#include "cs.h"
/* x=A\b where A can be rectangular; b overwritten with solution */
CS_INT cs_qrsol (CS_INT order, const cs *A, CS_ENTRY *b)
{
    CS_ENTRY *x ;
    css *S ;
    csn *N ;
    cs *AT = NULL ;
    CS_INT k, m, n, ok ;
    if (!CS_CSC (A) || !b) return (0) ;	/* check inputs */
    n = A->n ;
    m = A->m ;
    if (m >= n)
    {
	S = cs_sqr (order, A, 1) ;	    /* ordering and symbolic analysis */
	N = cs_qr (A, S) ;		    /* numeric QR factorization */
	x = cs_calloc (S ? S->m2 : 1, sizeof (CS_ENTRY)) ;    /* get workspace */
	ok = (S && N && x) ;
	if (ok)
	{
	    cs_ipvec (S->pinv, b, x, m) ;   /* x(0:m-1) = b(p(0:m-1) */
	    for (k = 0 ; k < n ; k++)	    /* apply Householder refl. to x */
	    {
		cs_happly (N->L, k, N->B [k], x) ;
	    }
	    cs_usolve (N->U, x) ;	    /* x = R\x */
	    cs_ipvec (S->q, x, b, n) ;	    /* b(q(0:n-1)) = x(0:n-1) */
	}
    }
    else
    {
	AT = cs_transpose (A, 1) ;	    /* Ax=b is underdetermined */
	S = cs_sqr (order, AT, 1) ;	    /* ordering and symbolic analysis */
	N = cs_qr (AT, S) ;		    /* numeric QR factorization of A' */
	x = cs_calloc (S ? S->m2 : 1, sizeof (CS_ENTRY)) ;    /* get workspace */
	ok = (AT && S && N && x) ;
	if (ok)
	{
	    cs_pvec (S->q, b, x, m) ;	    /* x(q(0:m-1)) = b(0:m-1) */
	    cs_utsolve (N->U, x) ;	    /* x = R'\x */
	    for (k = m-1 ; k >= 0 ; k--)    /* apply Householder refl. to x */
	    {
		cs_happly (N->L, k, CS_CONJ (N->B [k]), x) ;
	    }
	    cs_pvec (S->pinv, x, b, n) ;    /* b(0:n-1) = x(p(0:n-1)) */
	}
    }
    cs_free (x) ;
    cs_sfree (S) ;
    cs_nfree (N) ;
    cs_spfree (AT) ;
    return (ok) ;
}
