geexp
Signature: ([io,phys]A(n,n);int deg();scale();[io]trace();int [o]ns();int [o]info())
Computes exp(t*A), the matrix exponential of a general matrix, using the irreducible rational Pade
approximation to the exponential function exp(x) = r(x) = (+/-)( I + 2*(q(x)/p(x)) ), combined with
scaling-and-squaring and optionally normalization of the trace. The algorithm is described in Roger B.
Sidje (rbs.uq.edu.au) "EXPOKIT: Software Package for Computing Matrix Exponentials". ACM - Transactions
On Mathematical Software, 24(1):130-156, 1998
A: On input argument matrix. On output exp(t*A).
Use Fortran storage type.
deg: the degre of the diagonal Pade to be used.
a value of 6 is generally satisfactory.
scale: time-scale (can be < 0).
trace: on input, boolean value indicating whether or not perform
a trace normalization. On output value used.
ns: on output number of scaling-squaring used.
info: exit flag.
0 - no problem
> 0 - Singularity in LU factorization when solving
Pade approximation
= random(5,5);
= pdl(1);
->xchg(0,1)->geexp(6,1,, ( = null), ( = null));
geexp does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is
set for any of the input ndarrays.
cgeexp
Signature: ([io,phys]A(2,n,n);int deg();scale();int trace();int [o]ns();int [o]info())
Complex version of geexp. The value used for trace normalization is not returned. The algorithm is
described in Roger B. Sidje (rbs@maths.uq.edu.au) "EXPOKIT: Software Package for Computing Matrix
Exponentials". ACM - Transactions On Mathematical Software, 24(1):130-156, 1998
cgeexp does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is
set for any of the input ndarrays.
ctrsqrt
Signature: ([io,phys]A(2,n,n);int uplo();[phys,o] B(2,n,n);int [o]info())
Root square of complex triangular matrix. Uses a recurrence of Björck and Hammarling. (See Nicholas J.
Higham. A new sqrtm for MATLAB. Numerical Analysis Report No. 336, Manchester Centre for Computational
Mathematics, Manchester, England, January 1999. It's available at
http://www.ma.man.ac.uk/~higham/pap-mf.html) If uplo is true, A is lower triangular.
ctrsqrt does not process bad values. It will set the bad-value flag of all output ndarrays if the flag
is set for any of the input ndarrays.
ctrfun
Signature: ([io,phys]A(2,n,n);int uplo();[phys,o] B(2,n,n);int [o]info(); SV* func)
Apply an arbitrary function to a complex triangular matrix. Uses a recurrence of Parlett. If uplo is
true, A is lower triangular.
ctrfun does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is
set for any of the input ndarrays.
mlog
Return matrix logarithm of a square matrix.
PDL = mlog(PDL(A))
my $a = random(10,10);
my $log = mlog($a);
msqrt
Return matrix square root (principal) of a square matrix.
PDL = msqrt(PDL(A))
my $a = random(10,10);
my $sqrt = msqrt($a);
mexp
Return matrix exponential of a square matrix.
PDL = mexp(PDL(A))
my $a = random(10,10);
my $exp = mexp($a);
mpow
Return matrix power of a square matrix.
PDL = mpow(PDL(A), SCALAR(exponent))
my $a = random(10,10);
my $powered = mpow($a,2.5);
mcos
Return matrix cosine of a square matrix.
PDL = mcos(PDL(A))
my $a = random(10,10);
my $cos = mcos($a);
macos
Return matrix inverse cosine of a square matrix.
PDL = macos(PDL(A))
my $a = random(10,10);
my $acos = macos($a);
msin
Return matrix sine of a square matrix.
PDL = msin(PDL(A))
my $a = random(10,10);
my $sin = msin($a);
masin
Return matrix inverse sine of a square matrix.
PDL = masin(PDL(A))
my $a = random(10,10);
my $asin = masin($a);
mtan
Return matrix tangent of a square matrix.
PDL = mtan(PDL(A))
my $a = random(10,10);
my $tan = mtan($a);
matan
Return matrix inverse tangent of a square matrix.
PDL = matan(PDL(A))
my $a = random(10,10);
my $atan = matan($a);
mcot
Return matrix cotangent of a square matrix.
PDL = mcot(PDL(A))
my $a = random(10,10);
my $cot = mcot($a);
macot
Return matrix inverse cotangent of a square matrix.
PDL = macot(PDL(A))
my $a = random(10,10);
my $acot = macot($a);
msec
Return matrix secant of a square matrix.
PDL = msec(PDL(A))
my $a = random(10,10);
my $sec = msec($a);
masec
Return matrix inverse secant of a square matrix.
PDL = masec(PDL(A))
my $a = random(10,10);
my $asec = masec($a);
mcsc
Return matrix cosecant of a square matrix.
PDL = mcsc(PDL(A))
my $a = random(10,10);
my $csc = mcsc($a);
macsc
Return matrix inverse cosecant of a square matrix.
PDL = macsc(PDL(A))
my $a = random(10,10);
my $acsc = macsc($a);
mcosh
Return matrix hyperbolic cosine of a square matrix.
PDL = mcosh(PDL(A))
my $a = random(10,10);
my $cos = mcosh($a);
macosh
Return matrix hyperbolic inverse cosine of a square matrix.
PDL = macosh(PDL(A))
my $a = random(10,10);
my $acos = macosh($a);
msinh
Return matrix hyperbolic sine of a square matrix.
PDL = msinh(PDL(A))
my $a = random(10,10);
my $sinh = msinh($a);
masinh
Return matrix hyperbolic inverse sine of a square matrix.
PDL = masinh(PDL(A))
my $a = random(10,10);
my $asinh = masinh($a);
mtanh
Return matrix hyperbolic tangent of a square matrix.
PDL = mtanh(PDL(A))
my $a = random(10,10);
my $tanh = mtanh($a);
matanh
Return matrix hyperbolic inverse tangent of a square matrix.
PDL = matanh(PDL(A))
my $a = random(10,10);
my $atanh = matanh($a);
mcoth
Return matrix hyperbolic cotangent of a square matrix.
PDL = mcoth(PDL(A))
my $a = random(10,10);
my $coth = mcoth($a);
macoth
Return matrix hyperbolic inverse cotangent of a square matrix.
PDL = macoth(PDL(A))
my $a = random(10,10);
my $acoth = macoth($a);
msech
Return matrix hyperbolic secant of a square matrix.
PDL = msech(PDL(A))
my $a = random(10,10);
my $sech = msech($a);
masech
Return matrix hyperbolic inverse secant of a square matrix.
PDL = masech(PDL(A))
my $a = random(10,10);
my $asech = masech($a);
mcsch
Return matrix hyperbolic cosecant of a square matrix.
PDL = mcsch(PDL(A))
my $a = random(10,10);
my $csch = mcsch($a);
macsch
Return matrix hyperbolic inverse cosecant of a square matrix.
PDL = macsch(PDL(A))
my $a = random(10,10);
my $acsch = macsch($a);
mfun
Return matrix function of second argument of a square matrix. Function will be applied on a PDL::Complex
object.
PDL = mfun(PDL(A),'cos')
my $a = random(10,10);
my $fun = mfun($a,'cos');
sub sinbycos2{
$_[0]->set_inplace(0);
$_[0] .= $_[0]->Csin/$_[0]->Ccos**2;
}
# Try diagonalization
$fun = mfun($a, \&sinbycos2,1);
# Now try Schur/Parlett
$fun = mfun($a, \&sinbycos2);
# Now with function.
scalar msolve($a->mcos->mpow(2), $a->msin);
Install Now
PNG Icons
Emojis