#include <stdio.h>#include <math.h>
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Defines | |
| #define | nnls_max(a, b) ((a) >= (b) ? (a) : (b)) |
| #define | nnls_abs(x) ((x) >= 0 ? (x) : -(x)) |
Typedefs | |
| typedef int | integer |
| typedef double | doublereal |
Functions | |
| double | d_sign (double *a, double *b) |
| int | nnls_ (doublereal *a, integer *mda, integer *m, integer *n, doublereal *b, doublereal *x, doublereal *rnorm, doublereal *w, doublereal *zz, integer *index, integer *mode) |
| int | g1_ (doublereal *a, doublereal *b, doublereal *cterm, doublereal *sterm, doublereal *sig) |
| int | h12_ (integer *mode, integer *lpivot, integer *l1, integer *m, doublereal *u, integer *iue, doublereal *up, doublereal *c__, integer *ice, integer *icv, integer *ncv) |
| doublereal | diff_ (doublereal *x, doublereal *y) |
| 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) |
Variables | |
| static integer | c__1 = 1 |
| static integer | c__0 = 0 |
| static integer | c__2 = 2 |
Define Documentation
Typedef Documentation
| typedef double doublereal |
Function Documentation
| double d_sign | ( | double * | a, | |
| double * | b | |||
| ) |
| doublereal diff_ | ( | doublereal * | x, | |
| doublereal * | y | |||
| ) |
Definition at line 733 of file nnls.c.
{
/* 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_ */
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| int g1_ | ( | doublereal * | a, | |
| doublereal * | b, | |||
| doublereal * | cterm, | |||
| doublereal * | sterm, | |||
| doublereal * | sig | |||
| ) |
Definition at line 498 of file nnls.c.
{
/* 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_ */
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| int h12_ | ( | integer * | mode, | |
| integer * | lpivot, | |||
| integer * | l1, | |||
| integer * | m, | |||
| doublereal * | u, | |||
| integer * | iue, | |||
| doublereal * | up, | |||
| doublereal * | c__, | |||
| integer * | ice, | |||
| integer * | icv, | |||
| integer * | ncv | |||
| ) |
Definition at line 594 of file nnls.c.
{
/* 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_ */
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| int nnls_ | ( | doublereal * | a, | |
| integer * | mda, | |||
| integer * | m, | |||
| integer * | n, | |||
| doublereal * | b, | |||
| doublereal * | x, | |||
| doublereal * | rnorm, | |||
| doublereal * | w, | |||
| doublereal * | zz, | |||
| integer * | index, | |||
| integer * | mode | |||
| ) |
Definition at line 91 of file nnls.c.
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
doublereal d__1, d__2;
/* Builtin functions */
/* The following lines were commented out after the f2c translation */
/* double sqrt(); */
/* integer s_wsfe(), do_fio(), e_wsfe(); */
/* Local variables */
extern doublereal diff_();
static integer iter;
static doublereal temp, wmax;
static integer i__, j, l;
static doublereal t, alpha, asave;
static integer itmax, izmax, nsetp;
extern /* Subroutine */ int g1_();
static doublereal dummy, unorm, ztest, cc;
extern /* Subroutine */ int h12_();
static integer ii, jj, ip;
static doublereal sm;
static integer iz, jz;
static doublereal up, ss;
static integer rtnkey, iz1, iz2, npp1;
/* Fortran I/O blocks */
/* The following line was commented out after the f2c translation */
/* static cilist io___22 = { 0, 6, 0, "(/a)", 0 }; */
/* ------------------------------------------------------------------
*/
/* integer INDEX(N) */
/* double precision A(MDA,N), B(M), W(N), X(N), ZZ(M) */
/* ------------------------------------------------------------------
*/
/* Parameter adjustments */
a_dim1 = *mda;
a_offset = a_dim1 + 1;
a -= a_offset;
--b;
--x;
--w;
--zz;
--index;
/* Function Body */
*mode = 1;
if (*m <= 0 || *n <= 0) {
*mode = 2;
return 0;
}
iter = 0;
itmax = *n * 3;
/* INITIALIZE THE ARRAYS INDEX() AND X(). */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
x[i__] = 0.;
/* L20: */
index[i__] = i__;
}
iz2 = *n;
iz1 = 1;
nsetp = 0;
npp1 = 1;
/* ****** MAIN LOOP BEGINS HERE ****** */
L30:
/* QUIT IF ALL COEFFICIENTS ARE ALREADY IN THE SOLUTION.
*/
/* OR IF M COLS OF A HAVE BEEN TRIANGULARIZED. */
if (iz1 > iz2 || nsetp >= *m) {
goto L350;
}
/* COMPUTE COMPONENTS OF THE DUAL (NEGATIVE GRADIENT) VECTOR W().
*/
i__1 = iz2;
for (iz = iz1; iz <= i__1; ++iz) {
j = index[iz];
sm = 0.;
i__2 = *m;
for (l = npp1; l <= i__2; ++l) {
/* L40: */
sm += a[l + j * a_dim1] * b[l];
}
w[j] = sm;
/* L50: */
}
/* FIND LARGEST POSITIVE W(J). */
L60:
wmax = 0.;
i__1 = iz2;
for (iz = iz1; iz <= i__1; ++iz) {
j = index[iz];
if (w[j] > wmax) {
wmax = w[j];
izmax = iz;
}
/* L70: */
}
/* IF WMAX .LE. 0. GO TO TERMINATION. */
/* THIS INDICATES SATISFACTION OF THE KUHN-TUCKER CONDITIONS.
*/
if (wmax <= 0.) {
goto L350;
}
iz = izmax;
j = index[iz];
/* THE SIGN OF W(J) IS OK FOR J TO BE MOVED TO SET P. */
/* BEGIN THE TRANSFORMATION AND CHECK NEW DIAGONAL ELEMENT TO AVOID */
/* NEAR LINEAR DEPENDENCE. */
asave = a[npp1 + j * a_dim1];
i__1 = npp1 + 1;
h12_(&c__1, &npp1, &i__1, m, &a[j * a_dim1 + 1], &c__1, &up, &dummy, &
c__1, &c__1, &c__0);
unorm = 0.;
if (nsetp != 0) {
i__1 = nsetp;
for (l = 1; l <= i__1; ++l) {
/* L90: */
/* Computing 2nd power */
d__1 = a[l + j * a_dim1];
unorm += d__1 * d__1;
}
}
unorm = sqrt(unorm);
d__2 = unorm + (d__1 = a[npp1 + j * a_dim1], nnls_abs(d__1)) * .01;
if (diff_(&d__2, &unorm) > 0.) {
/* COL J IS SUFFICIENTLY INDEPENDENT. COPY B INTO ZZ, UPDATE Z
Z */
/* AND SOLVE FOR ZTEST ( = PROPOSED NEW VALUE FOR X(J) ). */
i__1 = *m;
for (l = 1; l <= i__1; ++l) {
/* L120: */
zz[l] = b[l];
}
i__1 = npp1 + 1;
h12_(&c__2, &npp1, &i__1, m, &a[j * a_dim1 + 1], &c__1, &up, &zz[1], &
c__1, &c__1, &c__1);
ztest = zz[npp1] / a[npp1 + j * a_dim1];
/* SEE IF ZTEST IS POSITIVE */
if (ztest > 0.) {
goto L140;
}
}
/* REJECT J AS A CANDIDATE TO BE MOVED FROM SET Z TO SET P. */
/* RESTORE A(NPP1,J), SET W(J)=0., AND LOOP BACK TO TEST DUAL */
/* COEFFS AGAIN. */
a[npp1 + j * a_dim1] = asave;
w[j] = 0.;
goto L60;
/* THE INDEX J=INDEX(IZ) HAS BEEN SELECTED TO BE MOVED FROM */
/* SET Z TO SET P. UPDATE B, UPDATE INDICES, APPLY HOUSEHOLDER */
/* TRANSFORMATIONS TO COLS IN NEW SET Z, ZERO SUBDIAGONAL ELTS IN */
/* COL J, SET W(J)=0. */
L140:
i__1 = *m;
for (l = 1; l <= i__1; ++l) {
/* L150: */
b[l] = zz[l];
}
index[iz] = index[iz1];
index[iz1] = j;
++iz1;
nsetp = npp1;
++npp1;
if (iz1 <= iz2) {
i__1 = iz2;
for (jz = iz1; jz <= i__1; ++jz) {
jj = index[jz];
h12_(&c__2, &nsetp, &npp1, m, &a[j * a_dim1 + 1], &c__1, &up, &a[
jj * a_dim1 + 1], &c__1, mda, &c__1);
/* L160: */
}
}
if (nsetp != *m) {
i__1 = *m;
for (l = npp1; l <= i__1; ++l) {
/* L180: */
a[l + j * a_dim1] = 0.;
}
}
w[j] = 0.;
/* SOLVE THE TRIANGULAR SYSTEM. */
/* STORE THE SOLUTION TEMPORARILY IN ZZ().
*/
rtnkey = 1;
goto L400;
L200:
/* ****** SECONDARY LOOP BEGINS HERE ****** */
/* ITERATION COUNTER. */
L210:
++iter;
if (iter > itmax) {
*mode = 3;
/* The following lines were replaced after the f2c translation */
/* s_wsfe(&io___22); */
/* do_fio(&c__1, " NNLS quitting on iteration count.", 34L); */
/* e_wsfe(); */
fprintf(stdout, "\n NNLS quitting on iteration count.\n");
fflush(stdout);
goto L350;
}
/* SEE IF ALL NEW CONSTRAINED COEFFS ARE FEASIBLE. */
/* IF NOT COMPUTE ALPHA. */
alpha = 2.;
i__1 = nsetp;
for (ip = 1; ip <= i__1; ++ip) {
l = index[ip];
if (zz[ip] <= 0.) {
t = -x[l] / (zz[ip] - x[l]);
if (alpha > t) {
alpha = t;
jj = ip;
}
}
/* L240: */
}
/* IF ALL NEW CONSTRAINED COEFFS ARE FEASIBLE THEN ALPHA WILL */
/* STILL = 2. IF SO EXIT FROM SECONDARY LOOP TO MAIN LOOP. */
if (alpha == 2.) {
goto L330;
}
/* OTHERWISE USE ALPHA WHICH WILL BE BETWEEN 0. AND 1. TO */
/* INTERPOLATE BETWEEN THE OLD X AND THE NEW ZZ. */
i__1 = nsetp;
for (ip = 1; ip <= i__1; ++ip) {
l = index[ip];
x[l] += alpha * (zz[ip] - x[l]);
/* L250: */
}
/* MODIFY A AND B AND THE INDEX ARRAYS TO MOVE COEFFICIENT I */
/* FROM SET P TO SET Z. */
i__ = index[jj];
L260:
x[i__] = 0.;
if (jj != nsetp) {
++jj;
i__1 = nsetp;
for (j = jj; j <= i__1; ++j) {
ii = index[j];
index[j - 1] = ii;
g1_(&a[j - 1 + ii * a_dim1], &a[j + ii * a_dim1], &cc, &ss, &a[j
- 1 + ii * a_dim1]);
a[j + ii * a_dim1] = 0.;
i__2 = *n;
for (l = 1; l <= i__2; ++l) {
if (l != ii) {
/* Apply procedure G2 (CC,SS,A(J-1,L),A(J,
L)) */
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_ */
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| 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 | |||
| ) |
