void ode_evaluate(
CppAD::vector<Float> &x ,
size_t m ,
CppAD::vector<Float> &fm )
{
typedef CppAD::vector<Float> Vector;
size_t n = x.size();
size_t ell;
CPPAD_ASSERT_KNOWN( m == 0 || m == 1,
"ode_evaluate: m is not zero or one"
);
CPPAD_ASSERT_KNOWN(
((m==0) & (fm.size()==n)) || ((m==1) & (fm.size()==n*n)),
"ode_evaluate: the size of fm is not correct"
);
if( m == 0 )
ell = n;
else ell = n + n * n;
// set up the case we are integrating
Float ti = 0.;
Float tf = 1.;
Float smin = 1e-5;
Float smax = 1.;
Float scur = 1.;
Float erel = 0.;
vector<Float> yi(ell), eabs(ell);
size_t i, j;
for(i = 0; i < ell; i++)
{ eabs[i] = 1e-10;
if( i < n )
yi[i] = 1.;
else yi[i] = 0.;
}
// return values
Vector yf(ell), ef(ell), maxabs(ell);
size_t nstep;
// construct ode method for taking one step
ode_evaluate_method<Float> method(m, x);
// solve differential equation
yf = OdeErrControl(method,
ti, tf, yi, smin, smax, scur, eabs, erel, ef, maxabs, nstep);
if( m == 0 )
{ for(i = 0; i < n; i++)
fm[i] = yf[i];
}
else
{ for(i = 0; i < n; i++)
for(j = 0; j < n; j++)
fm[i * n + j] = yf[n + i * n + j];
}
return;
}
bool OdeErrMaxabs(void)
{ bool ok = true; // initial return value
CppAD::vector<double> w(2);
w[0] = 10.;
w[1] = 1.;
Method method(w);
CppAD::vector<double> xi(2);
xi[0] = 1.;
xi[1] = 0.;
CppAD::vector<double> eabs(2);
eabs[0] = 0.;
eabs[1] = 0.;
CppAD::vector<double> ef(2);
CppAD::vector<double> xf(2);
CppAD::vector<double> maxabs(2);
double ti = 0.;
double tf = 1.;
double smin = .5;
double smax = 1.;
double scur = .5;
double erel = 1e-4;
bool accurate = false;
while( ! accurate )
{ xf = OdeErrControl(method,
ti, tf, xi, smin, smax, scur, eabs, erel, ef, maxabs);
accurate = true;
size_t i;
for(i = 0; i < 2; i++)
accurate &= ef[i] <= erel * maxabs[i];
if( ! accurate )
smin = smin / 2;
}
double x0 = exp(-w[0]*tf);
ok &= CppAD::NearEqual(x0, xf[0], erel, 0.);
ok &= CppAD::NearEqual(0., ef[0], erel, erel);
double x1 = w[0] * (exp(-w[0]*tf) - exp(-w[1]*tf))/(w[1] - w[0]);
ok &= CppAD::NearEqual(x1, xf[1], erel, 0.);
ok &= CppAD::NearEqual(0., ef[1], erel, erel);
return ok;
}
bool OdeErrControl_three(void)
{ bool ok = true; // initial return value
double alpha = 10.;
Method_three method(alpha);
CppAD::vector<double> xi(2);
xi[0] = 1.;
xi[1] = 0.;
CppAD::vector<double> eabs(2);
eabs[0] = 1e-4;
eabs[1] = 1e-4;
// inputs
double ti = 0.;
double tf = 1.;
double smin = 1e-4;
double smax = 1.;
double scur = 1.;
double erel = 0.;
// outputs
CppAD::vector<double> ef(2);
CppAD::vector<double> xf(2);
CppAD::vector<double> maxabs(2);
size_t nstep;
xf = OdeErrControl(method,
ti, tf, xi, smin, smax, scur, eabs, erel, ef, maxabs, nstep);
double x0 = exp( alpha * tf * tf );
ok &= CppAD::NearEqual(x0, xf[0], 1e-4, 1e-4);
ok &= CppAD::NearEqual(0., ef[0], 1e-4, 1e-4);
double root_pi = sqrt( 4. * atan(1.));
double root_alpha = sqrt( alpha );
double x1 = CppAD::erf(alpha * tf) * root_pi / (2 * root_alpha);
ok &= CppAD::NearEqual(x1, xf[1], 1e-4, 1e-4);
ok &= CppAD::NearEqual(0., ef[1], 1e-4, 1e-4);
ok &= method.F.was_negative();
return ok;
}
bool OdeGearControl(void)
{ bool ok = true; // initial return value
CPPAD_TEST_VECTOR<double> w(2);
w[0] = 10.;
w[1] = 1.;
Fun F(w);
CPPAD_TEST_VECTOR<double> xi(2);
xi[0] = 1.;
xi[1] = 0.;
CPPAD_TEST_VECTOR<double> eabs(2);
eabs[0] = 1e-4;
eabs[1] = 1e-4;
// return values
CPPAD_TEST_VECTOR<double> ef(2);
CPPAD_TEST_VECTOR<double> maxabs(2);
CPPAD_TEST_VECTOR<double> xf(2);
size_t nstep;
// input values
size_t M = 5;
double ti = 0.;
double tf = 1.;
double smin = 1e-8;
double smax = 1.;
double sini = 1e-10;
double erel = 0.;
xf = CppAD::OdeGearControl(F, M,
ti, tf, xi, smin, smax, sini, eabs, erel, ef, maxabs, nstep);
double x0 = exp(-w[0]*tf);
ok &= CppAD::NearEqual(x0, xf[0], 1e-4, 1e-4);
ok &= CppAD::NearEqual(0., ef[0], 1e-4, 1e-4);
double x1 = w[0] * (exp(-w[0]*tf) - exp(-w[1]*tf))/(w[1] - w[0]);
ok &= CppAD::NearEqual(x1, xf[1], 1e-4, 1e-4);
ok &= CppAD::NearEqual(0., ef[1], 1e-4, 1e-4);
return ok;
}
bool OdeErrControl_two(void)
{ bool ok = true; // initial return value
CppAD::vector<double> w(2);
w[0] = 10.;
w[1] = 1.;
Method_two method(w);
CppAD::vector<double> xi(2);
xi[0] = 1.;
xi[1] = 0.;
CppAD::vector<double> eabs(2);
eabs[0] = 1e-4;
eabs[1] = 1e-4;
// inputs
double ti = 0.;
double tf = 1.;
double smin = 1e-4;
double smax = 1.;
double scur = .5;
double erel = 0.;
// outputs
CppAD::vector<double> ef(2);
CppAD::vector<double> xf(2);
CppAD::vector<double> maxabs(2);
size_t nstep;
xf = OdeErrControl(method,
ti, tf, xi, smin, smax, scur, eabs, erel, ef, maxabs, nstep);
double x0 = exp(-w[0]*tf);
ok &= CppAD::NearEqual(x0, xf[0], 1e-4, 1e-4);
ok &= CppAD::NearEqual(0., ef[0], 1e-4, 1e-4);
double x1 = w[0] * (exp(-w[0]*tf) - exp(-w[1]*tf))/(w[1] - w[0]);
ok &= CppAD::NearEqual(x1, xf[1], 1e-4, 1e-4);
ok &= CppAD::NearEqual(0., ef[1], 1e-4, 1e-4);
return ok;
}
bool OdeErrControl_one(void)
{ bool ok = true; // initial return value
// Runge45 should yield exact results for x_i (t) = t^(i+1), i < 4
size_t n = 6;
// construct method for n component solution
Method_one method(n);
// inputs to OdeErrControl
double ti = 0.;
double tf = .9;
double smin = 1e-2;
double smax = 1.;
double scur = .5;
double erel = 1e-7;
CppAD::vector<double> xi(n);
CppAD::vector<double> eabs(n);
size_t i;
for(i = 0; i < n; i++)
{ xi[i] = 0.;
eabs[i] = 0.;
}
// outputs from OdeErrControl
CppAD::vector<double> ef(n);
CppAD::vector<double> xf(n);
xf = OdeErrControl(method,
ti, tf, xi, smin, smax, scur, eabs, erel, ef);
double check = 1.;
for(i = 0; i < n; i++)
{ check *= tf;
ok &= CppAD::NearEqual(check, xf[i], erel, 0.);
}
return ok;
}
bool OdeErrControl_four(void)
{ bool ok = true; // initial return value
// construct method for n component solution
size_t n = 6;
Method_four method(n);
// inputs to OdeErrControl
// special case where scur is converted to ti - tf
// (so it is not equal to smin)
double ti = 0.;
double tf = .9;
double smin = .8;
double smax = 1.;
double scur = smin;
double erel = 1e-7;
CppAD::vector<double> xi(n);
CppAD::vector<double> eabs(n);
size_t i;
for(i = 0; i < n; i++)
{ xi[i] = 0.;
eabs[i] = 0.;
}
// outputs from OdeErrControl
CppAD::vector<double> ef(n);
CppAD::vector<double> xf(n);
xf = OdeErrControl(method,
ti, tf, xi, smin, smax, scur, eabs, erel, ef);
// check that Fun_four always returning nan results in nan
for(i = 0; i < n; i++)
{ ok &= CppAD::isnan(xf[i]);
ok &= CppAD::isnan(ef[i]);
}
return ok;
}
void
compute_fringe_widths (struct frame *f, bool redraw_p)
{
int o_left = FRAME_LEFT_FRINGE_WIDTH (f);
int o_right = FRAME_RIGHT_FRINGE_WIDTH (f);
int o_cols = FRAME_FRINGE_COLS (f);
Lisp_Object left_fringe = Fassq (Qleft_fringe, f->param_alist);
Lisp_Object right_fringe = Fassq (Qright_fringe, f->param_alist);
int left_fringe_width, right_fringe_width;
if (!NILP (left_fringe))
left_fringe = Fcdr (left_fringe);
if (!NILP (right_fringe))
right_fringe = Fcdr (right_fringe);
left_fringe_width = ((NILP (left_fringe) || !INTEGERP (left_fringe)) ? 8 :
XINT (left_fringe));
right_fringe_width = ((NILP (right_fringe) || !INTEGERP (right_fringe)) ? 8 :
XINT (right_fringe));
if (left_fringe_width || right_fringe_width)
{
int left_wid = eabs (left_fringe_width);
int right_wid = eabs (right_fringe_width);
int conf_wid = left_wid + right_wid;
int font_wid = FRAME_COLUMN_WIDTH (f);
int cols = (left_wid + right_wid + font_wid-1) / font_wid;
int real_wid = cols * font_wid;
if (left_wid && right_wid)
{
if (left_fringe_width < 0)
{
/* Left fringe width is fixed, adjust right fringe if necessary */
FRAME_LEFT_FRINGE_WIDTH (f) = left_wid;
FRAME_RIGHT_FRINGE_WIDTH (f) = real_wid - left_wid;
}
else if (right_fringe_width < 0)
{
/* Right fringe width is fixed, adjust left fringe if necessary */
FRAME_LEFT_FRINGE_WIDTH (f) = real_wid - right_wid;
FRAME_RIGHT_FRINGE_WIDTH (f) = right_wid;
}
else
{
/* Adjust both fringes with an equal amount.
Note that we are doing integer arithmetic here, so don't
lose a pixel if the total width is an odd number. */
int fill = real_wid - conf_wid;
FRAME_LEFT_FRINGE_WIDTH (f) = left_wid + fill/2;
FRAME_RIGHT_FRINGE_WIDTH (f) = right_wid + fill - fill/2;
}
}
else if (left_fringe_width)
{
FRAME_LEFT_FRINGE_WIDTH (f) = real_wid;
FRAME_RIGHT_FRINGE_WIDTH (f) = 0;
}
else
{
FRAME_LEFT_FRINGE_WIDTH (f) = 0;
FRAME_RIGHT_FRINGE_WIDTH (f) = real_wid;
}
FRAME_FRINGE_COLS (f) = cols;
}
else
{
FRAME_LEFT_FRINGE_WIDTH (f) = 0;
FRAME_RIGHT_FRINGE_WIDTH (f) = 0;
FRAME_FRINGE_COLS (f) = 0;
}
if (redraw_p && FRAME_VISIBLE_P (f))
if (o_left != FRAME_LEFT_FRINGE_WIDTH (f) ||
o_right != FRAME_RIGHT_FRINGE_WIDTH (f) ||
o_cols != FRAME_FRINGE_COLS (f))
redraw_frame (f);
}
Lisp_Object
get_doc_string (Lisp_Object filepos, bool unibyte, bool definition)
{
char *from, *to, *name, *p, *p1;
int fd;
int offset;
EMACS_INT position;
Lisp_Object file, tem, pos;
ptrdiff_t count;
USE_SAFE_ALLOCA;
if (INTEGERP (filepos))
{
file = Vdoc_file_name;
pos = filepos;
}
else if (CONSP (filepos))
{
file = XCAR (filepos);
pos = XCDR (filepos);
}
else
return Qnil;
position = eabs (XINT (pos));
if (!STRINGP (Vdoc_directory))
return Qnil;
if (!STRINGP (file))
return Qnil;
/* Put the file name in NAME as a C string.
If it is relative, combine it with Vdoc_directory. */
tem = Ffile_name_absolute_p (file);
file = ENCODE_FILE (file);
Lisp_Object docdir
= NILP (tem) ? ENCODE_FILE (Vdoc_directory) : empty_unibyte_string;
ptrdiff_t docdir_sizemax = SBYTES (docdir) + 1;
#ifndef CANNOT_DUMP
docdir_sizemax = max (docdir_sizemax, sizeof sibling_etc);
#endif
name = SAFE_ALLOCA (docdir_sizemax + SBYTES (file));
lispstpcpy (lispstpcpy (name, docdir), file);
fd = emacs_open (name, O_RDONLY, 0);
if (fd < 0)
{
#ifndef CANNOT_DUMP
if (!NILP (Vpurify_flag))
{
/* Preparing to dump; DOC file is probably not installed.
So check in ../etc. */
lispstpcpy (stpcpy (name, sibling_etc), file);
fd = emacs_open (name, O_RDONLY, 0);
}
#endif
if (fd < 0)
{
if (errno == EMFILE || errno == ENFILE)
report_file_error ("Read error on documentation file", file);
SAFE_FREE ();
AUTO_STRING (cannot_open, "Cannot open doc string file \"");
AUTO_STRING (quote_nl, "\"\n");
return concat3 (cannot_open, file, quote_nl);
}
}
count = SPECPDL_INDEX ();
record_unwind_protect_int (close_file_unwind, fd);
/* Seek only to beginning of disk block. */
/* Make sure we read at least 1024 bytes before `position'
so we can check the leading text for consistency. */
offset = min (position, max (1024, position % (8 * 1024)));
if (TYPE_MAXIMUM (off_t) < position
|| lseek (fd, position - offset, 0) < 0)
error ("Position %"pI"d out of range in doc string file \"%s\"",
position, name);
/* Read the doc string into get_doc_string_buffer.
P points beyond the data just read. */
p = get_doc_string_buffer;
while (1)
{
ptrdiff_t space_left = (get_doc_string_buffer_size - 1
- (p - get_doc_string_buffer));
int nread;
/* Allocate or grow the buffer if we need to. */
if (space_left <= 0)
{
ptrdiff_t in_buffer = p - get_doc_string_buffer;
get_doc_string_buffer
= xpalloc (get_doc_string_buffer, &get_doc_string_buffer_size,
16 * 1024, -1, 1);
p = get_doc_string_buffer + in_buffer;
space_left = (get_doc_string_buffer_size - 1
- (p - get_doc_string_buffer));
}
/* Read a disk block at a time.
If we read the same block last time, maybe skip this? */
if (space_left > 1024 * 8)
space_left = 1024 * 8;
nread = emacs_read (fd, p, space_left);
if (nread < 0)
report_file_error ("Read error on documentation file", file);
p[nread] = 0;
if (!nread)
break;
if (p == get_doc_string_buffer)
p1 = strchr (p + offset, '\037');
else
p1 = strchr (p, '\037');
if (p1)
{
*p1 = 0;
p = p1;
break;
}
p += nread;
}
unbind_to (count, Qnil);
SAFE_FREE ();
/* Sanity checking. */
if (CONSP (filepos))
{
int test = 1;
/* A dynamic docstring should be either at the very beginning of a "#@
comment" or right after a dynamic docstring delimiter (in case we
pack several such docstrings within the same comment). */
if (get_doc_string_buffer[offset - test] != '\037')
{
if (get_doc_string_buffer[offset - test++] != ' ')
return Qnil;
while (get_doc_string_buffer[offset - test] >= '0'
&& get_doc_string_buffer[offset - test] <= '9')
test++;
if (get_doc_string_buffer[offset - test++] != '@'
|| get_doc_string_buffer[offset - test] != '#')
return Qnil;
}
}
else
{
int test = 1;
if (get_doc_string_buffer[offset - test++] != '\n')
return Qnil;
while (get_doc_string_buffer[offset - test] > ' ')
test++;
if (get_doc_string_buffer[offset - test] != '\037')
return Qnil;
}
/* Scan the text and perform quoting with ^A (char code 1).
^A^A becomes ^A, ^A0 becomes a null char, and ^A_ becomes a ^_. */
from = get_doc_string_buffer + offset;
to = get_doc_string_buffer + offset;
while (from != p)
{
if (*from == 1)
{
int c;
from++;
c = *from++;
if (c == 1)
*to++ = c;
else if (c == '0')
*to++ = 0;
else if (c == '_')
*to++ = 037;
else
{
unsigned char uc = c;
error ("\
Invalid data in documentation file -- %c followed by code %03o",
1, uc);
}
}
else
*to++ = *from++;
}
/* If DEFINITION, read from this buffer
the same way we would read bytes from a file. */
if (definition)
{
read_bytecode_pointer = (unsigned char *) get_doc_string_buffer + offset;
return Fread (Qlambda);
}
if (unibyte)
return make_unibyte_string (get_doc_string_buffer + offset,
to - (get_doc_string_buffer + offset));
else
{
/* The data determines whether the string is multibyte. */
ptrdiff_t nchars
= multibyte_chars_in_text (((unsigned char *) get_doc_string_buffer
+ offset),
to - (get_doc_string_buffer + offset));
return make_string_from_bytes (get_doc_string_buffer + offset,
nchars,
to - (get_doc_string_buffer + offset));
}
}
Lisp_Object
get_doc_string (Lisp_Object filepos, bool unibyte, bool definition)
{
char *from, *to, *name, *p, *p1;
int fd;
ptrdiff_t minsize;
int offset;
EMACS_INT position;
Lisp_Object file, tem, pos;
USE_SAFE_ALLOCA;
if (INTEGERP (filepos))
{
file = Vdoc_file_name;
pos = filepos;
}
else if (CONSP (filepos))
{
file = XCAR (filepos);
pos = XCDR (filepos);
}
else
return Qnil;
position = eabs (XINT (pos));
if (!STRINGP (Vdoc_directory))
return Qnil;
if (!STRINGP (file))
return Qnil;
/* Put the file name in NAME as a C string.
If it is relative, combine it with Vdoc_directory. */
tem = Ffile_name_absolute_p (file);
file = ENCODE_FILE (file);
if (NILP (tem))
{
Lisp_Object docdir = ENCODE_FILE (Vdoc_directory);
minsize = SCHARS (docdir);
/* sizeof ("../etc/") == 8 */
if (minsize < 8)
minsize = 8;
name = SAFE_ALLOCA (minsize + SCHARS (file) + 8);
strcpy (name, SSDATA (docdir));
strcat (name, SSDATA (file));
}
else
{
name = SSDATA (file);
}
fd = emacs_open (name, O_RDONLY, 0);
if (fd < 0)
{
#ifndef CANNOT_DUMP
if (!NILP (Vpurify_flag))
{
/* Preparing to dump; DOC file is probably not installed.
So check in ../etc. */
strcpy (name, "../etc/");
strcat (name, SSDATA (file));
fd = emacs_open (name, O_RDONLY, 0);
}
#endif
if (fd < 0)
return concat3 (build_string ("Cannot open doc string file \""),
file, build_string ("\"\n"));
}
/* Seek only to beginning of disk block. */
/* Make sure we read at least 1024 bytes before `position'
so we can check the leading text for consistency. */
offset = min (position, max (1024, position % (8 * 1024)));
if (TYPE_MAXIMUM (off_t) < position
|| lseek (fd, position - offset, 0) < 0)
{
emacs_close (fd);
error ("Position %"pI"d out of range in doc string file \"%s\"",
position, name);
}
SAFE_FREE ();
/* Read the doc string into get_doc_string_buffer.
P points beyond the data just read. */
p = get_doc_string_buffer;
while (1)
{
ptrdiff_t space_left = (get_doc_string_buffer_size - 1
- (p - get_doc_string_buffer));
int nread;
/* Allocate or grow the buffer if we need to. */
if (space_left <= 0)
{
ptrdiff_t in_buffer = p - get_doc_string_buffer;
get_doc_string_buffer =
xpalloc (get_doc_string_buffer, &get_doc_string_buffer_size,
16 * 1024, -1, 1);
p = get_doc_string_buffer + in_buffer;
space_left = (get_doc_string_buffer_size - 1
- (p - get_doc_string_buffer));
}
/* Read a disk block at a time.
If we read the same block last time, maybe skip this? */
if (space_left > 1024 * 8)
space_left = 1024 * 8;
nread = emacs_read (fd, p, space_left);
if (nread < 0)
{
emacs_close (fd);
error ("Read error on documentation file");
}
p[nread] = 0;
if (!nread)
break;
if (p == get_doc_string_buffer)
p1 = strchr (p + offset, '\037');
else
p1 = strchr (p, '\037');
if (p1)
{
*p1 = 0;
p = p1;
break;
}
p += nread;
}
emacs_close (fd);
/* Sanity checking. */
if (CONSP (filepos))
{
int test = 1;
if (get_doc_string_buffer[offset - test++] != ' ')
return Qnil;
while (get_doc_string_buffer[offset - test] >= '0'
&& get_doc_string_buffer[offset - test] <= '9')
test++;
if (get_doc_string_buffer[offset - test++] != '@'
|| get_doc_string_buffer[offset - test] != '#')
return Qnil;
}
else
{
int test = 1;
if (get_doc_string_buffer[offset - test++] != '\n')
return Qnil;
while (get_doc_string_buffer[offset - test] > ' ')
test++;
if (get_doc_string_buffer[offset - test] != '\037')
return Qnil;
}
/* Scan the text and perform quoting with ^A (char code 1).
^A^A becomes ^A, ^A0 becomes a null char, and ^A_ becomes a ^_. */
from = get_doc_string_buffer + offset;
to = get_doc_string_buffer + offset;
while (from != p)
{
if (*from == 1)
{
int c;
from++;
c = *from++;
if (c == 1)
*to++ = c;
else if (c == '0')
*to++ = 0;
else if (c == '_')
*to++ = 037;
else
{
unsigned char uc = c;
error ("\
Invalid data in documentation file -- %c followed by code %03o",
1, uc);
}
}
else
*to++ = *from++;
}
/* If DEFINITION, read from this buffer
the same way we would read bytes from a file. */
if (definition)
{
read_bytecode_pointer = (unsigned char *) get_doc_string_buffer + offset;
return Fread (Qlambda);
}
if (unibyte)
return make_unibyte_string (get_doc_string_buffer + offset,
to - (get_doc_string_buffer + offset));
else
{
/* The data determines whether the string is multibyte. */
ptrdiff_t nchars =
multibyte_chars_in_text (((unsigned char *) get_doc_string_buffer
+ offset),
to - (get_doc_string_buffer + offset));
return make_string_from_bytes (get_doc_string_buffer + offset,
nchars,
to - (get_doc_string_buffer + offset));
}
}
