Also, sync'ing up with the CPAN version of the module.
p4raw-id: //depot/perl@28494
'CPAN' => 1,
},
+ 'Math::Complex' =>
+ {
+ 'MAINTAINER' => 'jhi',
+ 'FILES' => q[lib/Math/Complex.pm lib/Math/Trig.pm],
+ 'CPAN' => 1,
+ },
+
'Memoize' =>
{
'MAINTAINER' => 'mjd',
use vars qw($VERSION @ISA @EXPORT @EXPORT_OK %EXPORT_TAGS $Inf);
-$VERSION = 1.35;
+$VERSION = 1.36;
BEGIN {
unless ($^O eq 'unicosmk') {
),
@trig);
-@EXPORT_OK = qw(decplx);
+my @pi = qw(pi pi2 pi4 pip2 pip4);
+
+@EXPORT_OK = @pi;
%EXPORT_TAGS = (
'trig' => [@trig],
+ 'pi' => [@pi],
);
use overload
- '+' => \&plus,
- '-' => \&minus,
- '*' => \&multiply,
- '/' => \÷,
- '**' => \&power,
- '==' => \&numeq,
- '<=>' => \&spaceship,
- 'neg' => \&negate,
- '~' => \&conjugate,
+ '+' => \&_plus,
+ '-' => \&_minus,
+ '*' => \&_multiply,
+ '/' => \&_divide,
+ '**' => \&_power,
+ '==' => \&_numeq,
+ '<=>' => \&_spaceship,
+ 'neg' => \&_negate,
+ '~' => \&_conjugate,
'abs' => \&abs,
'sqrt' => \&sqrt,
'exp' => \&exp,
'cos' => \&cos,
'tan' => \&tan,
'atan2' => \&atan2,
- qw("" stringify);
+ '""' => \&_stringify;
#
# Package "privates"
# c_dirty cartesian form not up-to-date
# p_dirty polar form not up-to-date
# display display format (package's global when not set)
+# bn_cartesian
+# bnc_dirty
#
# Die on bad *make() arguments.
}
$im ||= 0;
_cannot_make("imaginary part", $im) unless $im =~ /^$gre$/;
- $self->set_cartesian([$re, $im ]);
+ $self->_set_cartesian([$re, $im ]);
$self->display_format('cartesian');
return $self;
}
$theta ||= 0;
_cannot_make("theta", $theta) unless $theta =~ /^$gre$/;
- $self->set_polar([$rho, $theta]);
+ $self->_set_polar([$rho, $theta]);
$self->display_format('polar');
return $self;
sub pi () { 4 * CORE::atan2(1, 1) }
#
-# pit2
+# pi2
#
# The full circle
#
-sub pit2 () { 2 * pi }
+sub pi2 () { 2 * pi }
+
+#
+# pi4
+#
+# The full circle twice.
+#
+sub pi4 () { 4 * pi }
#
# pip2
sub pip2 () { pi / 2 }
#
-# deg1
+# pip4
#
-# One degree in radians, used in stringify_polar.
+# The eighth circle.
#
-
-sub deg1 () { pi / 180 }
+sub pip4 () { pi / 4 }
#
-# uplog10
+# _uplog10
#
# Used in log10().
#
-sub uplog10 () { 1 / CORE::log(10) }
+sub _uplog10 () { 1 / CORE::log(10) }
#
# i
}
#
-# ip2
+# _ip2
#
# Half of i.
#
-sub ip2 () { i / 2 }
+sub _ip2 () { i / 2 }
#
# Attribute access/set routines
#
-sub cartesian {$_[0]->{c_dirty} ?
- $_[0]->update_cartesian : $_[0]->{'cartesian'}}
-sub polar {$_[0]->{p_dirty} ?
- $_[0]->update_polar : $_[0]->{'polar'}}
+sub _cartesian {$_[0]->{c_dirty} ?
+ $_[0]->_update_cartesian : $_[0]->{'cartesian'}}
+sub _polar {$_[0]->{p_dirty} ?
+ $_[0]->_update_polar : $_[0]->{'polar'}}
-sub set_cartesian { $_[0]->{p_dirty}++; $_[0]->{c_dirty} = 0;
- $_[0]->{'cartesian'} = $_[1] }
-sub set_polar { $_[0]->{c_dirty}++; $_[0]->{p_dirty} = 0;
- $_[0]->{'polar'} = $_[1] }
+sub _set_cartesian { $_[0]->{p_dirty}++; $_[0]->{c_dirty} = 0;
+ $_[0]->{'cartesian'} = $_[1] }
+sub _set_polar { $_[0]->{c_dirty}++; $_[0]->{p_dirty} = 0;
+ $_[0]->{'polar'} = $_[1] }
#
-# ->update_cartesian
+# ->_update_cartesian
#
# Recompute and return the cartesian form, given accurate polar form.
#
-sub update_cartesian {
+sub _update_cartesian {
my $self = shift;
my ($r, $t) = @{$self->{'polar'}};
$self->{c_dirty} = 0;
#
#
-# ->update_polar
+# ->_update_polar
#
# Recompute and return the polar form, given accurate cartesian form.
#
-sub update_polar {
+sub _update_polar {
my $self = shift;
my ($x, $y) = @{$self->{'cartesian'}};
$self->{p_dirty} = 0;
}
#
-# (plus)
+# (_plus)
#
# Computes z1+z2.
#
-sub plus {
+sub _plus {
my ($z1, $z2, $regular) = @_;
- my ($re1, $im1) = @{$z1->cartesian};
+ my ($re1, $im1) = @{$z1->_cartesian};
$z2 = cplx($z2) unless ref $z2;
- my ($re2, $im2) = ref $z2 ? @{$z2->cartesian} : ($z2, 0);
+ my ($re2, $im2) = ref $z2 ? @{$z2->_cartesian} : ($z2, 0);
unless (defined $regular) {
- $z1->set_cartesian([$re1 + $re2, $im1 + $im2]);
+ $z1->_set_cartesian([$re1 + $re2, $im1 + $im2]);
return $z1;
}
return (ref $z1)->make($re1 + $re2, $im1 + $im2);
}
#
-# (minus)
+# (_minus)
#
# Computes z1-z2.
#
-sub minus {
+sub _minus {
my ($z1, $z2, $inverted) = @_;
- my ($re1, $im1) = @{$z1->cartesian};
+ my ($re1, $im1) = @{$z1->_cartesian};
$z2 = cplx($z2) unless ref $z2;
- my ($re2, $im2) = @{$z2->cartesian};
+ my ($re2, $im2) = @{$z2->_cartesian};
unless (defined $inverted) {
- $z1->set_cartesian([$re1 - $re2, $im1 - $im2]);
+ $z1->_set_cartesian([$re1 - $re2, $im1 - $im2]);
return $z1;
}
return $inverted ?
}
#
-# (multiply)
+# (_multiply)
#
# Computes z1*z2.
#
-sub multiply {
+sub _multiply {
my ($z1, $z2, $regular) = @_;
if ($z1->{p_dirty} == 0 and ref $z2 and $z2->{p_dirty} == 0) {
# if both polar better use polar to avoid rounding errors
- my ($r1, $t1) = @{$z1->polar};
- my ($r2, $t2) = @{$z2->polar};
+ my ($r1, $t1) = @{$z1->_polar};
+ my ($r2, $t2) = @{$z2->_polar};
my $t = $t1 + $t2;
- if ($t > pi()) { $t -= pit2 }
- elsif ($t <= -pi()) { $t += pit2 }
+ if ($t > pi()) { $t -= pi2 }
+ elsif ($t <= -pi()) { $t += pi2 }
unless (defined $regular) {
- $z1->set_polar([$r1 * $r2, $t]);
+ $z1->_set_polar([$r1 * $r2, $t]);
return $z1;
}
return (ref $z1)->emake($r1 * $r2, $t);
} else {
- my ($x1, $y1) = @{$z1->cartesian};
+ my ($x1, $y1) = @{$z1->_cartesian};
if (ref $z2) {
- my ($x2, $y2) = @{$z2->cartesian};
+ my ($x2, $y2) = @{$z2->_cartesian};
return (ref $z1)->make($x1*$x2-$y1*$y2, $x1*$y2+$y1*$x2);
} else {
return (ref $z1)->make($x1*$z2, $y1*$z2);
}
#
-# (divide)
+# (_divide)
#
# Computes z1/z2.
#
-sub divide {
+sub _divide {
my ($z1, $z2, $inverted) = @_;
if ($z1->{p_dirty} == 0 and ref $z2 and $z2->{p_dirty} == 0) {
# if both polar better use polar to avoid rounding errors
- my ($r1, $t1) = @{$z1->polar};
- my ($r2, $t2) = @{$z2->polar};
+ my ($r1, $t1) = @{$z1->_polar};
+ my ($r2, $t2) = @{$z2->_polar};
my $t;
if ($inverted) {
_divbyzero "$z2/0" if ($r1 == 0);
$t = $t2 - $t1;
- if ($t > pi()) { $t -= pit2 }
- elsif ($t <= -pi()) { $t += pit2 }
+ if ($t > pi()) { $t -= pi2 }
+ elsif ($t <= -pi()) { $t += pi2 }
return (ref $z1)->emake($r2 / $r1, $t);
} else {
_divbyzero "$z1/0" if ($r2 == 0);
$t = $t1 - $t2;
- if ($t > pi()) { $t -= pit2 }
- elsif ($t <= -pi()) { $t += pit2 }
+ if ($t > pi()) { $t -= pi2 }
+ elsif ($t <= -pi()) { $t += pi2 }
return (ref $z1)->emake($r1 / $r2, $t);
}
} else {
my ($d, $x2, $y2);
if ($inverted) {
- ($x2, $y2) = @{$z1->cartesian};
+ ($x2, $y2) = @{$z1->_cartesian};
$d = $x2*$x2 + $y2*$y2;
_divbyzero "$z2/0" if $d == 0;
return (ref $z1)->make(($x2*$z2)/$d, -($y2*$z2)/$d);
} else {
- my ($x1, $y1) = @{$z1->cartesian};
+ my ($x1, $y1) = @{$z1->_cartesian};
if (ref $z2) {
- ($x2, $y2) = @{$z2->cartesian};
+ ($x2, $y2) = @{$z2->_cartesian};
$d = $x2*$x2 + $y2*$y2;
_divbyzero "$z1/0" if $d == 0;
my $u = ($x1*$x2 + $y1*$y2)/$d;
}
#
-# (power)
+# (_power)
#
# Computes z1**z2 = exp(z2 * log z1)).
#
-sub power {
+sub _power {
my ($z1, $z2, $inverted) = @_;
if ($inverted) {
return 1 if $z1 == 0 || $z2 == 1;
# If both arguments cartesian, return cartesian, else polar.
return $z1->{c_dirty} == 0 &&
(not ref $z2 or $z2->{c_dirty} == 0) ?
- cplx(@{$w->cartesian}) : $w;
+ cplx(@{$w->_cartesian}) : $w;
}
#
-# (spaceship)
+# (_spaceship)
#
# Computes z1 <=> z2.
# Sorts on the real part first, then on the imaginary part. Thus 2-4i < 3+8i.
#
-sub spaceship {
+sub _spaceship {
my ($z1, $z2, $inverted) = @_;
- my ($re1, $im1) = ref $z1 ? @{$z1->cartesian} : ($z1, 0);
- my ($re2, $im2) = ref $z2 ? @{$z2->cartesian} : ($z2, 0);
+ my ($re1, $im1) = ref $z1 ? @{$z1->_cartesian} : ($z1, 0);
+ my ($re2, $im2) = ref $z2 ? @{$z2->_cartesian} : ($z2, 0);
my $sgn = $inverted ? -1 : 1;
return $sgn * ($re1 <=> $re2) if $re1 != $re2;
return $sgn * ($im1 <=> $im2);
}
#
-# (numeq)
+# (_numeq)
#
# Computes z1 == z2.
#
-# (Required in addition to spaceship() because of NaNs.)
-sub numeq {
+# (Required in addition to _spaceship() because of NaNs.)
+sub _numeq {
my ($z1, $z2, $inverted) = @_;
- my ($re1, $im1) = ref $z1 ? @{$z1->cartesian} : ($z1, 0);
- my ($re2, $im2) = ref $z2 ? @{$z2->cartesian} : ($z2, 0);
+ my ($re1, $im1) = ref $z1 ? @{$z1->_cartesian} : ($z1, 0);
+ my ($re2, $im2) = ref $z2 ? @{$z2->_cartesian} : ($z2, 0);
return $re1 == $re2 && $im1 == $im2 ? 1 : 0;
}
#
-# (negate)
+# (_negate)
#
# Computes -z.
#
-sub negate {
+sub _negate {
my ($z) = @_;
if ($z->{c_dirty}) {
- my ($r, $t) = @{$z->polar};
+ my ($r, $t) = @{$z->_polar};
$t = ($t <= 0) ? $t + pi : $t - pi;
return (ref $z)->emake($r, $t);
}
- my ($re, $im) = @{$z->cartesian};
+ my ($re, $im) = @{$z->_cartesian};
return (ref $z)->make(-$re, -$im);
}
#
-# (conjugate)
+# (_conjugate)
#
-# Compute complex's conjugate.
+# Compute complex's _conjugate.
#
-sub conjugate {
+sub _conjugate {
my ($z) = @_;
if ($z->{c_dirty}) {
- my ($r, $t) = @{$z->polar};
+ my ($r, $t) = @{$z->_polar};
return (ref $z)->emake($r, -$t);
}
- my ($re, $im) = @{$z->cartesian};
+ my ($re, $im) = @{$z->_cartesian};
return (ref $z)->make($re, -$im);
}
}
}
if (defined $rho) {
- $z->{'polar'} = [ $rho, ${$z->polar}[1] ];
+ $z->{'polar'} = [ $rho, ${$z->_polar}[1] ];
$z->{p_dirty} = 0;
$z->{c_dirty} = 1;
return $rho;
} else {
- return ${$z->polar}[0];
+ return ${$z->_polar}[0];
}
}
sub _theta {
my $theta = $_[0];
- if ($$theta > pi()) { $$theta -= pit2 }
- elsif ($$theta <= -pi()) { $$theta += pit2 }
+ if ($$theta > pi()) { $$theta -= pi2 }
+ elsif ($$theta <= -pi()) { $$theta += pi2 }
}
#
return $z unless ref $z;
if (defined $theta) {
_theta(\$theta);
- $z->{'polar'} = [ ${$z->polar}[0], $theta ];
+ $z->{'polar'} = [ ${$z->_polar}[0], $theta ];
$z->{p_dirty} = 0;
$z->{c_dirty} = 1;
} else {
- $theta = ${$z->polar}[1];
+ $theta = ${$z->_polar}[1];
_theta(\$theta);
}
return $theta;
#
sub sqrt {
my ($z) = @_;
- my ($re, $im) = ref $z ? @{$z->cartesian} : ($z, 0);
+ my ($re, $im) = ref $z ? @{$z->_cartesian} : ($z, 0);
return $re < 0 ? cplx(0, CORE::sqrt(-$re)) : CORE::sqrt($re)
if $im == 0;
- my ($r, $t) = @{$z->polar};
+ my ($r, $t) = @{$z->_polar};
return (ref $z)->emake(CORE::sqrt($r), $t/2);
}
-CORE::exp(CORE::log(-$z)/3) :
($z > 0 ? CORE::exp(CORE::log($z)/3): 0)
unless ref $z;
- my ($r, $t) = @{$z->polar};
+ my ($r, $t) = @{$z->_polar};
return 0 if $r == 0;
return (ref $z)->emake(CORE::exp(CORE::log($r)/3), $t/3);
}
my ($z, $n, $k) = @_;
_rootbad($n) if ($n < 1 or int($n) != $n);
my ($r, $t) = ref $z ?
- @{$z->polar} : (CORE::abs($z), $z >= 0 ? 0 : pi);
- my $theta_inc = pit2 / $n;
+ @{$z->_polar} : (CORE::abs($z), $z >= 0 ? 0 : pi);
+ my $theta_inc = pi2 / $n;
my $rho = $r ** (1/$n);
my $cartesian = ref $z && $z->{c_dirty} == 0;
if (@_ == 2) {
$i++, $theta += $theta_inc) {
my $w = cplxe($rho, $theta);
# Yes, $cartesian is loop invariant.
- push @root, $cartesian ? cplx(@{$w->cartesian}) : $w;
+ push @root, $cartesian ? cplx(@{$w->_cartesian}) : $w;
}
return @root;
} elsif (@_ == 3) {
my $w = cplxe($rho, $t / $n + $k * $theta_inc);
- return $cartesian ? cplx(@{$w->cartesian}) : $w;
+ return $cartesian ? cplx(@{$w->_cartesian}) : $w;
}
}
my ($z, $Re) = @_;
return $z unless ref $z;
if (defined $Re) {
- $z->{'cartesian'} = [ $Re, ${$z->cartesian}[1] ];
+ $z->{'cartesian'} = [ $Re, ${$z->_cartesian}[1] ];
$z->{c_dirty} = 0;
$z->{p_dirty} = 1;
} else {
- return ${$z->cartesian}[0];
+ return ${$z->_cartesian}[0];
}
}
my ($z, $Im) = @_;
return 0 unless ref $z;
if (defined $Im) {
- $z->{'cartesian'} = [ ${$z->cartesian}[0], $Im ];
+ $z->{'cartesian'} = [ ${$z->_cartesian}[0], $Im ];
$z->{c_dirty} = 0;
$z->{p_dirty} = 1;
} else {
- return ${$z->cartesian}[1];
+ return ${$z->_cartesian}[1];
}
}
#
sub exp {
my ($z) = @_;
- my ($x, $y) = @{$z->cartesian};
+ my ($x, $y) = @{$z->_cartesian};
return (ref $z)->emake(CORE::exp($x), $y);
}
_logofzero("log") if $z == 0;
return $z > 0 ? CORE::log($z) : cplx(CORE::log(-$z), pi);
}
- my ($r, $t) = @{$z->polar};
+ my ($r, $t) = @{$z->_polar};
_logofzero("log") if $r == 0;
- if ($t > pi()) { $t -= pit2 }
- elsif ($t <= -pi()) { $t += pit2 }
+ if ($t > pi()) { $t -= pi2 }
+ elsif ($t <= -pi()) { $t += pi2 }
return (ref $z)->make(CORE::log($r), $t);
}
#
sub log10 {
- return Math::Complex::log($_[0]) * uplog10;
+ return Math::Complex::log($_[0]) * _uplog10;
}
#
sub cos {
my ($z) = @_;
return CORE::cos($z) unless ref $z;
- my ($x, $y) = @{$z->cartesian};
+ my ($x, $y) = @{$z->_cartesian};
my $ey = CORE::exp($y);
my $sx = CORE::sin($x);
my $cx = CORE::cos($x);
sub sin {
my ($z) = @_;
return CORE::sin($z) unless ref $z;
- my ($x, $y) = @{$z->cartesian};
+ my ($x, $y) = @{$z->_cartesian};
my $ey = CORE::exp($y);
my $sx = CORE::sin($x);
my $cx = CORE::cos($x);
return CORE::atan2(CORE::sqrt(1-$z*$z), $z)
if (! ref $z) && CORE::abs($z) <= 1;
$z = cplx($z, 0) unless ref $z;
- my ($x, $y) = @{$z->cartesian};
+ my ($x, $y) = @{$z->_cartesian};
return 0 if $x == 1 && $y == 0;
my $t1 = CORE::sqrt(($x+1)*($x+1) + $y*$y);
my $t2 = CORE::sqrt(($x-1)*($x-1) + $y*$y);
return CORE::atan2($z, CORE::sqrt(1-$z*$z))
if (! ref $z) && CORE::abs($z) <= 1;
$z = cplx($z, 0) unless ref $z;
- my ($x, $y) = @{$z->cartesian};
+ my ($x, $y) = @{$z->_cartesian};
return 0 if $x == 0 && $y == 0;
my $t1 = CORE::sqrt(($x+1)*($x+1) + $y*$y);
my $t2 = CORE::sqrt(($x-1)*($x-1) + $y*$y);
sub atan {
my ($z) = @_;
return CORE::atan2($z, 1) unless ref $z;
- my ($x, $y) = ref $z ? @{$z->cartesian} : ($z, 0);
+ my ($x, $y) = ref $z ? @{$z->_cartesian} : ($z, 0);
return 0 if $x == 0 && $y == 0;
_divbyzero "atan(i)" if ( $z == i);
_logofzero "atan(-i)" if (-$z == i); # -i is a bad file test...
my $log = &log((i + $z) / (i - $z));
- return ip2 * $log;
+ return _ip2 * $log;
}
#
$ex = CORE::exp($z);
return $ex ? ($ex + 1/$ex)/2 : $Inf;
}
- my ($x, $y) = @{$z->cartesian};
+ my ($x, $y) = @{$z->_cartesian};
$ex = CORE::exp($x);
my $ex_1 = $ex ? 1 / $ex : $Inf;
return (ref $z)->make(CORE::cos($y) * ($ex + $ex_1)/2,
$ex = CORE::exp($z);
return $ex ? ($ex - 1/$ex)/2 : "-$Inf";
}
- my ($x, $y) = @{$z->cartesian};
+ my ($x, $y) = @{$z->_cartesian};
my $cy = CORE::cos($y);
my $sy = CORE::sin($y);
$ex = CORE::exp($x);
unless (ref $z) {
$z = cplx($z, 0);
}
- my ($re, $im) = @{$z->cartesian};
+ my ($re, $im) = @{$z->_cartesian};
if ($im == 0) {
return CORE::log($re + CORE::sqrt($re*$re - 1))
if $re >= 1;
my ($z1, $z2, $inverted) = @_;
my ($re1, $im1, $re2, $im2);
if ($inverted) {
- ($re1, $im1) = ref $z2 ? @{$z2->cartesian} : ($z2, 0);
- ($re2, $im2) = ref $z1 ? @{$z1->cartesian} : ($z1, 0);
+ ($re1, $im1) = ref $z2 ? @{$z2->_cartesian} : ($z2, 0);
+ ($re2, $im2) = ref $z1 ? @{$z1->_cartesian} : ($z1, 0);
} else {
- ($re1, $im1) = ref $z1 ? @{$z1->cartesian} : ($z1, 0);
- ($re2, $im2) = ref $z2 ? @{$z2->cartesian} : ($z2, 0);
+ ($re1, $im1) = ref $z1 ? @{$z1->_cartesian} : ($z1, 0);
+ ($re2, $im2) = ref $z2 ? @{$z2->_cartesian} : ($z2, 0);
}
if ($im1 || $im2) {
# In MATLAB the imaginary parts are ignored.
}
#
-# (stringify)
+# (_stringify)
#
# Show nicely formatted complex number under its cartesian or polar form,
# depending on the current display format:
# . Otherwise, use the generic current default for all complex numbers,
# which is a package global variable.
#
-sub stringify {
+sub _stringify {
my ($z) = shift;
my $style = $z->display_format;
$style = $DISPLAY_FORMAT{style} unless defined $style;
- return $z->stringify_polar if $style =~ /^p/i;
- return $z->stringify_cartesian;
+ return $z->_stringify_polar if $style =~ /^p/i;
+ return $z->_stringify_cartesian;
}
#
-# ->stringify_cartesian
+# ->_stringify_cartesian
#
# Stringify as a cartesian representation 'a+bi'.
#
-sub stringify_cartesian {
+sub _stringify_cartesian {
my $z = shift;
- my ($x, $y) = @{$z->cartesian};
+ my ($x, $y) = @{$z->_cartesian};
my ($re, $im);
my %format = $z->display_format;
#
-# ->stringify_polar
+# ->_stringify_polar
#
# Stringify as a polar representation '[r,t]'.
#
-sub stringify_polar {
+sub _stringify_polar {
my $z = shift;
- my ($r, $t) = @{$z->polar};
+ my ($r, $t) = @{$z->_polar};
my $theta;
my %format = $z->display_format;
# Try to identify pi/n and friends.
#
- $t -= int(CORE::abs($t) / pit2) * pit2;
+ $t -= int(CORE::abs($t) / pi2) * pi2;
if ($format{polar_pretty_print} && $t) {
my ($a, $b);
In other words, it's the projection of the vector onto the I<x> and I<y>
axes. Mathematicians call I<rho> the I<norm> or I<modulus> and I<theta>
-the I<argument> of the complex number. The I<norm> of C<z> will be
-noted C<abs(z)>.
+the I<argument> of the complex number. The I<norm> of C<z> is
+marked here as C<abs(z)>.
-The polar notation (also known as the trigonometric
-representation) is much more handy for performing multiplications and
-divisions of complex numbers, whilst the cartesian notation is better
-suited for additions and subtractions. Real numbers are on the I<x>
-axis, and therefore I<theta> is zero or I<pi>.
+The polar notation (also known as the trigonometric representation) is
+much more handy for performing multiplications and divisions of
+complex numbers, whilst the cartesian notation is better suited for
+additions and subtractions. Real numbers are on the I<x> axis, and
+therefore I<y> or I<theta> is zero or I<pi>.
All the common operations that can be performed on a real number have
been defined to work on complex numbers as well, and are merely
-i log((x + iy)/sqrt(x*x+y*y))
+Note that atan2(0, 0) is not well-defined.
+
The following extra operations are supported on both real and complex
numbers:
$j->arg(2); # (the last two aka rho, theta)
# can be used also as mutators.
+=head2 PI
+
+The constant C<pi> and some handy multiples of it (pi2, pi4,
+and pip2 (pi/2) and pip4 (pi/4)) are also available if separately
+exported:
+
+ use Math::Complex ':pi';
+ $third_of_circle = pi2 / 3;
+
=head1 ERRORS DUE TO DIVISION BY ZERO OR LOGARITHM OF ZERO
The division (/) and the following functions
=head1 AUTHORS
-Daniel S. Lewart <F<d-lewart@uiuc.edu>>
-
-Original authors Raphael Manfredi <F<Raphael_Manfredi@pobox.com>> and
-Jarkko Hietaniemi <F<jhi@iki.fi>>
+Daniel S. Lewart <F<lewart!at!uiuc.edu>>
+Jarkko Hietaniemi <F<jhi!at!iki.fi>>
+Raphael Manfredi <F<Raphael_Manfredi!at!pobox.com>>
=cut
# check the op= works
push @script, <<EOB;
{
- my \$za = cplx(ref \$z0 ? \@{\$z0->cartesian} : (\$z0, 0));
+ my \$za = cplx(ref \$z0 ? \@{\$z0->_cartesian} : (\$z0, 0));
- my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->cartesian} : (\$z1, 0);
+ my (\$z1r, \$z1i) = ref \$z1 ? \@{\$z1->_cartesian} : (\$z1, 0);
my \$zb = cplx(\$z1r, \$z1i);
\$za $op= \$zb;
- my (\$zbr, \$zbi) = \@{\$zb->cartesian};
+ my (\$zbr, \$zbi) = \@{\$zb->_cartesian};
check($test, '\$z0 $op= \$z1', \$za, \$z$#args, $args);
EOB
(-100,0):(0,10)
(16,-30):(5,-3)
-&stringify_cartesian
+&_stringify_cartesian
(-100,0):"-100"
(0,1):"i"
(4,-3):"4-3i"
(-2,4):"-2+4i"
(-2,-1):"-2-i"
-&stringify_polar
+&_stringify_polar
[-1, 0]:"[1,pi]"
[1, pi/3]:"[1,pi/3]"
[6, -2*pi/3]:"[6,-2pi/3]"
require Exporter;
package Math::Trig;
-use 5.006;
+use 5.005;
use strict;
-use Math::Complex 1.35;
-use Math::Complex qw(:trig);
+use Math::Complex 1.36;
+use Math::Complex qw(:trig :pi);
-our($VERSION, $PACKAGE, @ISA, @EXPORT, @EXPORT_OK, %EXPORT_TAGS);
+use vars qw($VERSION $PACKAGE @ISA @EXPORT @EXPORT_OK %EXPORT_TAGS);
@ISA = qw(Exporter);
-$VERSION = 1.03;
+$VERSION = 1.04;
my @angcnv = qw(rad2deg rad2grad
deg2rad deg2grad
great_circle_destination
);
-my @pi = qw(pi2 pip2 pip4);
+my @pi = qw(pi pi2 pi4 pip2 pip4);
@EXPORT_OK = (@rdlcnv, @greatcircle, @pi);
'great_circle' => [ @greatcircle ],
'pi' => [ @pi ]);
-sub pi2 () { 2 * pi }
-sub pip2 () { pi / 2 }
-sub pip4 () { pi / 4 }
-
-sub DR () { pi2/360 }
-sub RD () { 360/pi2 }
-sub DG () { 400/360 }
-sub GD () { 360/400 }
-sub RG () { 400/pi2 }
-sub GR () { pi2/400 }
+sub _DR () { pi2/360 }
+sub _RD () { 360/pi2 }
+sub _DG () { 400/360 }
+sub _GD () { 360/400 }
+sub _RG () { 400/pi2 }
+sub _GR () { pi2/400 }
#
# Truncating remainder.
#
-sub remt ($$) {
+sub _remt ($$) {
# Oh yes, POSIX::fmod() would be faster. Possibly. If it is available.
$_[0] - $_[1] * int($_[0] / $_[1]);
}
# Angle conversions.
#
-sub rad2rad($) { remt($_[0], pi2) }
+sub rad2rad($) { _remt($_[0], pi2) }
-sub deg2deg($) { remt($_[0], 360) }
+sub deg2deg($) { _remt($_[0], 360) }
-sub grad2grad($) { remt($_[0], 400) }
+sub grad2grad($) { _remt($_[0], 400) }
-sub rad2deg ($;$) { my $d = RD * $_[0]; $_[1] ? $d : deg2deg($d) }
+sub rad2deg ($;$) { my $d = _RD * $_[0]; $_[1] ? $d : deg2deg($d) }
-sub deg2rad ($;$) { my $d = DR * $_[0]; $_[1] ? $d : rad2rad($d) }
+sub deg2rad ($;$) { my $d = _DR * $_[0]; $_[1] ? $d : rad2rad($d) }
-sub grad2deg ($;$) { my $d = GD * $_[0]; $_[1] ? $d : deg2deg($d) }
+sub grad2deg ($;$) { my $d = _GD * $_[0]; $_[1] ? $d : deg2deg($d) }
-sub deg2grad ($;$) { my $d = DG * $_[0]; $_[1] ? $d : grad2grad($d) }
+sub deg2grad ($;$) { my $d = _DG * $_[0]; $_[1] ? $d : grad2grad($d) }
-sub rad2grad ($;$) { my $d = RG * $_[0]; $_[1] ? $d : grad2grad($d) }
+sub rad2grad ($;$) { my $d = _RG * $_[0]; $_[1] ? $d : grad2grad($d) }
-sub grad2rad ($;$) { my $d = GR * $_[0]; $_[1] ? $d : rad2rad($d) }
+sub grad2rad ($;$) { my $d = _GR * $_[0]; $_[1] ? $d : rad2rad($d) }
sub cartesian_to_spherical {
my ( $x, $y, $z ) = @_;
=head1 SYNOPSIS
- use Math::Trig;
+ use Math::Trig;
- $x = tan(0.9);
- $y = acos(3.7);
- $z = asin(2.4);
+ $x = tan(0.9);
+ $y = acos(3.7);
+ $z = asin(2.4);
- $halfpi = pi/2;
+ $halfpi = pi/2;
- $rad = deg2rad(120);
+ $rad = deg2rad(120);
- # Import constants pi2, pip2, pip4 (2*pi, pi/2, pi/4).
- use Math::Trig ':pi';
+ # Import constants pi2, pip2, pip4 (2*pi, pi/2, pi/4).
+ use Math::Trig ':pi';
- # Import the conversions between cartesian/spherical/cylindrical.
- use Math::Trig ':radial';
+ # Import the conversions between cartesian/spherical/cylindrical.
+ use Math::Trig ':radial';
# Import the great circle formulas.
- use Math::Trig ':great_circle';
+ use Math::Trig ':great_circle';
=head1 DESCRIPTION
B<atan2>(y, x)
The arcus cofunctions of the sine, cosine, and tangent (acosec/acsc
-and acotan/acot are aliases)
+and acotan/acot are aliases). Note that atan2(0, 0) is not well-defined.
B<acsc>, B<acosec>, B<asec>, B<acot>, B<acotan>
B<acsch>, B<acosech>, B<asech>, B<acoth>, B<acotanh>
-The trigonometric constant B<pi> is also defined.
+The trigonometric constant B<pi> and some of handy multiples
+of it are also defined.
-$pi2 = 2 * B<pi>;
+B<pi, pi2, pi4, pip2, pip4>
=head2 ERRORS DUE TO DIVISION BY ZERO
The following functions
- acoth
- acsc
- acsch
- asec
- asech
- atanh
- cot
- coth
- csc
- csch
- sec
- sech
- tan
- tanh
+ acoth
+ acsc
+ acsch
+ asec
+ asech
+ atanh
+ cot
+ coth
+ csc
+ csch
+ sec
+ sech
+ tan
+ tanh
cannot be computed for all arguments because that would mean dividing
by zero or taking logarithm of zero. These situations cause fatal
runtime errors looking like this
- cot(0): Division by zero.
- (Because in the definition of cot(0), the divisor sin(0) is 0)
- Died at ...
+ cot(0): Division by zero.
+ (Because in the definition of cot(0), the divisor sin(0) is 0)
+ Died at ...
or
- atanh(-1): Logarithm of zero.
- Died at...
+ atanh(-1): Logarithm of zero.
+ Died at...
For the C<csc>, C<cot>, C<asec>, C<acsc>, C<acot>, C<csch>, C<coth>,
C<asech>, C<acsch>, the argument cannot be C<0> (zero). For the
C<atanh>, C<acoth>, the argument cannot be C<1> (one). For the
C<atanh>, C<acoth>, the argument cannot be C<-1> (minus one). For the
C<tan>, C<sec>, C<tanh>, C<sech>, the argument cannot be I<pi/2 + k *
-pi>, where I<k> is any integer. atan2(0, 0) is undefined.
+pi>, where I<k> is any integer.
+
+Note that atan2(0, 0) is not well-defined.
=head2 SIMPLE (REAL) ARGUMENTS, COMPLEX RESULTS
complex numbers as results because the C<Math::Complex> takes care of
details like for example how to display complex numbers. For example:
- print asin(2), "\n";
+ print asin(2), "\n";
should produce something like this (take or leave few last decimals):
- 1.5707963267949-1.31695789692482i
+ 1.5707963267949-1.31695789692482i
That is, a complex number with the real part of approximately C<1.571>
and the imaginary part of approximately C<-1.317>.
(Plane, 2-dimensional) angles may be converted with the following functions.
- $radians = deg2rad($degrees);
- $radians = grad2rad($gradians);
+=over
+
+=item deg2rad
+
+ $radians = deg2rad($degrees);
+
+=item grad2rad
+
+ $radians = grad2rad($gradians);
+
+=item rad2deg
+
+ $degrees = rad2deg($radians);
- $degrees = rad2deg($radians);
- $degrees = grad2deg($gradians);
+=item grad2deg
- $gradians = deg2grad($degrees);
- $gradians = rad2grad($radians);
+ $degrees = grad2deg($gradians);
+
+=item deg2grad
+
+ $gradians = deg2grad($degrees);
+
+=item rad2grad
+
+ $gradians = rad2grad($radians);
+
+=back
The full circle is 2 I<pi> radians or I<360> degrees or I<400> gradians.
The result is by default wrapped to be inside the [0, {2pi,360,400}[ circle.
If you don't want this, supply a true second argument:
- $zillions_of_radians = deg2rad($zillions_of_degrees, 1);
- $negative_degrees = rad2deg($negative_radians, 1);
+ $zillions_of_radians = deg2rad($zillions_of_degrees, 1);
+ $negative_degrees = rad2deg($negative_radians, 1);
You can also do the wrapping explicitly by rad2rad(), deg2deg(), and
grad2grad().
+=over 4
+
+=item rad2rad
+
+ $radians_wrapped_by_2pi = rad2rad($radians);
+
+=item deg2deg
+
+ $degrees_wrapped_by_360 = deg2deg($degrees);
+
+=item grad2grad
+
+ $gradians_wrapped_by_400 = grad2grad($gradians);
+
+=back
+
=head1 RADIAL COORDINATE CONVERSIONS
B<Radial coordinate systems> are the B<spherical> and the B<cylindrical>
=item cartesian_to_cylindrical
- ($rho, $theta, $z) = cartesian_to_cylindrical($x, $y, $z);
+ ($rho, $theta, $z) = cartesian_to_cylindrical($x, $y, $z);
=item cartesian_to_spherical
- ($rho, $theta, $phi) = cartesian_to_spherical($x, $y, $z);
+ ($rho, $theta, $phi) = cartesian_to_spherical($x, $y, $z);
=item cylindrical_to_cartesian
- ($x, $y, $z) = cylindrical_to_cartesian($rho, $theta, $z);
+ ($x, $y, $z) = cylindrical_to_cartesian($rho, $theta, $z);
=item cylindrical_to_spherical
- ($rho_s, $theta, $phi) = cylindrical_to_spherical($rho_c, $theta, $z);
+ ($rho_s, $theta, $phi) = cylindrical_to_spherical($rho_c, $theta, $z);
Notice that when C<$z> is not 0 C<$rho_s> is not equal to C<$rho_c>.
=item spherical_to_cartesian
- ($x, $y, $z) = spherical_to_cartesian($rho, $theta, $phi);
+ ($x, $y, $z) = spherical_to_cartesian($rho, $theta, $phi);
=item spherical_to_cylindrical
- ($rho_c, $theta, $z) = spherical_to_cylindrical($rho_s, $theta, $phi);
+ ($rho_c, $theta, $z) = spherical_to_cylindrical($rho_s, $theta, $phi);
Notice that when C<$z> is not 0 C<$rho_c> is not equal to C<$rho_s>.
=head1 GREAT CIRCLE DISTANCES AND DIRECTIONS
+A great circle is section of a circle that contains the circle
+diameter: the shortest distance between two (non-antipodal) points on
+the spherical surface goes along the great circle connecting those two
+points.
+
+=head2 great_circle_distance
+
You can compute spherical distances, called B<great circle distances>,
by importing the great_circle_distance() function:
$distance = great_circle_distance($lon0, pi/2 - $lat0,
$lon1, pi/2 - $lat1, $rho);
+=head2 great_circle_direction
+
The direction you must follow the great circle (also known as I<bearing>)
can be computed by the great_circle_direction() function:
$direction = great_circle_direction($theta0, $phi0, $theta1, $phi1);
-(Alias 'great_circle_bearing' is also available.)
-The result is in radians, zero indicating straight north, pi or -pi
-straight south, pi/2 straight west, and -pi/2 straight east.
+=head2 great_circle_bearing
+
+Alias 'great_circle_bearing' for 'great_circle_direction' is also available.
+
+ use Math::Trig 'great_circle_bearing';
+
+ $direction = great_circle_bearing($theta0, $phi0, $theta1, $phi1);
+
+The result of great_circle_direction is in radians, zero indicating
+straight north, pi or -pi straight south, pi/2 straight west, and
+-pi/2 straight east.
You can inversely compute the destination if you know the
starting point, direction, and distance:
+=head2 great_circle_destination
+
use Math::Trig 'great_circle_destination';
# thetad and phid are the destination coordinates,
or the midpoint if you know the end points:
+=head2 great_circle_midpoint
+
use Math::Trig 'great_circle_midpoint';
($thetam, $phim) =
The great_circle_midpoint() is just a special case of
+=head2 great_circle_waypoint
+
use Math::Trig 'great_circle_waypoint';
($thetai, $phii) =
To calculate the distance between London (51.3N 0.5W) and Tokyo
(35.7N 139.8E) in kilometers:
- use Math::Trig qw(great_circle_distance deg2rad);
+ use Math::Trig qw(great_circle_distance deg2rad);
- # Notice the 90 - latitude: phi zero is at the North Pole.
- sub NESW { deg2rad($_[0]), deg2rad(90 - $_[1]) }
- my @L = NESW( -0.5, 51.3);
- my @T = NESW(139.8, 35.7);
- my $km = great_circle_distance(@L, @T, 6378); # About 9600 km.
+ # Notice the 90 - latitude: phi zero is at the North Pole.
+ sub NESW { deg2rad($_[0]), deg2rad(90 - $_[1]) }
+ my @L = NESW( -0.5, 51.3);
+ my @T = NESW(139.8, 35.7);
+ my $km = great_circle_distance(@L, @T, 6378); # About 9600 km.
The direction you would have to go from London to Tokyo (in radians,
straight north being zero, straight east being pi/2).
- use Math::Trig qw(great_circle_direction);
+ use Math::Trig qw(great_circle_direction);
- my $rad = great_circle_direction(@L, @T); # About 0.547 or 0.174 pi.
+ my $rad = great_circle_direction(@L, @T); # About 0.547 or 0.174 pi.
The midpoint between London and Tokyo being
- use Math::Trig qw(great_circle_midpoint);
+ use Math::Trig qw(great_circle_midpoint);
- my @M = great_circle_midpoint(@L, @T);
+ my @M = great_circle_midpoint(@L, @T);
or about 68.11N 24.74E, in the Finnish Lapland.
=head1 AUTHORS
-Jarkko Hietaniemi <F<jhi@iki.fi>> and
-Raphael Manfredi <F<Raphael_Manfredi@pobox.com>>.
+Jarkko Hietaniemi <F<jhi!at!iki.fi>> and
+Raphael Manfredi <F<Raphael_Manfredi!at!pobox.com>>.
=cut
}
}
+BEGIN {
+ eval { require Test::More };
+ if ($@) {
+ # We are willing to lose testing in e.g. 5.00504.
+ print "1..0 # No Test::More, skipping\n";
+ exit(0);
+ } else {
+ import Test::More;
+ }
+}
+
+plan(tests => 69);
+
use Math::Trig 1.03;
my $pip2 = pi / 2;
sub near ($$;$) {
my $e = defined $_[2] ? $_[2] : $eps;
- print "# near? $_[0] $_[1] $e\n";
- $_[1] ? (abs($_[0]/$_[1] - 1) < $e) : abs($_[0]) < $e;
+ my $d = $_[1] ? abs($_[0]/$_[1] - 1) : abs($_[0]);
+ print "# near? $_[0] $_[1] : $d : $e\n";
+ $_[1] ? ($d < $e) : abs($_[0]) < $e;
}
-print "1..49\n";
-
$x = 0.9;
-print 'not ' unless (near(tan($x), sin($x) / cos($x)));
-print "ok 1\n";
+ok(near(tan($x), sin($x) / cos($x)));
-print 'not ' unless (near(sinh(2), 3.62686040784702));
-print "ok 2\n";
+ok(near(sinh(2), 3.62686040784702));
-print 'not ' unless (near(acsch(0.1), 2.99822295029797));
-print "ok 3\n";
+ok(near(acsch(0.1), 2.99822295029797));
$x = asin(2);
-print 'not ' unless (ref $x eq 'Math::Complex');
-print "ok 4\n";
+is(ref $x, 'Math::Complex');
# avoid using Math::Complex here
$x =~ /^([^-]+)(-[^i]+)i$/;
($y, $z) = ($1, $2);
-print 'not ' unless (near($y, 1.5707963267949) and
- near($z, -1.31695789692482));
-print "ok 5\n";
+ok(near($y, 1.5707963267949));
+ok(near($z, -1.31695789692482));
-print 'not ' unless (near(deg2rad(90), pi/2));
-print "ok 6\n";
+ok(near(deg2rad(90), pi/2));
-print 'not ' unless (near(rad2deg(pi), 180));
-print "ok 7\n";
+ok(near(rad2deg(pi), 180));
use Math::Trig ':radial';
{
my ($r,$t,$z) = cartesian_to_cylindrical(1,1,1);
- print 'not ' unless (near($r, sqrt(2))) and
- (near($t, deg2rad(45))) and
- (near($z, 1));
- print "ok 8\n";
+ ok(near($r, sqrt(2)));
+ ok(near($t, deg2rad(45)));
+ ok(near($z, 1));
($x,$y,$z) = cylindrical_to_cartesian($r, $t, $z);
- print 'not ' unless (near($x, 1)) and
- (near($y, 1)) and
- (near($z, 1));
- print "ok 9\n";
+ ok(near($x, 1));
+ ok(near($y, 1));
+ ok(near($z, 1));
($r,$t,$z) = cartesian_to_cylindrical(1,1,0);
- print 'not ' unless (near($r, sqrt(2))) and
- (near($t, deg2rad(45))) and
- (near($z, 0));
- print "ok 10\n";
+ ok(near($r, sqrt(2)));
+ ok(near($t, deg2rad(45)));
+ ok(near($z, 0));
($x,$y,$z) = cylindrical_to_cartesian($r, $t, $z);
- print 'not ' unless (near($x, 1)) and
- (near($y, 1)) and
- (near($z, 0));
- print "ok 11\n";
+ ok(near($x, 1));
+ ok(near($y, 1));
+ ok(near($z, 0));
}
{
my ($r,$t,$f) = cartesian_to_spherical(1,1,1);
- print 'not ' unless (near($r, sqrt(3))) and
- (near($t, deg2rad(45))) and
- (near($f, atan2(sqrt(2), 1)));
- print "ok 12\n";
+ ok(near($r, sqrt(3)));
+ ok(near($t, deg2rad(45)));
+ ok(near($f, atan2(sqrt(2), 1)));
($x,$y,$z) = spherical_to_cartesian($r, $t, $f);
- print 'not ' unless (near($x, 1)) and
- (near($y, 1)) and
- (near($z, 1));
- print "ok 13\n";
-
+ ok(near($x, 1));
+ ok(near($y, 1));
+ ok(near($z, 1));
+
($r,$t,$f) = cartesian_to_spherical(1,1,0);
- print 'not ' unless (near($r, sqrt(2))) and
- (near($t, deg2rad(45))) and
- (near($f, deg2rad(90)));
- print "ok 14\n";
+ ok(near($r, sqrt(2)));
+ ok(near($t, deg2rad(45)));
+ ok(near($f, deg2rad(90)));
($x,$y,$z) = spherical_to_cartesian($r, $t, $f);
- print 'not ' unless (near($x, 1)) and
- (near($y, 1)) and
- (near($z, 0));
- print "ok 15\n";
+ ok(near($x, 1));
+ ok(near($y, 1));
+ ok(near($z, 0));
}
{
my ($r,$t,$z) = cylindrical_to_spherical(spherical_to_cylindrical(1,1,1));
- print 'not ' unless (near($r, 1)) and
- (near($t, 1)) and
- (near($z, 1));
- print "ok 16\n";
+ ok(near($r, 1));
+ ok(near($t, 1));
+ ok(near($z, 1));
($r,$t,$z) = spherical_to_cylindrical(cylindrical_to_spherical(1,1,1));
- print 'not ' unless (near($r, 1)) and
- (near($t, 1)) and
- (near($z, 1));
- print "ok 17\n";
+ ok(near($r, 1));
+ ok(near($t, 1));
+ ok(near($z, 1));
}
{
use Math::Trig 'great_circle_distance';
- print 'not '
- unless (near(great_circle_distance(0, 0, 0, pi/2), pi/2));
- print "ok 18\n";
+ ok(near(great_circle_distance(0, 0, 0, pi/2), pi/2));
- print 'not '
- unless (near(great_circle_distance(0, 0, pi, pi), pi));
- print "ok 19\n";
+ ok(near(great_circle_distance(0, 0, pi, pi), pi));
# London to Tokyo.
my @L = (deg2rad(-0.5), deg2rad(90 - 51.3));
my $km = great_circle_distance(@L, @T, 6378);
- print 'not ' unless (near($km, 9605.26637021388));
- print "ok 20\n";
+ ok(near($km, 9605.26637021388));
}
{
sub frac { $_[0] - int($_[0]) }
my $lotta_radians = deg2rad(1E+20, 1);
- print "not " unless near($lotta_radians, 1E+20/$R2D);
- print "ok 21\n";
+ ok(near($lotta_radians, 1E+20/$R2D));
my $negat_degrees = rad2deg(-1E20, 1);
- print "not " unless near($negat_degrees, -1E+20*$R2D);
- print "ok 22\n";
+ ok(near($negat_degrees, -1E+20*$R2D));
my $posit_degrees = rad2deg(-10000, 1);
- print "not " unless near($posit_degrees, -10000*$R2D);
- print "ok 23\n";
+ ok(near($posit_degrees, -10000*$R2D));
}
{
use Math::Trig 'great_circle_direction';
- print 'not '
- unless (near(great_circle_direction(0, 0, 0, pi/2), pi));
- print "ok 24\n";
+ ok(near(great_circle_direction(0, 0, 0, pi/2), pi));
# Retired test: Relies on atan2(0, 0), which is not portable.
-# print 'not '
-# unless (near(great_circle_direction(0, 0, pi, pi), -pi()/2));
- print "ok 25\n";
+# ok(near(great_circle_direction(0, 0, pi, pi), -pi()/2));
my @London = (deg2rad( -0.167), deg2rad(90 - 51.3));
my @Tokyo = (deg2rad( 139.5), deg2rad(90 - 35.7));
my @Berlin = (deg2rad ( 13.417), deg2rad(90 - 52.533));
my @Paris = (deg2rad ( 2.333), deg2rad(90 - 48.867));
- print 'not '
- unless (near(rad2deg(great_circle_direction(@London, @Tokyo)),
- 31.791945393073));
- print "ok 26\n";
+ ok(near(rad2deg(great_circle_direction(@London, @Tokyo)),
+ 31.791945393073));
- print 'not '
- unless (near(rad2deg(great_circle_direction(@Tokyo, @London)),
- 336.069766430326));
- print "ok 27\n";
+ ok(near(rad2deg(great_circle_direction(@Tokyo, @London)),
+ 336.069766430326));
- print 'not '
- unless (near(rad2deg(great_circle_direction(@Berlin, @Paris)),
- 246.800348034667));
+ ok(near(rad2deg(great_circle_direction(@Berlin, @Paris)),
+ 246.800348034667));
- print "ok 28\n";
-
- print 'not '
- unless (near(rad2deg(great_circle_direction(@Paris, @Berlin)),
- 58.2079877553156));
- print "ok 29\n";
+ ok(near(rad2deg(great_circle_direction(@Paris, @Berlin)),
+ 58.2079877553156));
use Math::Trig 'great_circle_bearing';
- print 'not '
- unless (near(rad2deg(great_circle_bearing(@Paris, @Berlin)),
- 58.2079877553156));
- print "ok 30\n";
+ ok(near(rad2deg(great_circle_bearing(@Paris, @Berlin)),
+ 58.2079877553156));
use Math::Trig 'great_circle_waypoint';
use Math::Trig 'great_circle_midpoint';
($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.0);
- print 'not ' unless (near($lon, $London[0]));
- print "ok 31\n";
+ ok(near($lon, $London[0]));
- print 'not ' unless (near($lat, $pip2 - $London[1]));
- print "ok 32\n";
+ ok(near($lat, $pip2 - $London[1]));
($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 1.0);
- print 'not ' unless (near($lon, $Tokyo[0]));
- print "ok 33\n";
+ ok(near($lon, $Tokyo[0]));
- print 'not ' unless (near($lat, $pip2 - $Tokyo[1]));
- print "ok 34\n";
+ ok(near($lat, $pip2 - $Tokyo[1]));
($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.5);
- print 'not ' unless (near($lon, 1.55609593577679)); # 89.1577 E
- print "ok 35\n";
+ ok(near($lon, 1.55609593577679)); # 89.1577 E
- print 'not ' unless (near($lat, 1.20296099733328)); # 68.9246 N
- print "ok 36\n";
+ ok(near($lat, 1.20296099733328)); # 68.9246 N
($lon, $lat) = great_circle_midpoint(@London, @Tokyo);
- print 'not ' unless (near($lon, 1.55609593577679)); # 89.1577 E
- print "ok 37\n";
+ ok(near($lon, 1.55609593577679)); # 89.1577 E
- print 'not ' unless (near($lat, 1.20296099733328)); # 68.9246 N
- print "ok 38\n";
+ ok(near($lat, 1.20296099733328)); # 68.9246 N
($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.25);
- print 'not ' unless (near($lon, 0.516073562850837)); # 29.5688 E
- print "ok 39\n";
+ ok(near($lon, 0.516073562850837)); # 29.5688 E
+
+ ok(near($lat, 1.170565013391510)); # 67.0684 N
- print 'not ' unless (near($lat, 1.170565013391510)); # 67.0684 N
- print "ok 40\n";
($lon, $lat) = great_circle_waypoint(@London, @Tokyo, 0.75);
- print 'not ' unless (near($lon, 2.17494903805952)); # 124.6154 E
- print "ok 41\n";
+ ok(near($lon, 2.17494903805952)); # 124.6154 E
- print 'not ' unless (near($lat, 0.952987032741305)); # 54.6021 N
- print "ok 42\n";
+ ok(near($lat, 0.952987032741305)); # 54.6021 N
use Math::Trig 'great_circle_destination';
($lon, $lat) = great_circle_destination(@London, $dir1, $dst1);
- print 'not ' unless (near($lon, $Tokyo[0]));
- print "ok 43\n";
+ ok(near($lon, $Tokyo[0]));
- print 'not ' unless (near($lat, $pip2 - $Tokyo[1]));
- print "ok 44\n";
+ ok(near($lat, $pip2 - $Tokyo[1]));
my $dir2 = great_circle_direction(@Tokyo, @London);
my $dst2 = great_circle_distance(@Tokyo, @London);
($lon, $lat) = great_circle_destination(@Tokyo, $dir2, $dst2);
- print 'not ' unless (near($lon, $London[0]));
- print "ok 45\n";
+ ok(near($lon, $London[0]));
- print 'not ' unless (near($lat, $pip2 - $London[1]));
- print "ok 46\n";
+ ok(near($lat, $pip2 - $London[1]));
my $dir3 = (great_circle_destination(@London, $dir1, $dst1))[2];
- print 'not ' unless (near($dir3, 2.69379263839118)); # about 154.343 deg
- print "ok 47\n";
+ ok(near($dir3, 2.69379263839118)); # about 154.343 deg
my $dir4 = (great_circle_destination(@Tokyo, $dir2, $dst2))[2];
- print 'not ' unless (near($dir4, 3.6993902625701)); # about 211.959 deg
- print "ok 48\n";
+ ok(near($dir4, 3.6993902625701)); # about 211.959 deg
- print 'not ' unless (near($dst1, $dst2));
- print "ok 49\n";
+ ok(near($dst1, $dst2));
}
# eof
projects / p5sagit/p5-mst-13.2.git / commitdiff