use machine precision from eigen instead of the one from cminpack. The test

pass though they would not if using a value of 2.220e-16 (the real value
for 'double' is 2.22044604926e-16). How sensitive those tests are :)

unsupported/Eigen/src/NonLinear/chkder.h

@@ -14,7 +14,7 @@ void chkder_template(int m, int n, const T *x,
 
     /* Local variables */
     int i__, j;
-    T eps, epsf, temp, epsmch;
+    T eps, epsf, temp;
     T epslog;
 
     /* Parameter adjustments */
@@ -29,11 +29,7 @@ void chkder_template(int m, int n, const T *x,
 
     /* Function Body */
 
-/*     epsmch is the machine precision. */
-
-    epsmch = dpmpar(1);
-
-    eps = sqrt(epsmch);
+    eps = ei_sqrt(epsilon<T>());
 
     if (mode == 2) {
 	goto L20;
@@ -56,7 +52,7 @@ L20:
 
 /*        mode = 2. */
 
-    epsf = chkder_factor * epsmch;
+    epsf = chkder_factor * epsilon<T>();
     epslog = chkder_log10e * log(eps);
     i__1 = m;
     for (i__ = 1; i__ <= i__1; ++i__) {
@@ -87,7 +83,7 @@ L20:
                        fabs(fvecp[i__]));
 	}
 	err[i__] = 1.;
-	if (temp > epsmch && temp < eps) {
+	if (temp > epsilon<T>() && temp < eps) {
 	    err[i__] = (chkder_log10e * log(temp) - epslog) / epslog;
 	}
 	if (temp >= eps) {

unsupported/Eigen/src/NonLinear/hybrd.h

@@ -28,7 +28,7 @@ int hybrd_template(minpack_func_nn fcn, void *p, int n, T *x, T *
     T pnorm, xnorm, fnorm1;
     int nslow1, nslow2;
     int ncfail;
-    T actred, epsmch, prered;
+    T actred, prered;
     int info;
 
     /* Parameter adjustments */
@@ -47,10 +47,6 @@ int hybrd_template(minpack_func_nn fcn, void *p, int n, T *x, T *
 
     /* Function Body */
 
-/*     epsmch is the machine precision. */
-
-    epsmch = dpmpar(1);
-
     info = 0;
     iflag = 0;
     *nfev = 0;
@@ -382,7 +378,7 @@ L260:
     }
 /* Computing MAX */
     d__1 = p1 * delta;
-    if (p1 * max(d__1,pnorm) <= epsmch * xnorm) {
+    if (p1 * max(d__1,pnorm) <= epsilon<T>() * xnorm) {
 	info = 3;
     }
     if (nslow2 == 5) {

unsupported/Eigen/src/NonLinear/hybrj.h

@@ -28,7 +28,7 @@ int hybrj_template(minpack_funcder_nn fcn, void *p, int n, T *x, T *
     T pnorm, xnorm, fnorm1;
     int nslow1, nslow2;
     int ncfail;
-    T actred, epsmch, prered;
+    T actred, prered;
     int info;
 
     /* Parameter adjustments */
@@ -47,10 +47,6 @@ int hybrj_template(minpack_funcder_nn fcn, void *p, int n, T *x, T *
 
     /* Function Body */
 
-/*     epsmch is the machine precision. */
-
-    epsmch = dpmpar(1);
-
     info = 0;
     iflag = 0;
     *nfev = 0;
@@ -375,7 +371,7 @@ L260:
     }
 /* Computing MAX */
     d__1 = p1 * delta;
-    if (p1 * max(d__1,pnorm) <= epsmch * xnorm) {
+    if (p1 * max(d__1,pnorm) <= epsilon<T>() * xnorm) {
 	info = 3;
     }
     if (nslow2 == 5) {

unsupported/Eigen/src/NonLinear/lmder.h

@@ -21,8 +21,7 @@ int lmder_template(minpack_funcder_mn fcn, void *p, int m, int n, T *x,
     int iflag;
     T delta;
     T ratio;
-    T fnorm, gnorm, pnorm, xnorm, fnorm1, actred, dirder, 
-	    epsmch, prered;
+    T fnorm, gnorm, pnorm, xnorm, fnorm1, actred, dirder, prered;
     int info;
 
     /* Parameter adjustments */
@@ -41,10 +40,6 @@ int lmder_template(minpack_funcder_mn fcn, void *p, int m, int n, T *x,
 
     /* Function Body */
 
-/*     epsmch is the machine precision. */
-
-    epsmch = dpmpar(1);
-
     info = 0;
     iflag = 0;
     *nfev = 0;
@@ -382,13 +377,13 @@ L290:
     if (*nfev >= maxfev) {
 	info = 5;
     }
-    if (fabs(actred) <= epsmch && prered <= epsmch && p5 * ratio <= 1.) {
+    if (fabs(actred) <= epsilon<T>() && prered <= epsilon<T>() && p5 * ratio <= 1.) {
 	info = 6;
     }
-    if (delta <= epsmch * xnorm) {
+    if (delta <= epsilon<T>() * xnorm) {
 	info = 7;
     }
-    if (gnorm <= epsmch) {
+    if (gnorm <= epsilon<T>()) {
 	info = 8;
     }
     if (info != 0) {

unsupported/Eigen/src/NonLinear/lmdif.h

@@ -24,7 +24,7 @@ int lmdif_template(minpack_func_mn fcn, void *p, int m, int n, T *x,
     T delta;
     T ratio;
     T fnorm, gnorm;
-    T pnorm, xnorm, fnorm1, actred, dirder, epsmch, prered;
+    T pnorm, xnorm, fnorm1, actred, dirder, prered;
     int info;
 
     /* Parameter adjustments */
@@ -43,10 +43,6 @@ int lmdif_template(minpack_func_mn fcn, void *p, int m, int n, T *x,
 
     /* Function Body */
 
-/*     epsmch is the machine precision. */
-
-    epsmch = dpmpar(1);
-
     info = 0;
     iflag = 0;
     *nfev = 0;
@@ -384,13 +380,13 @@ L290:
     if (*nfev >= maxfev) {
 	info = 5;
     }
-    if (fabs(actred) <= epsmch && prered <= epsmch && p5 * ratio <= 1.) {
+    if (fabs(actred) <= epsilon<T>() && prered <= epsilon<T>() && p5 * ratio <= 1.) {
 	info = 6;
     }
-    if (delta <= epsmch * xnorm) {
+    if (delta <= epsilon<T>() * xnorm) {
 	info = 7;
     }
-    if (gnorm <= epsmch) {
+    if (gnorm <= epsilon<T>()) {
 	info = 8;
     }
     if (info != 0) {

unsupported/Eigen/src/NonLinear/lmstr.h

@@ -22,8 +22,7 @@ int lmstr_template(minpack_funcderstr_mn fcn, void *p, int m, int n, T *x,
     int iflag;
     T delta;
     T ratio;
-    T fnorm, gnorm, pnorm, xnorm, fnorm1, actred, dirder, 
-	    epsmch, prered;
+    T fnorm, gnorm, pnorm, xnorm, fnorm1, actred, dirder, prered;
     int info;
 
     /* Parameter adjustments */
@@ -42,10 +41,6 @@ int lmstr_template(minpack_funcderstr_mn fcn, void *p, int m, int n, T *x,
 
     /* Function Body */
 
-/*     epsmch is the machine precision. */
-
-    epsmch = dpmpar(1);
-
     info = 0;
     iflag = 0;
     *nfev = 0;
@@ -409,13 +404,13 @@ L330:
     if (*nfev >= maxfev) {
 	info = 5;
     }
-    if (abs(actred) <= epsmch && prered <= epsmch && p5 * ratio <= 1.) {
+    if (abs(actred) <= epsilon<T>() && prered <= epsilon<T>() && p5 * ratio <= 1.) {
 	info = 6;
     }
-    if (delta <= epsmch * xnorm) {
+    if (delta <= epsilon<T>() * xnorm) {
 	info = 7;
     }
-    if (gnorm <= epsmch) {
+    if (gnorm <= epsilon<T>()) {
 	info = 8;
     }
     if (info != 0) {