| function | argument type(s) | return type | description |
|
| acos | double in the range [-1.0, 1.0] or complex | double in
the range [0.0, pi] or NaN if out of range or complex | arc
cosine
complex case: acos(z) = −i log(z + i √{i−z2}) |
| asin | double in the range [-1.0, 1.0] or complex | double in
the range [-pi/2, pi/2] or NaN if out of range or complex | arc
sine
complex case: asin(z) = −i log(iz + √{i−z2}) |
| atan | double or complex | double in the range [-pi/2, pi/2] or
complex | arc tangent
complex case: atan(z) = − [i/2]log[(i−z)/(i+z)] |
| atan2 | double, double | double in the range [-pi, pi] | angle of a vector (note: the arguments are (y, x), not (x, y) as one might expect). |
| acosh | double greater than 1 or complex | double or
complex | hyperbolic arc cosine, defined for both double
and complex case by: acosh(z) = logz+√{z2 −1} |
| asinh | double or complex | double or complex | hyperbolic arc sine complex case:
asinh(z) = logz+√{z2 +1} |
| cos | double or complex | double in the range , or complex | cosine
complex case:
cos(z) = [(exp(iz) + exp(−iz))/2] |
| cosh | double or complex | double or complex | hyperbolic cosine, defined for double or complex by:
cosh(z) = [(exp(z) + exp(−z))/2] |
| sin | double or complex | double or complex | sine
function complex case:
sin(z) = [(exp(iz) − exp(−iz))/2i] |
| sinh | double or complex | double or complex | hyperbolic sine, defined for double or complex by:
sinh(z) = [(exp(z) − exp(−z))/2] |
| tan | double or complex | double or complex | tangent function, defined for double or complex by:
tan(z) = [sin(z)/cos(z)] |
| tanh | double or complex | double or complex | hyperbolic tangent, defined for double or complex by:
tanh(z) = [sinh(z)/cosh(z)] |
| function | argument type(s) | return type | description |
|
| abs | double or complex | double or int or long (complex
returns double) | absolute value
complex case: abs(a+ib) = |z| = √{a2 + b2} |
| angle | complex | double in the range [-pi, pi] | angle or
argument of the complex number: ∠z |
| ceil | double or float | double | ceiling function, which returns the
smallest (closest to negative infinity) double value that is
not less than the argument and is an integer. |
| compare | double, double | int | compare two numbers,
returning -1, 0, or 1 if the first argument is less than, equal to, or
greater than the second. |
| conjugate | complex | complex | complex conjugate |
| exp | double or complex | double in the range [0.0, infinity] or
complex | exponential function (eârgument)
complex case: ea+ib = ea(cosb + isinb) |
| floor | double | double | floor function, which is the largest
(closest to positive infinity) value not greater than the argument
that is an integer. |
| gaussian | double, double or
double, double, int, or
double, double, int, int | double or double or
[double] | one or more Gaussian random variables with the specified
mean and standard deviation (see 8.0.2). |
| imag | complex | double | imaginary part |
| isInfinite | double | boolean | return true if the argument is
infinite |
| isNaN | double | boolean | return true if the argument is "not a
number" |
| log | double or complex | double or complex | natural
logarithm complex case: log(z) = log(abs(z) +i ∠z) |
| log10 | double | double | log base 10 |
| log2 | double | double | log base 2 |
| function | argument type(s) | return type | description |
|
| max | double, double or
double | a scalar of the same type as the arguments | maximum |
| min | double, double or
double | a scalar of the same type as the arguments | minimum |
| pow | double, double or
complex, complex | double or
complex | first argument to the power of the second |
| random | no arguments or
int or
int, int | double or
double or
[double] | one or more random numbers between 0.0 and 1.0 (see
8.0.2) |
| real | complex | double | real part |
| remainder | double, double | double | remainder after division,
according to the IEEE 754 floating-point standard (see
8.0.4. |
| round | double | long | round to the nearest long, choosing the next
greater integer when exactly in between, and throwing an exception if
out of range. If the argument is NaN, the result is 0L. If the
argument is out of range, the result is either MaxLong or MinLong,
depending on the sign. |
| roundToInt | double | int | round to the nearest int, choosing
the next greater integer when exactly in between, and throwing an
exception if out of range. If the argument is NaN, the result is 0. If
the argument is out of range, the result is either MaxInt or MinInt,
depending on the sign. |
| sgn | double | int | -1 if the argument is negative, 1 otherwise |
| sqrt | double or
complex | double or
complex | square root. If the argument is double with value less than zero, then the result is NaN.
complex case:
sqrt(z) = √{|z|}(cos[(∠z)/2] + isin[(∠z)/2]) |
| function | argument type(s) | return type | description |
|
| arrayToMatrix | type, int, int | [type] | Create a matrix
from the specified array with the specified number of rows and columns |
| concatenate | type, type | type | Concatenate two arrays. |
| concatenate | type | type | Concatenate arrays in an array of
arrays. |
| conjugateTranspose | [complex] | [complex] | Return the conjugate
transpose of the specified matrix. |
| createSequence | type, type, int | type | Create an array with
values starting with the first argument, incremented by the second
argument, of length given by the third argument. |
| crop | [int], int, int, int, int or
[double], int, int, int, int or
[complex], int, int, int, int or
[long], int, int, int, int or | [int] or
[double] or
[complex] or
[long] or | Given a matrix of any type, return a submatrix starting at the specified row and column with the specified number of rows and columns. |
| determinant | [double] or
[complex] | double or
complex | Return the determinant of the specified matrix. |
| diag | type | [type] | Return a diagonal matrix with the values
along the diagonal given by the specified array. |
| divideElements | [type], [type] | [type] | Return the
element-by-element division of two matrices |
| emptyArray | type | type | Return an empty array whose element type
matches the specified token. |
| emptyRecord | | record | Return an empty record. |
| find | type, type | int | Return an array of the indices where
elements of the specified array match the specified token. |
| function | argument type(s) | return type | description |
|
| find | boolean | int | Return an array of the indices where
elements of the specified array have value true. |
| hilbert | int | [double] | Return a square Hilbert matrix, where
Aij = [1/(i + j + 1)].
A Hilbert matrix is nearly, but not quite singular. |
| identityMatrixComplex | int | [complex] | Return an identity matrix
with the specified dimension. |
| identityMatrixDouble | int | [double] | Return an identity matrix with
the specified dimension. |
| identityMatrixInt | int | [int] | Return an identity matrix with the
specified dimension. |
| identityMatrixLong | int | [long] | Return an identity matrix with the
specified dimension. |
| intersect | record, record | record | Return a record that contains
only fields that are present in both arguments, where the value of the
field is taken from the first record. |
| inverse | [double] or
[complex] | [double] or
[complex] | Return the inverse of the specified matrix, or throw an
exception if it is singular. |
| matrixToArray | [type] | type | Create an array containing the
values in the matrix |
| merge | record, record | record | Merge two records, giving priority
to the first one when they have matching record labels. |
| multiplyElements | [type], [type] | [type] | Multiply element wise the
two specified matrices. |
| orthogonalizeColumns | [double] or [complex] | [double] or [complex] | Return a similar matrix with orthogonal columns. |
| orthogonalizeRows | [double] or [complex] | [double] or [complex] | Return a similar matrix with orthogonal rows. |
| orthonormalizeColumns | [double] or [complex] | [double] or [complex] | Return a similar matrix with orthonormal columns. |
| orthonormalizeRows | [double] or [complex] | [double] or
[complex] | Return a similar matrix with orthonormal rows. |
| repeat | int, type | type | Create an array by repeating the
specified token the specified number of times. |
| function | argument type(s) | return type | description |
|
| sort | stringor realScalar | string or realScalar | Return the
specified array, but sorted in ascending order. realScalar is any
scalar token except complex. |
| sortAscending | stringor realScalar | string or realScalar | Return the specified array, but sorted in ascending order. realScalar
is any scalar token except complex. |
| sortDescending | stringor
realScalar | string or
realScalar | Return the specified array, but sorted in descending
order. realScalar is any scalar token except complex. |
| subarray | type, int, int | type | Extract a subarray
starting at the specified index with the specified length. |
| sum | type or [type] | type | Sum the elements of the specified
array or matrix. This throws an exception if the elements do not
support addition or if the array is empty (an empty matrix will return
zero). |
| trace | [type] | type | Return the trace of the specified matrix. |
| transpose | [type] | [type] | Return the transpose of the specified
matrix. |
| zeroMatrixComplex | int, int | [complex] | Return a zero matrix
with the specified number of rows and columns. |
| zeroMatrixDouble | int, int | [double] | Return a zero matrix
with the specified number of rows and columns. |
| zeroMatrixInt | int, int | [int] | Return a zero matrix with
the specified number of rows and columns. |
| zeroMatrixLong | int, int | [long] | Return a zero matrix with
the specified number of rows and columns. |
| function | argument type(s) | return type | description |
|
| eval | string | any type | evaluate the specified expression (see
8.0.1). |
| parseInt | string or string, int | int | return an int read
from a string, using the given radix if a second argument is
provided. |
| parseLong | string or string, int | int | return a long read from a
string, using the given radix if a second argument is provided. |
| toBinaryString | int or long | string | return a binary representation
of the argument |
| toOctalString | int or long | string | return an octal representation
of the argument |
| toString | double or int or int, int or long or long,
int | string | return a string representation of the argument, using
the given radix if a second argument is provided. |
| traceEvaluation | string | string | evaluate the specified expression
and report details on how it was evaluated (see 8.0.1). |
| function | argument type(s) | return type | description |
|
| close | double, double | boolean
? | Return true if the first argument is close to the second (within
EPSILON, where EPSILON is a static public variable of this class). |
| convolve | double, double or
complex, complex | double or
complex | Convolve two arrays and return an array whose length is
sum of the lengths of the two arguments minus one. Convolution of two
arrays is the same as polynomial
multiplication. |
| DCT | double or
double, int or
double, int, int | double | Return the discrete cosine
transform of the specified array, using the specified (optional)
length and normalization strategy (see 8.0.5). |
| downsample | double, int or
double, int, int | double | Return a new array with every
n-th element of the argument array, where n is the second
argument. If a third argument is given, then it must be between 0 and
n − 1, and it specifies an offset into the array (by giving the
index of the first output). |
| FFT | double or
complex or
double, int
complex, int | complex | Return the fast
Fourier transform of the specified array. If the second argument is
given with value n, then the length of the transform is
2n. Otherwise, the length is the next power of two greater than or
equal to the length of the input array. If the input length does not match
this length, then input is padded with zeros. |
| function | argument type(s) |
return type | description |
|
| generateBartlettWindow |
int |
double |
Bartlett (
rectangular) window with the specified length. The end points have
value 0.0, and if the length is odd, the center point has value
1.0. For length M + 1, the formula is:
w(n) = 2[n/M];
if 0 ≤ n ≤ [M/2]
2 − 2[n/M];
if [M/2] ≤ n ≤ M
|
| generateBlackmanWindow |
int |
double | Return a
Blackman window with the specified length. For length M + 1, the formula is:
w(n) = 0.42 + 0.5 cos[(2 πn)/M] + 0.08 cos[(4 πn)/M] |
| generateBlackmanHarrisWindow |
int |
double |
Return a Blackman-Harris window with the specified length. For length M + 1, the formula is:
w(n) = 0.35875 + 0.48829 cosfrac2 πnM + 0.14128 cos[(4
πn)/M] + 0.01168 cos[(6 πn)/M] |
| generateGaussianCurve | double, double, int | double | Return a Gaussian curve with the specified standard deviation, extent,
and length. The extent is a multiple of the standard deviation. For
instance, to get 100 samples of a Gaussian curve with standard
deviation 1.0 out to four standard deviations, use
generateGaussianCurve(1.0, 4.0, 100). |
| function | argument type(s) | return type | description |
|
| generateHammingWindow | int | double | Return a
Hamming window with the specified length. For length M + 1, the formula is:
w(n) = 0.54 − 0.46 cos[(2 πn )/M] |
| generateHanningWindow | int | double | Return a
Hanning window with the specified length. For length M + 1, the
formula is: w(n) = 0.5 − 0.5 cos[(2 πn)/(/)]M |
| generatePolynomialCurve | double, double, double, int
| double | Return samples of a curve specified by a polynomial. The
first argument is an array with the polynomial coefficients, beginning
with the constant term, the linear term, the squared term, etc. The
second argument is the value of the polynomial variable at which to
begin, and the third argument is the increment on this variable for
each successive sample. The final argument is the length of the
returned array. |
| function | argument type(s) | return type | description |
|
| IDCT | double or
double, int or
double, int, int | double | Return the inverse discrete
cosine transform of the specified array, using the specified
(optional) length and normalization strategy (see 8.0.5). |
| IFFT | double or
complex or
double, int
complex, int | complex | inverse fast
Fourier transform of the specified array. If the second argument is
given with value n, then the length of the transform is
2n. Otherwise, the length is the next power of two greater than or
equal to the length of the input array. If the input length does not match
this length, then input is padded with zeros. |
| nextPowerOfTwo | double | int | Return the next power of two larger
than or equal to the argument. |
| poleZeroToFrequency | complex, complex, complex,
int | complex | Given an array of pole locations, an array of
zero locations, a gain term, and a size, return an array of the
specified size representing the frequency response specified by these
poles, zeros, and gain. This is calculated by walking around the unit
circle and forming the product of the distances to the zeros, dividing
by the product of the distances to the poles, and multiplying by the
gain. |
| function | argument type(s) | return type | description |
|
| sinc | double | double | Return the sinc function,
sin(x)/x, where special care is taken to ensure that 1.0 is returned if the
argument is 0.0. |
| toDecibels | double | double | Return
20 ×log10z, where z is the argument. |
| unwrap | double | double | Modify the specified array to unwrap
the angles. That is, if the difference between successive values is
greater than π in magnitude, then the second value is modified by
multiples of 2π until the difference is less than or equal to
π. In addition, the first element is modified so that its
difference from zero is less than or equal to π in magnitude. |
| upsample | double, int | double | Return a new array that
is the result of inserting n−1 zeroes between each successive sample
in the input array, where n is the second argument. The returned array has length
nL, where L is the length of the argument array. It is required that
n > 0. |
| function | argument type(s) | return type | description |
|
| asURL | string | string | Return a URL representation of the
argument. |
| cast | type1, type2 | type1 | Return the second argument converted to
the type of the first, or throw an exception if the conversion is
invalid. |
| constants | none | record | Return a record identifying all the
globally defined constants in the expression language. |
| findFile | string | string | Given a file name relative to the user
directory, current directory, or classpath, return the absolute file
name of the first match, or return the name unchanged if no match is
found. |
| filter | function, type | type | Extract a sub-array consisting of
all of the elements of an array for which the given predicate function
returns true. |
| filter | function, type, int | type | Extract a sub-array with a
limited size consisting of all of the elements of an array for which
the given predicate function returns true. |
| freeMemory | none | long | Return the approximate number of bytes
available for future memory allocation. |
| iterate | function, int, type | type | Return an array that
results from first applying the specified function to the third
argument, then applying it to the result of that application, and
repeating to get an array whose length is given by the second
argument. |
| function | argument type(s) | return type | description |
|
| map | function, type | type | Return an array that results from
applying the specified function to the elements of the specified
array. |
| property | string | string | Return a system property with the
specified name from the environment, or an empty string if there is
none. Some useful properties are java.version, ptolemy.ptII.dir,
ptolemy.ptII.dirAsURL, and user.dir. |
| readFile | string | string | Get the string text in the specified
file, or throw an exception if the file cannot be found. The file can
be absolute, or relative to the current working directory (user.dir),
the user's home directory (user.home), or the classpath. |
| readResource | string | string | Get the string text in the specified
resource (which is a file found relative to the classpath), or throw
an exception if the file cannot be found. |
| totalMemory | none | long | Return the approximate number of bytes
used by current objects plus those available for future object
allocation. |
