multi-method.txt

最小二乘算法 Fortran实现 比较简单

		    temp = a[j - 1 + l * a_dim1];
		    a[j - 1 + l * a_dim1] = cc * temp + ss * a[j + l * a_dim1]
			    ;
		    a[j + l * a_dim1] = -ss * temp + cc * a[j + l * a_dim1];
		}
/* L270: */
	    }

/*                 Apply procedure G2 (CC,SS,B(J-1),B(J)) */

	    temp = b[j - 1];
	    b[j - 1] = cc * temp + ss * b[j];
	    b[j] = -ss * temp + cc * b[j];
/* L280: */
	}
    }

    npp1 = nsetp;
    --nsetp;
    --iz1;
    index[iz1] = i__;

/*        SEE IF THE REMAINING COEFFS IN SET P ARE FEASIBLE.  THEY SHOULD 
*/
/*        BE BECAUSE OF THE WAY ALPHA WAS DETERMINED. */
/*        IF ANY ARE INFEASIBLE IT IS DUE TO ROUND-OFF ERROR.  ANY */
/*        THAT ARE NONPOSITIVE WILL BE SET TO ZERO */
/*        AND MOVED FROM SET P TO SET Z. */

    i__1 = nsetp;
    for (jj = 1; jj <= i__1; ++jj) {
	i__ = index[jj];
	if (x[i__] <= 0.) {
	    goto L260;
	}
/* L300: */
    }

/*         COPY B( ) INTO ZZ( ).  THEN SOLVE AGAIN AND LOOP BACK. */

    i__1 = *m;
    for (i__ = 1; i__ <= i__1; ++i__) {
/* L310: */
	zz[i__] = b[i__];
    }
    rtnkey = 2;
    goto L400;
L320:
    goto L210;
/*                      ******  END OF SECONDARY LOOP  ****** */

L330:
    i__1 = nsetp;
    for (ip = 1; ip <= i__1; ++ip) {
	i__ = index[ip];
/* L340: */
	x[i__] = zz[ip];
    }
/*        ALL NEW COEFFS ARE POSITIVE.  LOOP BACK TO BEGINNING. */
    goto L30;

/*                        ******  END OF MAIN LOOP  ****** */

/*                        COME TO HERE FOR TERMINATION. */
/*                     COMPUTE THE NORM OF THE FINAL RESIDUAL VECTOR. */

L350:
    sm = 0.;
    if (npp1 <= *m) {
	i__1 = *m;
	for (i__ = npp1; i__ <= i__1; ++i__) {
/* L360: */
/* Computing 2nd power */
	    d__1 = b[i__];
	    sm += d__1 * d__1;
	}
    } else {
	i__1 = *n;
	for (j = 1; j <= i__1; ++j) {
/* L380: */
	    w[j] = 0.;
	}
    }
    *rnorm = sqrt(sm);
    return 0;

/*     THE FOLLOWING BLOCK OF CODE IS USED AS AN INTERNAL SUBROUTINE */
/*     TO SOLVE THE TRIANGULAR SYSTEM, PUTTING THE SOLUTION IN ZZ(). */

L400:
    i__1 = nsetp;
    for (l = 1; l <= i__1; ++l) {
	ip = nsetp + 1 - l;
	if (l != 1) {
	    i__2 = ip;
	    for (ii = 1; ii <= i__2; ++ii) {
		zz[ii] -= a[ii + jj * a_dim1] * zz[ip + 1];
/* L410: */
	    }
	}
	jj = index[ip];
	zz[ip] /= a[ip + jj * a_dim1];
/* L430: */
    }
    switch ((int)rtnkey) {
	case 1:  goto L200;
	case 2:  goto L320;
    }

    /* The next line was added after the f2c translation to keep
       compilers from complaining about a void return from a non-void
       function. */
    return 0;

} /* nnls_ */

/* Subroutine */ int g1_(a, b, cterm, sterm, sig)
doublereal *a, *b, *cterm, *sterm, *sig;
{
    /* System generated locals */
    doublereal d__1;

    /* Builtin functions */
    /* The following line was commented out after the f2c translation */
    /* double sqrt(), d_sign(); */

    /* Local variables */
    static doublereal xr, yr;


/*     COMPUTE ORTHOGONAL ROTATION MATRIX.. */

/*  The original version of this code was developed by */
/*  Charles L. Lawson and Richard J. Hanson at Jet Propulsion Laboratory 
*/
/*  1973 JUN 12, and published in the book */
/*  "SOLVING LEAST SQUARES PROBLEMS", Prentice-HalL, 1974. */
/*  Revised FEB 1995 to accompany reprinting of the book by SIAM. */

/*     COMPUTE.. MATRIX   (C, S) SO THAT (C, S)(A) = (SQRT(A**2+B**2)) */
/*                        (-S,C)         (-S,C)(B)   (   0          ) */
/*     COMPUTE SIG = SQRT(A**2+B**2) */
/*        SIG IS COMPUTED LAST TO ALLOW FOR THE POSSIBILITY THAT */
/*        SIG MAY BE IN THE SAME LOCATION AS A OR B . */
/*     ------------------------------------------------------------------ 
*/
/*     ------------------------------------------------------------------ 
*/
    if (nnls_abs(*a) > nnls_abs(*b)) {
	xr = *b / *a;
/* Computing 2nd power */
	d__1 = xr;
	yr = sqrt(d__1 * d__1 + 1.);
	d__1 = 1. / yr;
	*cterm = d_sign(&d__1, a);
	*sterm = *cterm * xr;
	*sig = nnls_abs(*a) * yr;
	return 0;
    }
    if (*b != 0.) {
	xr = *a / *b;
/* Computing 2nd power */
	d__1 = xr;
	yr = sqrt(d__1 * d__1 + 1.);
	d__1 = 1. / yr;
	*sterm = d_sign(&d__1, b);
	*cterm = *sterm * xr;
	*sig = nnls_abs(*b) * yr;
	return 0;
    }
    *sig = 0.;
    *cterm = 0.;
    *sterm = 1.;
    return 0;
} /* g1_ */

/*     SUBROUTINE H12 (MODE,LPIVOT,L1,M,U,IUE,UP,C,ICE,ICV,NCV) */

/*  CONSTRUCTION AND/OR APPLICATION OF A SINGLE */
/*  HOUSEHOLDER TRANSFORMATION..     Q = I + U*(U**T)/B */

/*  The original version of this code was developed by */
/*  Charles L. Lawson and Richard J. Hanson at Jet Propulsion Laboratory */
/*  1973 JUN 12, and published in the book */
/*  "SOLVING LEAST SQUARES PROBLEMS", Prentice-HalL, 1974. */
/*  Revised FEB 1995 to accompany reprinting of the book by SIAM. */
/*     ------------------------------------------------------------------ */
/*                     Subroutine Arguments */

/*     MODE   = 1 OR 2   Selects Algorithm H1 to construct and apply a */
/*            Householder transformation, or Algorithm H2 to apply a */
/*            previously constructed transformation. */
/*     LPIVOT IS THE INDEX OF THE PIVOT ELEMENT. */
/*     L1,M   IF L1 .LE. M   THE TRANSFORMATION WILL BE CONSTRUCTED TO */
/*            ZERO ELEMENTS INDEXED FROM L1 THROUGH M.   IF L1 GT. M */
/*            THE SUBROUTINE DOES AN IDENTITY TRANSFORMATION. */
/*     U(),IUE,UP    On entry with MODE = 1, U() contains the pivot */
/*            vector.  IUE is the storage increment between elements. */
/*            On exit when MODE = 1, U() and UP contain quantities */
/*            defining the vector U of the Householder transformation. */
/*            on entry with MODE = 2, U() and UP should contain */
/*            quantities previously computed with MODE = 1.  These will */
/*            not be modified during the entry with MODE = 2. */
/*     C()    ON ENTRY with MODE = 1 or 2, C() CONTAINS A MATRIX WHICH */
/*            WILL BE REGARDED AS A SET OF VECTORS TO WHICH THE */
/*            HOUSEHOLDER TRANSFORMATION IS TO BE APPLIED. */
/*            ON EXIT C() CONTAINS THE SET OF TRANSFORMED VECTORS. */
/*     ICE    STORAGE INCREMENT BETWEEN ELEMENTS OF VECTORS IN C(). */
/*     ICV    STORAGE INCREMENT BETWEEN VECTORS IN C(). */
/*     NCV    NUMBER OF VECTORS IN C() TO BE TRANSFORMED. IF NCV .LE. 0 */
/*            NO OPERATIONS WILL BE DONE ON C(). */
/*     ------------------------------------------------------------------ */
/* Subroutine */ int h12_(mode, lpivot, l1, m, u, iue, up, c__, ice, icv, ncv)
integer *mode, *lpivot, *l1, *m;
doublereal *u;
integer *iue;
doublereal *up, *c__;
integer *ice, *icv, *ncv;
{
    /* System generated locals */
    integer u_dim1, u_offset, i__1, i__2;
    doublereal d__1, d__2;

    /* Builtin functions */
    /* The following line was commented out after the f2c translation */
    /* double sqrt(); */

    /* Local variables */
    static integer incr;
    static doublereal b;
    static integer i__, j;
    static doublereal clinv;
    static integer i2, i3, i4;
    static doublereal cl, sm;

/*     ------------------------------------------------------------------ 
*/
/*     double precision U(IUE,M) */
/*     ------------------------------------------------------------------ 
*/
    /* Parameter adjustments */
    u_dim1 = *iue;
    u_offset = u_dim1 + 1;
    u -= u_offset;
    --c__;

    /* Function Body */
    if (0 >= *lpivot || *lpivot >= *l1 || *l1 > *m) {
	return 0;
    }
    cl = (d__1 = u[*lpivot * u_dim1 + 1], nnls_abs(d__1));
    if (*mode == 2) {
	goto L60;
    }
/*                            ****** CONSTRUCT THE TRANSFORMATION. ****** 
*/
    i__1 = *m;
    for (j = *l1; j <= i__1; ++j) {
/* L10: */
/* Computing MAX */
	d__2 = (d__1 = u[j * u_dim1 + 1], nnls_abs(d__1));
	cl = nnls_max(d__2,cl);
    }
    if (cl <= 0.) {
	goto L130;
    } else {
	goto L20;
    }
L20:
    clinv = 1. / cl;
/* Computing 2nd power */
    d__1 = u[*lpivot * u_dim1 + 1] * clinv;
    sm = d__1 * d__1;
    i__1 = *m;
    for (j = *l1; j <= i__1; ++j) {
/* L30: */
/* Computing 2nd power */
	d__1 = u[j * u_dim1 + 1] * clinv;
	sm += d__1 * d__1;
    }
    cl *= sqrt(sm);
    if (u[*lpivot * u_dim1 + 1] <= 0.) {
	goto L50;
    } else {
	goto L40;
    }
L40:
    cl = -cl;
L50:
    *up = u[*lpivot * u_dim1 + 1] - cl;
    u[*lpivot * u_dim1 + 1] = cl;
    goto L70;
/*            ****** APPLY THE TRANSFORMATION  I+U*(U**T)/B  TO C. ****** 
*/

L60:
    if (cl <= 0.) {
	goto L130;
    } else {
	goto L70;
    }
L70:
    if (*ncv <= 0) {
	return 0;
    }
    b = *up * u[*lpivot * u_dim1 + 1];
/*                       B  MUST BE NONPOSITIVE HERE.  IF B = 0., RETURN. 
*/

    if (b >= 0.) {
	goto L130;
    } else {
	goto L80;
    }
L80:
    b = 1. / b;
    i2 = 1 - *icv + *ice * (*lpivot - 1);
    incr = *ice * (*l1 - *lpivot);
    i__1 = *ncv;
    for (j = 1; j <= i__1; ++j) {
	i2 += *icv;
	i3 = i2 + incr;
	i4 = i3;
	sm = c__[i2] * *up;
	i__2 = *m;
	for (i__ = *l1; i__ <= i__2; ++i__) {
	    sm += c__[i3] * u[i__ * u_dim1 + 1];
/* L90: */
	    i3 += *ice;
	}
	if (sm != 0.) {
	    goto L100;
	} else {
	    goto L120;
	}
L100:
	sm *= b;
	c__[i2] += sm * *up;
	i__2 = *m;
	for (i__ = *l1; i__ <= i__2; ++i__) {
	    c__[i4] += sm * u[i__ * u_dim1 + 1];
/* L110: */
	    i4 += *ice;
	}
L120:
	;
    }
L130:
    return 0;
} /* h12_ */

doublereal diff_(x, y)
doublereal *x, *y;
{
    /* System generated locals */
    doublereal ret_val;


/*  Function used in tests that depend on machine precision. */

/*  The original version of this code was developed by */
/*  Charles L. Lawson and Richard J. Hanson at Jet Propulsion Laboratory 
*/
/*  1973 JUN 7, and published in the book */
/*  "SOLVING LEAST SQUARES PROBLEMS", Prentice-HalL, 1974. */
/*  Revised FEB 1995 to accompany reprinting of the book by SIAM. */

    ret_val = *x - *y;
    return ret_val;
} /* diff_ */


/* The following subroutine was added after the f2c translation */
int nnls_c(double* a, const int* mda, const int* m, const int* n, double* b, 
	 double* x, double* rnorm, double* w, double* zz, int* index, 
	 int* mode)
{
  return (nnls_(a, mda, m, n, b, x, rnorm, w, zz, index, mode));
}