of U[*,j] in topological order
*/
k = nseg - 1;
for (ksub = 0; ksub < nseg; ksub++) {
krep = segrep[k];
k--;
ksupno = supno[krep];
#if ( DEBUGlvel>=2 )
if (jcol==BADCOL)
printf("(%d) pcgstrf_column_bmod[1]: %d, nseg %d, krep %d, jsupno %d, ksupno %d\n",
pnum, jcol, nseg, krep, jsupno, ksupno);
#endif
if ( jsupno != ksupno ) { /* Outside the rectangular supernode */
fsupc = xsup[ksupno];
fst_col = SUPERLU_MAX ( fsupc, fpanelc );
/* Distance from the current supernode to the current panel;
d_fsupc=0 if fsupc >= fpanelc. */
d_fsupc = fst_col - fsupc;
luptr = xlusup[fst_col] + d_fsupc;
lptr = xlsub[fsupc] + d_fsupc;
kfnz = repfnz[krep];
kfnz = SUPERLU_MAX ( kfnz, fpanelc );
segsze = krep - kfnz + 1;
nsupc = krep - fst_col + 1;
nsupr = xlsub_end[fsupc] - xlsub[fsupc]; /* Leading dimension */
nrow = nsupr - d_fsupc - nsupc;
krep_ind = lptr + nsupc - 1;
flopcnt = segsze * (segsze - 1) + 2 * nrow * segsze;//sj
Gstat->procstat[pnum].fcops += flopcnt;
#if ( DEBUGlevel>=2 )
if (jcol==BADCOL)
printf("(%d) pcgstrf_column_bmod[2]: %d, krep %d, kfnz %d, segsze %d, d_fsupc %d,\
fsupc %d, nsupr %d, nsupc %d\n",
pnum, jcol, krep, kfnz, segsze, d_fsupc, fsupc, nsupr, nsupc);
#endif
/*
* Case 1: Update U-segment of size 1 -- col-col update
*/
if ( segsze == 1 ) {
ukj = dense[lsub[krep_ind]];
luptr += nsupr*(nsupc-1) + nsupc;
for (i = lptr + nsupc; i < xlsub_end[fsupc]; ++i) {
irow = lsub[i];
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
c_sub(&dense[irow], &dense[irow], &comp_temp);
luptr++;
}
} else if ( segsze <= 3 ) {
ukj = dense[lsub[krep_ind]];
luptr += nsupr*(nsupc-1) + nsupc-1;
ukj1 = dense[lsub[krep_ind - 1]];
luptr1 = luptr - nsupr;
if ( segsze == 2 ) { /* Case 2: 2cols-col update */
cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
c_sub(&ukj, &ukj, &comp_temp);
dense[lsub[krep_ind]] = ukj;
for (i = lptr + nsupc; i < xlsub_end[fsupc]; ++i) {
irow = lsub[i];
luptr++;
luptr1++;
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&dense[irow], &dense[irow], &comp_temp);
}
} else { /* Case 3: 3cols-col update */
ukj2 = dense[lsub[krep_ind - 2]];
luptr2 = luptr1 - nsupr;
cc_mult(&comp_temp, &ukj2, &lusup[luptr2-1]);
c_sub(&ukj1, &ukj1, &comp_temp);
cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&ukj, &ukj, &comp_temp);
dense[lsub[krep_ind]] = ukj;
dense[lsub[krep_ind-1]] = ukj1;
for (i = lptr + nsupc; i < xlsub_end[fsupc]; ++i) {
irow = lsub[i];
luptr++;
luptr1++;
luptr2++;
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&dense[irow], &dense[irow], &comp_temp);
}
}
} else {
/*
* Case: sup-col update
* Perform a triangular solve and block update,
* then scatter the result of sup-col update to dense
*/
no_zeros = kfnz - fst_col;
/* Copy U[*,j] segment from dense[*] to tempv[*] */
isub = lptr + no_zeros;
for (i = 0; i < segsze; i++) {
irow = lsub[isub];
tempv[i] = dense[irow];
++isub;
}
/* Dense triangular solve -- start effective triangle */
luptr += nsupr * no_zeros + no_zeros;
#ifdef USE_VENDOR_BLAS
#if ( MACH==CRAY_PVP )
CTRSV( ftcs1, ftcs2, ftcs3, &segsze, &lusup[luptr],
&nsupr, tempv, &incx );
#else
ctrsv_( "L", "N", "U", &segsze, &lusup[luptr],
&nsupr, tempv, &incx );
#endif
luptr += segsze; /* Dense matrix-vector */
tempv1 = &tempv[segsze];
alpha = one;
beta = zero;
#if ( MACH==CRAY_PVP )
CGEMV( ftcs2, &nrow, &segsze, &alpha, &lusup[luptr],
&nsupr, tempv, &incx, &beta, tempv1, &incy );
#else
cgemv_( "N", &nrow, &segsze, &alpha, &lusup[luptr],
&nsupr, tempv, &incx, &beta, tempv1, &incy );
#endif
#else
clsolve ( nsupr, segsze, &lusup[luptr], tempv );
luptr += segsze; /* Dense matrix-vector */
tempv1 = &tempv[segsze];
cmatvec (nsupr, nrow , segsze, &lusup[luptr], tempv, tempv1);
#endif
/* Scatter tempv[] into SPA dense[*] */
isub = lptr + no_zeros;
for (i = 0; i < segsze; i++) {
irow = lsub[isub];
dense[irow] = tempv[i]; /* Scatter */
tempv[i] = zero;
isub++;
}
/* Scatter tempv1[] into SPA dense[*] */
for (i = 0; i < nrow; i++) {
irow = lsub[isub];
c_sub(&dense[irow], &dense[irow], &tempv1[i]);
tempv1[i] = zero;
++isub;
}
} /* else segsze >= 4 */
} /* if jsupno ... */
} /* for each segment... */
/* ------------------------------------------
Process the supernodal portion of L\U[*,j]
------------------------------------------ */
fsupc = SUPER_FSUPC (jsupno);
nsupr = xlsub_end[fsupc] - xlsub[fsupc];
if ( (mem_error = Glu_alloc(pnum, jcol, nsupr, LUSUP, &nextlu,
pxgstrf_shared)) )
return mem_error;
xlusup[jcol] = nextlu;
lusup = Glu->lusup;
/* Gather the nonzeros from SPA dense[*,j] into L\U[*,j] */
for (isub = xlsub[fsupc]; isub < xlsub_end[fsupc]; ++isub) {
irow = lsub[isub];
lusup[nextlu] = dense[irow];
dense[irow] = zero;
#ifdef DEBUG
if (jcol == -1)
printf("(%d) pcgstrf_column_bmod[lusup] jcol %d, irow %d, lusup %.10e\n",
pnum, jcol, irow, lusup[nextlu]);
#endif
++nextlu;
}
xlusup_end[jcol] = nextlu; /* close L\U[*,jcol] */
#if ( DEBUGlevel>=2 )
if (jcol == -1) {
nrow = xlusup_end[jcol] - xlusup[jcol];
print_double_vec("before sup-col update", nrow, &lsub[xlsub[fsupc]],
&lusup[xlusup[jcol]]);
}
#endif
/*
* For more updates within the panel (also within the current supernode),
* should start from the first column of the panel, or the first column
* of the supernode, whichever is bigger. There are 2 cases:
* (1) fsupc < fpanelc, then fst_col := fpanelc
* (2) fsupc >= fpanelc, then fst_col := fsupc
*/
fst_col = SUPERLU_MAX ( fsupc, fpanelc );
if ( fst_col < jcol ) {
/* distance between the current supernode and the current panel;
d_fsupc=0 if fsupc >= fpanelc. */
d_fsupc = fst_col - fsupc;
lptr = xlsub[fsupc] + d_fsupc;
luptr = xlusup[fst_col] + d_fsupc;
nsupr = xlsub_end[fsupc] - xlsub[fsupc]; /* Leading dimension */
nsupc = jcol - fst_col; /* Excluding jcol */
nrow = nsupr - d_fsupc - nsupc;
/* points to the beginning of jcol in supernode L\U[*,jsupno] */
ufirst = xlusup[jcol] + d_fsupc;
#if ( DEBUGlevel>=2 )
if (jcol==BADCOL)
printf("(%d) pcgstrf_column_bmod[3] jcol %d, fsupc %d, nsupr %d, nsupc %d, nrow %d\n",
pnum, jcol, fsupc, nsupr, nsupc, nrow);
#endif
flopcnt = nsupc * (nsupc - 1) + 2 * nrow * nsupc; //sj
Gstat->procstat[pnum].fcops += flopcnt;
/* ops[TRSV] += nsupc * (nsupc - 1);
ops[GEMV] += 2 * nrow * nsupc; */
#ifdef USE_VENDOR_BLAS
alpha = none; beta = one; /* y := beta*y + alpha*A*x */
#if ( MACH==CRAY_PVP )
CTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &lusup[luptr],
&nsupr, &lusup[ufirst], &incx );
CGEMV( ftcs2, &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr,
&lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#else
ctrsv_( "L", "N", "U", &nsupc, &lusup[luptr],
&nsupr, &lusup[ufirst], &incx );
cgemv_( "N", &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr,
&lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#endif
#else
clsolve ( nsupr, nsupc, &lusup[luptr], &lusup[ufirst] );
cmatvec ( nsupr, nrow, nsupc, &lusup[luptr+nsupc],
&lusup[ufirst], tempv );
/* Copy updates from tempv[*] into lusup[*] */
isub = ufirst + nsupc;
for (i = 0; i < nrow; i++) {
c_sub(&lusup[isub], &lusup[isub], &tempv[i]);
tempv[i] = zero;
++isub;
}
#endif
} /* if fst_col < jcol ... */
return 0;
}
int main(int argc, char *argv[])
{
void cmatvec_mult(complex alpha, complex x[], complex beta, complex y[]);
void cpsolve(int n, complex x[], complex y[]);
extern int cfgmr( int n,
void (*matvec_mult)(complex, complex [], complex, complex []),
void (*psolve)(int n, complex [], complex[]),
complex *rhs, complex *sol, double tol, int restrt, int *itmax,
FILE *fits);
extern int cfill_diag(int n, NCformat *Astore);
char equed[1] = {'B'};
yes_no_t equil;
trans_t trans;
SuperMatrix A, L, U;
SuperMatrix B, X;
NCformat *Astore;
NCformat *Ustore;
SCformat *Lstore;
complex *a;
int *asub, *xa;
int *etree;
int *perm_c; /* column permutation vector */
int *perm_r; /* row permutations from partial pivoting */
int nrhs, ldx, lwork, info, m, n, nnz;
complex *rhsb, *rhsx, *xact;
complex *work = NULL;
float *R, *C;
float u, rpg, rcond;
complex zero = {0.0, 0.0};
complex one = {1.0, 0.0};
complex none = {-1.0, 0.0};
mem_usage_t mem_usage;
superlu_options_t options;
SuperLUStat_t stat;
int restrt, iter, maxit, i;
double resid;
complex *x, *b;
#ifdef DEBUG
extern int num_drop_L, num_drop_U;
#endif
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Enter main()");
#endif
/* Defaults */
lwork = 0;
nrhs = 1;
equil = YES;
u = 0.1; /* u=1.0 for complete factorization */
trans = NOTRANS;
/* Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 0.1; //different from complete LU
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
options.RowPerm = LargeDiag;
options.ILU_DropTol = 1e-4;
options.ILU_FillTol = 1e-2;
options.ILU_FillFactor = 10.0;
options.ILU_DropRule = DROP_BASIC | DROP_AREA;
options.ILU_Norm = INF_NORM;
options.ILU_MILU = SMILU_2;
*/
ilu_set_default_options(&options);
/* Modify the defaults. */
options.PivotGrowth = YES; /* Compute reciprocal pivot growth */
options.ConditionNumber = YES;/* Compute reciprocal condition number */
if ( lwork > 0 ) {
work = SUPERLU_MALLOC(lwork);
if ( !work ) ABORT("Malloc fails for work[].");
}
/* Read matrix A from a file in Harwell-Boeing format.*/
if (argc < 2)
{
printf("Usage:\n%s [OPTION] < [INPUT] > [OUTPUT]\nOPTION:\n"
"-h -hb:\n\t[INPUT] is a Harwell-Boeing format matrix.\n"
"-r -rb:\n\t[INPUT] is a Rutherford-Boeing format matrix.\n"
"-t -triplet:\n\t[INPUT] is a triplet format matrix.\n",
argv[0]);
return 0;
}
else
{
switch (argv[1][1])
{
case 'H':
case 'h':
printf("Input a Harwell-Boeing format matrix:\n");
creadhb(&m, &n, &nnz, &a, &asub, &xa);
break;
case 'R':
case 'r':
printf("Input a Rutherford-Boeing format matrix:\n");
creadrb(&m, &n, &nnz, &a, &asub, &xa);
break;
case 'T':
case 't':
printf("Input a triplet format matrix:\n");
creadtriple(&m, &n, &nnz, &a, &asub, &xa);
break;
default:
printf("Unrecognized format.\n");
return 0;
}
}
cCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_C, SLU_GE);
Astore = A.Store;
cfill_diag(n, Astore);
printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
fflush(stdout);
if ( !(rhsb = complexMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb[].");
if ( !(rhsx = complexMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsx[].");
cCreate_Dense_Matrix(&B, m, nrhs, rhsb, m, SLU_DN, SLU_C, SLU_GE);
cCreate_Dense_Matrix(&X, m, nrhs, rhsx, m, SLU_DN, SLU_C, SLU_GE);
xact = complexMalloc(n * nrhs);
ldx = n;
cGenXtrue(n, nrhs, xact, ldx);
cFillRHS(trans, nrhs, xact, ldx, &A, &B);
if ( !(etree = intMalloc(n)) ) ABORT("Malloc fails for etree[].");
if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
if ( !(R = (float *) SUPERLU_MALLOC(A.nrow * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for R[].");
if ( !(C = (float *) SUPERLU_MALLOC(A.ncol * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for C[].");
info = 0;
#ifdef DEBUG
num_drop_L = 0;
num_drop_U = 0;
#endif
/* Initialize the statistics variables. */
StatInit(&stat);
/* Compute the incomplete factorization and compute the condition number
and pivot growth using dgsisx. */
cgsisx(&options, &A, perm_c, perm_r, etree, equed, R, C, &L, &U, work,
lwork, &B, &X, &rpg, &rcond, &mem_usage, &stat, &info);
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf("cgsisx(): info %d\n", info);
if (info > 0 || rcond < 1e-8 || rpg > 1e8)
printf("WARNING: This preconditioner might be unstable.\n");
if ( info == 0 || info == n+1 ) {
if ( options.PivotGrowth == YES )
printf("Recip. pivot growth = %e\n", rpg);
if ( options.ConditionNumber == YES )
printf("Recip. condition number = %e\n", rcond);
} else if ( info > 0 && lwork == -1 ) {
printf("** Estimated memory: %d bytes\n", info - n);
}
printf("n(A) = %d, nnz(A) = %d\n", n, Astore->nnz);
printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
printf("Fill ratio: nnz(F)/nnz(A) = %.3f\n",
((double)(Lstore->nnz) + (double)(Ustore->nnz) - (double)n)
/ (double)Astore->nnz);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
fflush(stdout);
/* Set the global variables. */
GLOBAL_A = &A;
GLOBAL_L = &L;
GLOBAL_U = &U;
GLOBAL_STAT = &stat;
GLOBAL_PERM_C = perm_c;
GLOBAL_PERM_R = perm_r;
/* Set the variables used by GMRES. */
restrt = SUPERLU_MIN(n / 3 + 1, 50);
maxit = 1000;
iter = maxit;
resid = 1e-8;
if (!(b = complexMalloc(m))) ABORT("Malloc fails for b[].");
if (!(x = complexMalloc(n))) ABORT("Malloc fails for x[].");
sp_cgemv("N", one, &A, xact, 1, zero, b, 1);
if (info <= n + 1)
{
int i_1 = 1;
double maxferr = 0.0, nrmA, nrmB, res, t;
complex temp;
extern float scnrm2_(int *, complex [], int *);
extern void caxpy_(int *, complex *, complex [], int *, complex [], int *);
/* Call GMRES. */
/*double *sol = (double*) ((DNformat*) X.Store)->nzval;
for (i = 0; i < n; i++) x[i] = sol[i];*/
for (i = 0; i < n; i++) x[i] = zero;
t = SuperLU_timer_();
cfgmr(n, cmatvec_mult, cpsolve, b, x, resid, restrt, &iter, stdout);
t = SuperLU_timer_() - t;
/* Output the result. */
nrmA = scnrm2_(&(Astore->nnz), (complex *)((DNformat *)A.Store)->nzval,
&i_1);
nrmB = scnrm2_(&m, b, &i_1);
sp_cgemv("N", none, &A, x, 1, one, b, 1);
res = scnrm2_(&m, b, &i_1);
resid = res / nrmB;
printf("||A||_F = %.1e, ||B||_2 = %.1e, ||B-A*X||_2 = %.1e, "
"relres = %.1e\n", nrmA, nrmB, res, resid);
if (iter >= maxit)
{
if (resid >= 1.0) iter = -180;
else if (resid > 1e-8) iter = -111;
}
printf("iteration: %d\nresidual: %.1e\nGMRES time: %.2f seconds.\n",
iter, resid, t);
for (i = 0; i < m; i++)
c_sub(&temp, &x[i], &xact[i]);
maxferr = SUPERLU_MAX(maxferr, c_abs1(&temp));
printf("||X-X_true||_oo = %.1e\n", maxferr);
}
#ifdef DEBUG
printf("%d entries in L and %d entries in U dropped.\n",
num_drop_L, num_drop_U);
#endif
fflush(stdout);
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
SUPERLU_FREE (rhsb);
SUPERLU_FREE (rhsx);
SUPERLU_FREE (xact);
SUPERLU_FREE (etree);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
SUPERLU_FREE (R);
SUPERLU_FREE (C);
Destroy_CompCol_Matrix(&A);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperMatrix_Store(&X);
if ( lwork >= 0 ) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
}
SUPERLU_FREE(b);
SUPERLU_FREE(x);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Exit main()");
#endif
return 0;
}
void polydiv (header *hd)
{ header *st=hd,*hd1,*result,*rest;
int c1,c2,i,r,j;
double *m1,*m2,*mr,*mh,x,l;
complex *mc1,*mc2,*mcr,*mch,xc,lc,hc;
interval *mi1,*mi2,*mir,*mih,xi,li,hi;
hd1=next_param(st);
equal_params_2(&hd,&hd1); if (error) return;
getmatrix(hd,&r,&c1,&m1); if (r!=1) wrong_arg();
getmatrix(hd1,&r,&c2,&m2); if (r!=1) wrong_arg();
if (c1<c2)
{ result=new_real(0.0,"");
rest=(header *)newram;
moveresult(rest,hd1);
}
else if (iscomplex(hd))
{ mc1=(complex *)m1; mc2=(complex *)m2;
result=new_cmatrix(1,c1-c2+1,""); if (error) return;
mcr=(complex *)matrixof(result);
rest=new_cmatrix(1,c2,""); if (error) return;
mch=(complex *)newram;
if (!freeram(c1*sizeof(complex)))
{ output("Out of memory!\n"); error=190; return;
}
memmove((char *)mch,(char *)mc1,c1*sizeof(complex));
c_copy(lc,mc2[c2-1]);
if (lc[0]==0.0 && lc[1]==0.0) wrong_arg();
for (i=c1-c2; i>=0; i--)
{ c_div(mch[c2+i-1],lc,xc); c_copy(mcr[i],xc);
for(j=0; j<c2; j++)
{ c_mult(mc2[j],xc,hc);
c_sub(mch[i+j],hc,mch[i+j]);
}
}
memmove((char *)matrixof(rest),(char *)mch,c2*sizeof(complex));
}
else if (isinterval(hd))
{ mi1=(interval *)m1; mi2=(interval *)m2;
result=new_imatrix(1,c1-c2+1,""); if (error) return;
mir=(interval *)matrixof(result);
rest=new_imatrix(1,c2,""); if (error) return;
mih=(complex *)newram;
if (!freeram(c1*sizeof(complex)))
{ output("Out of memory!\n"); error=190; return;
}
memmove((char *)mih,(char *)mi1,c1*sizeof(interval));
i_copy(li,mi2[c2-1]);
if (li[0]<=0.0 && li[1]>=0.0) wrong_arg();
for (i=c1-c2; i>=0; i--)
{ i_div(mih[c2+i-1],li,xi); c_copy(mir[i],xi);
for(j=0; j<c2; j++)
{ i_mult(mi2[j],xi,hi);
i_sub(mih[i+j],hi,mih[i+j]);
}
}
memmove((char *)matrixof(rest),(char *)mih,c2*sizeof(interval));
}
else if (isreal(hd))
{ result=new_matrix(1,c1-c2+1,""); if (error) return;
mr=matrixof(result);
rest=new_matrix(1,c2,""); if (error) return;
mh=(double *)newram;
if (!freeram(c1*sizeof(double)))
{ output("Out of memory!\n"); error=190; return;
}
memmove((char *)mh,(char *)m1,c1*sizeof(double));
l=m2[c2-1];
if (l==0.0) wrong_arg();
for (i=c1-c2; i>=0; i--)
{ x=mh[c2+i-1]/l; mr[i]=x;
for(j=0; j<c2; j++) mh[i+j]-=m2[j]*x;
}
memmove((char *)matrixof(rest),(char *)mh,c2*sizeof(double));
}
else wrong_arg();
moveresult(st,result);
moveresult(nextof(st),rest);
}
void recalculate (int plane, number_t * x1, number_t * y1)
{
number_t x = *x1, y = *y1;
switch (plane) {
case 1:
{ /* 1/mu */
number_t t;
if (myabs (x) + myabs (y) < 0.000001)
t = INT_MAX, y = INT_MAX;
else {
c_div (1, 0, x, y, t, y);
}
x = t;
}
break;
case 2:
{ /* 1/(mu + 0.25) */
number_t t;
if (myabs (x) + myabs (y) < 0.000001)
t = INT_MAX, y = INT_MAX;
else {
c_div (1, 0, x, y, t, y);
}
x = t;
x += 0.25;
}
break;
case 3: /* lambda */
{
number_t tr, ti, mr, mi;
mr = x, mi = y;
c_pow2 (x, y, tr, ti);
c_div (tr, ti, 4, 0, x, y);
c_div (mr, mi, 2, 0, tr, ti);
c_sub (tr, ti, x, y, mr, mi);
x = mr, y = mi;
}
break;
case 4: /* 1/lambda */
{
number_t tr, ti, mr, mi;
c_div (1, 0, x, y, tr, y);
x = tr;
mr = x, mi = y;
c_pow2 (x, y, tr, ti);
c_div (tr, ti, 4, 0, x, y);
c_div (mr, mi, 2, 0, tr, ti);
c_sub (tr, ti, x, y, mr, mi);
x = mr, y = mi;
}
break;
case 5: /* 1/(lambda-1) */
{
number_t tr, ti, mr, mi;
c_div (1, 0, x, y, tr, y);
x = tr + 1;
mr = x, mi = y;
c_pow2 (x, y, tr, ti);
c_div (tr, ti, 4, 0, x, y);
c_div (mr, mi, 2, 0, tr, ti);
c_sub (tr, ti, x, y, mr, mi);
x = mr, y = mi;
}
break;
case 6:
{ /* 1/(mu + 0.25) */
number_t t;
if (myabs (x) + myabs (y) < 0.000001)
t = INT_MAX, y = INT_MAX;
else {
c_div (1, 0, x, y, t, y);
}
x = t;
x -= 1.40115;
}
break;
default:
break;
}
*x1 = x;
*y1 = y;
}
