zqrsl.c

InsightToolkit-1.4.0(有大量的优化算法程序)

#include "f2c.h"
#include "netlib.h"

/* Modified by Peter Vanroose, June 2001: manual optimisation and clean-up */

/* Table of constant values */
static integer c__1 = 1;

/* Subroutine */ void zqrsl_(x, ldx, n, k, qraux, y, qy, qty, b, rsd, xb, job, info)
const doublecomplex *x;
const integer *ldx, *n, *k;
const doublecomplex *qraux, *y;
doublecomplex *qy, *qty, *b, *rsd, *xb;
const integer *job;
integer *info;
{
    /* System generated locals */
    integer i__1, i__2;

    /* Local variables */
    static doublecomplex temp;
    static logical cqty;
    static integer i, j;
    static doublecomplex t;
    static logical cb;
    static logical cr;
    static integer ju;
    static logical cxb, cqy;

/************************************************************************/
/*                                                                      */
/*     zqrsl applies the output of zqrdc to compute coordinate          */
/*     transformations, projections, and least squares solutions.       */
/*     for k .le. min(n,p), let xk be the matrix                        */
/*                                                                      */
/*            xk = (x(jpvt(1)),x(jpvt(2)), ... ,x(jpvt(k)))             */
/*                                                                      */
/*     formed from columnns jpvt(1), ... ,jpvt(k) of the original       */
/*     n x p matrix x that was input to zqrdc (if no pivoting was       */
/*     done, xk consists of the first k columns of x in their           */
/*     original order). zqrdc produces a factored unitary matrix q      */
/*     and an upper triangular matrix r such that                       */
/*                                                                      */
/*              xk = q * (r)                                            */
/*                       (0)                                            */
/*                                                                      */
/*     this information is contained in coded form in the arrays        */
/*     x and qraux.                                                     */
/*                                                                      */
/*     on entry                                                         */
/*                                                                      */
/*        x      complex*16(ldx,p).                                     */
/*               x contains the output of zqrdc.                        */
/*                                                                      */
/*        ldx    integer.                                               */
/*               ldx is the leading dimension of the array x.           */
/*                                                                      */
/*        n      integer.                                               */
/*               n is the number of rows of the matrix xk. it must      */
/*               have the same value as n in zqrdc.                     */
/*                                                                      */
/*        k      integer.                                               */
/*               k is the number of columns of the matrix xk.  k        */
/*               must not be greater than min(n,p), where p is the      */
/*               same as in the calling sequence to zqrdc.              */
/*                                                                      */
/*        qraux  complex*16(p).                                         */
/*               qraux contains the auxiliary output from zqrdc.        */
/*                                                                      */
/*        y      complex*16(n)                                          */
/*               y contains an n-vector that is to be manipulated       */
/*               by zqrsl.                                              */
/*                                                                      */
/*        job    integer.                                               */
/*               job specifies what is to be computed.  job has         */
/*               the decimal expansion abcde, with the following        */
/*               meaning.                                               */
/*                                                                      */
/*                    if a.ne.0, compute qy.                            */
/*                    if b,c,d, or e .ne. 0, compute qty.               */
/*                    if c.ne.0, compute b.                             */
/*                    if d.ne.0, compute rsd.                           */
/*                    if e.ne.0, compute xb.                            */
/*                                                                      */
/*               note that a request to compute b, rsd, or xb           */
/*               automatically triggers the computation of qty,         */
/*               for which an array must be provided in the             */
/*               calling sequence.                                      */
/*                                                                      */
/*     on return                                                        */
/*                                                                      */
/*        qy     complex*16(n).                                         */
/*               qy contains q*y, if its computation has been           */
/*               requested.                                             */
/*                                                                      */
/*        qty    complex*16(n).                                         */
/*               qty contains ctrans(q)*y, if its computation has       */
/*               been requested.  here ctrans(q) is the conjugate       */
/*               transpose of the matrix q.                             */
/*                                                                      */
/*        b      complex*16(k)                                          */
/*               b contains the solution of the least squares problem   */
/*                                                                      */
/*                    minimize norm2(y - xk*b),                         */
/*                                                                      */
/*               if its computation has been requested.  (note that     */
/*               if pivoting was requested in zqrdc, the j-th           */
/*               component of b will be associated with column jpvt(j)  */
/*               of the original matrix x that was input into zqrdc.)   */
/*                                                                      */
/*        rsd    complex*16(n).                                         */
/*               rsd contains the least squares residual y - xk*b,      */
/*               if its computation has been requested.  rsd is         */
/*               also the orthogonal projection of y onto the           */
/*               orthogonal complement of the column space of xk.       */
/*                                                                      */
/*        xb     complex*16(n).                                         */
/*               xb contains the least squares approximation xk*b,      */
/*               if its computation has been requested.  xb is also     */
/*               the orthogonal projection of y onto the column space   */
/*               of x.                                                  */
/*                                                                      */
/*        info   integer.                                               */
/*               info is zero unless the computation of b has           */
/*               been requested and r is exactly singular.  in          */
/*               this case, info is the index of the first zero         */
/*               diagonal element of r and b is left unaltered.         */
/*                                                                      */
/*     the parameters qy, qty, b, rsd, and xb are not referenced        */
/*     if their computation is not requested and in this case           */
/*     can be replaced by dummy variables in the calling program.       */
/*     to save storage, the user may in some cases use the same         */
/*     array for different parameters in the calling sequence.  a       */
/*     frequently occuring example is when one wishes to compute        */
/*     any of b, rsd, or xb and does not need y or qty.  in this        */
/*     case one may identify y, qty, and one of b, rsd, or xb, while    */
/*     providing separate arrays for anything else that is to be        */
/*     computed.  thus the calling sequence                             */
/*                                                                      */
/*          call zqrsl(x,ldx,n,k,qraux,y,dum,y,b,y,dum,110,info)        */
/*                                                                      */
/*     will result in the computation of b and rsd, with rsd            */
/*     overwriting y.  more generally, each item in the following       */
/*     list contains groups of permissible identifications for          */
/*     a single callinng sequence.                                      */
/*                                                                      */
/*          1. (y,qty,b) (rsd) (xb) (qy)                                */
/*          2. (y,qty,rsd) (b) (xb) (qy)                                */
/*          3. (y,qty,xb) (b) (rsd) (qy)                                */
/*          4. (y,qy) (qty,b) (rsd) (xb)                                */
/*          5. (y,qy) (qty,rsd) (b) (xb)                                */
/*          6. (y,qy) (qty,xb) (b) (rsd)                                */
/*                                                                      */
/*     in any group the value returned in the array allocated to        */
/*     the group corresponds to the last member of the group.           */
/*                                                                      */
/*     linpack. this version dated 08/14/78 .                           */