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#include "cminpack.h"
#include <math.h>
#ifdef USE_LAPACK
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#endif
#include "cminpackP.h"
__cminpack_attr__
void __cminpack_func__(qrfac)(int m, int n, real *a, int
lda, int pivot, int *ipvt, int lipvt, real *rdiag,
real *acnorm, real *wa)
{
#ifdef USE_LAPACK
__CLPK_integer m_ = m;
__CLPK_integer n_ = n;
__CLPK_integer lda_ = lda;
__CLPK_integer *jpvt;
int i, j, k;
double t;
double* tau = wa;
const __CLPK_integer ltau = m > n ? n : m;
__CLPK_integer lwork = -1;
__CLPK_integer info = 0;
double* work;
if (pivot) {
assert( lipvt >= n );
if (sizeof(__CLPK_integer) != sizeof(ipvt[0])) {
jpvt = malloc(n*sizeof(__CLPK_integer));
} else {
/* __CLPK_integer is actually an int, just do a cast */
jpvt = (__CLPK_integer *)ipvt;
}
/* set all columns free */
memset(jpvt, 0, sizeof(int)*n);
}
/* query optimal size of work */
lwork = -1;
if (pivot) {
dgeqp3_(&m_,&n_,a,&lda_,jpvt,tau,tau,&lwork,&info);
lwork = (int)tau[0];
assert( lwork >= 3*n+1 );
} else {
dgeqrf_(&m_,&n_,a,&lda_,tau,tau,&lwork,&info);
lwork = (int)tau[0];
assert( lwork >= 1 && lwork >= n );
}
assert( info == 0 );
/* alloc work area */
work = (double *)malloc(sizeof(double)*lwork);
assert(work != NULL);
/* set acnorm first (from the doc of qrfac, acnorm may point to the same area as rdiag) */
if (acnorm != rdiag) {
for (j = 0; j < n; ++j) {
acnorm[j] = __cminpack_enorm__(m, &a[j * lda]);
}
}
/* QR decomposition */
if (pivot) {
dgeqp3_(&m_,&n_,a,&lda_,jpvt,tau,work,&lwork,&info);
} else {
dgeqrf_(&m_,&n_,a,&lda_,tau,work,&lwork,&info);
}
assert(info == 0);
/* set rdiag, before the diagonal is replaced */
memset(rdiag, 0, sizeof(double)*n);
for(i=0 ; i<n ; ++i) {
rdiag[i] = a[i*lda+i];
}
/* modify lower trinagular part to look like qrfac's output */
for(i=0 ; i<ltau ; ++i) {
k = i*lda+i;
t = tau[i];
a[k] = t;
for(j=i+1 ; j<m ; j++) {
k++;
a[k] *= t;
}
}
free(work);
if (pivot) {
/* convert back jpvt to ipvt */
if (sizeof(__CLPK_integer) != sizeof(ipvt[0])) {
for(i=0; i<n; ++i) {
ipvt[i] = jpvt[i];
}
free(jpvt);
}
}
#else /* !USE_LAPACK */
/* Initialized data */
#define p05 .05
/* System generated locals */
real d1;
/* Local variables */
int i, j, k, jp1;
real sum;
real temp;
int minmn;
real epsmch;
real ajnorm;
/* ********** */
/* subroutine qrfac */
/* this subroutine uses householder transformations with column */
/* pivoting (optional) to compute a qr factorization of the */
/* m by n matrix a. that is, qrfac determines an orthogonal */
/* matrix q, a permutation matrix p, and an upper trapezoidal */
/* matrix r with diagonal elements of nonincreasing magnitude, */
/* such that a*p = q*r. the householder transformation for */
/* column k, k = 1,2,...,min(m,n), is of the form */
/* t */
/* i - (1/u(k))*u*u */
/* where u has zeros in the first k-1 positions. the form of */
/* this transformation and the method of pivoting first */
/* appeared in the corresponding linpack subroutine. */
/* the subroutine statement is */
/* subroutine qrfac(m,n,a,lda,pivot,ipvt,lipvt,rdiag,acnorm,wa) */
/* where */
/* m is a positive integer input variable set to the number */
/* of rows of a. */
/* n is a positive integer input variable set to the number */
/* of columns of a. */
/* a is an m by n array. on input a contains the matrix for */
/* which the qr factorization is to be computed. on output */
/* the strict upper trapezoidal part of a contains the strict */
/* upper trapezoidal part of r, and the lower trapezoidal */
/* part of a contains a factored form of q (the non-trivial */
/* elements of the u vectors described above). */
/* lda is a positive integer input variable not less than m */
/* which specifies the leading dimension of the array a. */
/* pivot is a logical input variable. if pivot is set true, */
/* then column pivoting is enforced. if pivot is set false, */
/* then no column pivoting is done. */
/* ipvt is an integer output array of length lipvt. ipvt */
/* defines the permutation matrix p such that a*p = q*r. */
/* column j of p is column ipvt(j) of the identity matrix. */
/* if pivot is false, ipvt is not referenced. */
/* lipvt is a positive integer input variable. if pivot is false, */
/* then lipvt may be as small as 1. if pivot is true, then */
/* lipvt must be at least n. */
/* rdiag is an output array of length n which contains the */
/* diagonal elements of r. */
/* acnorm is an output array of length n which contains the */
/* norms of the corresponding columns of the input matrix a. */
/* if this information is not needed, then acnorm can coincide */
/* with rdiag. */
/* wa is a work array of length n. if pivot is false, then wa */
/* can coincide with rdiag. */
/* subprograms called */
/* minpack-supplied ... dpmpar,enorm */
/* fortran-supplied ... dmax1,dsqrt,min0 */
/* argonne national laboratory. minpack project. march 1980. */
/* burton s. garbow, kenneth e. hillstrom, jorge j. more */
/* ********** */
(void)lipvt;
/* epsmch is the machine precision. */
epsmch = __cminpack_func__(dpmpar)(1);
/* compute the initial column norms and initialize several arrays. */
for (j = 0; j < n; ++j) {
acnorm[j] = __cminpack_enorm__(m, &a[j * lda + 0]);
rdiag[j] = acnorm[j];
wa[j] = rdiag[j];
if (pivot) {
ipvt[j] = j+1;
}
}
/* reduce a to r with householder transformations. */
minmn = min(m,n);
for (j = 0; j < minmn; ++j) {
if (pivot) {
/* bring the column of largest norm into the pivot position. */
int kmax = j;
for (k = j; k < n; ++k) {
if (rdiag[k] > rdiag[kmax]) {
kmax = k;
}
}
if (kmax != j) {
for (i = 0; i < m; ++i) {
temp = a[i + j * lda];
a[i + j * lda] = a[i + kmax * lda];
a[i + kmax * lda] = temp;
}
rdiag[kmax] = rdiag[j];
wa[kmax] = wa[j];
k = ipvt[j];
ipvt[j] = ipvt[kmax];
ipvt[kmax] = k;
}
}
/* compute the householder transformation to reduce the */
/* j-th column of a to a multiple of the j-th unit vector. */
ajnorm = __cminpack_enorm__(m - (j+1) + 1, &a[j + j * lda]);
if (ajnorm != 0.) {
if (a[j + j * lda] < 0.) {
ajnorm = -ajnorm;
}
for (i = j; i < m; ++i) {
a[i + j * lda] /= ajnorm;
}
a[j + j * lda] += 1.;
/* apply the transformation to the remaining columns */
/* and update the norms. */
jp1 = j + 1;
if (n > jp1) {
for (k = jp1; k < n; ++k) {
sum = 0.;
for (i = j; i < m; ++i) {
sum += a[i + j * lda] * a[i + k * lda];
}
temp = sum / a[j + j * lda];
for (i = j; i < m; ++i) {
a[i + k * lda] -= temp * a[i + j * lda];
}
if (pivot && rdiag[k] != 0.) {
temp = a[j + k * lda] / rdiag[k];
/* Computing MAX */
d1 = 1. - temp * temp;
rdiag[k] *= sqrt((max((real)0.,d1)));
/* Computing 2nd power */
d1 = rdiag[k] / wa[k];
if (p05 * (d1 * d1) <= epsmch) {
rdiag[k] = __cminpack_enorm__(m - (j+1), &a[jp1 + k * lda]);
wa[k] = rdiag[k];
}
}
}
}
}
rdiag[j] = -ajnorm;
}
/* last card of subroutine qrfac. */
#endif /* !USE_LAPACK */
} /* qrfac_ */
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