Spectrogram¶

class gwpy.spectrogram.Spectrogram(data, unit=
None
, t0=None
, dt=None
, f0=None
, df=None
, times=None
, frequencies=None
, name=None
, channel=None
, **kwargs)[source]¶ A 2D array holding a spectrogram of timefrequency data
 Parameters¶
 valuearraylike
input data array
 unit
Unit
, optional physical unit of these data
 epoch
LIGOTimeGPS
,float
,str
, optional GPS epoch associated with these data, any input parsable by
to_gps
is fine sample_rate
float
,Quantity
, optional, default:1
the rate of samples per second (Hertz)
 times
arraylike
the complete array of GPS times accompanying the data for this series. This argument takes precedence over
epoch
andsample_rate
so should be given in place of these if relevant, not alongside f0
float
,Quantity
, optional, default:0
starting frequency for these data
 df
float
,Quantity
, optional, default:1
frequency resolution for these data
 frequencies
arraylike
the complete array of frequencies indexing the data. This argument takes precedence over
f0
anddf
so should be given in place of these if relevant, not alongside epoch
LIGOTimeGPS
,float
,str
, optional GPS epoch associated with these data, any input parsable by
to_gps
is fine name
str
, optional descriptive title for this array
 channel
Channel
,str
, optional source data stream for these data
 dtype
dtype
, optional input data type
 copy
bool
, optional, default:False
choose to copy the input data to new memory
 subok
bool
, optional, default:True
allow passing of subclasses by the array generator
Notes
Key methods:
read
(source, *args, **kwargs)Read data into a
Spectrogram
write
(target, *args, **kwargs)Write this
Spectrogram
to a fileplot
([method, figsize, xscale])Plot the data for this
Spectrogram
zpk
(zeros, poles, gain[, analog])Filter this
Spectrogram
by applying a zeropolegain filterAttributes Summary
View of the transposed array.
Frequency band described by this
Spectrogram
Base object if memory is from some other object.
Returns a copy of the current
Quantity
instance with CGS units.Instrumental channel associated with these data
An object to simplify the interaction of the array with the ctypes module.
Python buffer object pointing to the start of the array's data.
Frequency spacing of this
Spectrogram
Timespacing for this
Spectrogram
Datatype of the array's elements.
Xaxis sample separation
Yaxis sample separation
Starting GPS epoch for this
Spectrogram
A list of equivalencies that will be applied by default during unit conversions.
Starting frequency for this
Spectrogram
Information about the memory layout of the array.
A 1D iterator over the Quantity array.
Series of frequencies for this Spectrogram
The imaginary part of the array.
Container for meta information like name, description, format.
True if the
value
of this quantity is a scalar, or False if it is an arraylike object.Length of one array element in bytes.
Name for this data set
Total bytes consumed by the elements of the array.
Number of array dimensions.
The real part of the array.
Tuple of array dimensions.
Returns a copy of the current
Quantity
instance with SI units.Number of elements in the array.
GPS [start, stop) span for this
Spectrogram
Tuple of bytes to step in each dimension when traversing an array.
GPS time of first time bin
Series of GPS times for each sample
The physical unit of these data
The numerical value of this instance.
Xaxis coordinate of the first data point
Positions of the data on the xaxis
Xaxis [low, high) segment encompassed by these data
Unit of xaxis index
Yaxis coordinate of the first data point
Positions of the data on the yaxis
Yaxis [low, high) segment encompassed by these data
Unit of Yaxis index
Methods Summary
abs
(x, /[, out, where, casting, order, ...])Calculate the absolute value elementwise.
all
([axis, out, keepdims, where])Returns True if all elements evaluate to True.
any
([axis, out, keepdims, where])Returns True if any of the elements of
a
evaluate to True.append
(other[, inplace, pad, gap, resize])Connect another series onto the end of the current one.
argmax
([axis, out, keepdims])Return indices of the maximum values along the given axis.
argmin
([axis, out, keepdims])Return indices of the minimum values along the given axis.
argpartition
(kth[, axis, kind, order])Returns the indices that would partition this array.
argsort
([axis, kind, order])Returns the indices that would sort this array.
astype
(dtype[, order, casting, subok, copy])Copy of the array, cast to a specified type.
byteswap
([inplace])Swap the bytes of the array elements
choose
(choices[, out, mode])Use an index array to construct a new array from a set of choices.
clip
([min, max, out])Return an array whose values are limited to
[min, max]
.compress
(condition[, axis, out])Return selected slices of this array along given axis.
conj
()Complexconjugate all elements.
Return the complex conjugate, elementwise.
copy
([order])Return a copy of the array.
crop
([start, end, copy])Crop this series to the given xaxis extent.
crop_frequencies
([low, high, copy])Crop this
Spectrogram
to the specified frequenciescumprod
([axis, dtype, out])Return the cumulative product of the elements along the given axis.
cumsum
([axis, dtype, out])Return the cumulative sum of the elements along the given axis.
decompose
([bases])Generates a new
Quantity
with the units decomposed.diagonal
([offset, axis1, axis2])Return specified diagonals.
diff
([n, axis])Calculate the nth order discrete difference along given axis.
dot
(b[, out])dump
(file)Not implemented, use
.value.dump()
instead.dumps
()Returns the pickle of the array as a string.
ediff1d
([to_end, to_begin])fill
(value)Fill the array with a scalar value.
filter
(*filt, **kwargs)Apply the given filter to this
Spectrogram
.flatten
([order])Return a copy of the array collapsed into one dimension.
from_spectra
(*spectra, **kwargs)Build a new
Spectrogram
from a list of spectra.getfield
(dtype[, offset])Returns a field of the given array as a certain type.
imshow
(**kwargs)inject
(other)Add two compatible
Series
along their shared xaxis values.insert
(obj, values[, axis])Insert values along the given axis before the given indices and return a new
Quantity
object.is_compatible
(other)Check whether this series and other have compatible metadata
is_contiguous
(other[, tol])Check whether other is contiguous with self.
item
(*args)Copy an element of an array to a scalar Quantity and return it.
itemset
(*args)Insert scalar into an array (scalar is cast to array's dtype, if possible)
max
([axis, out, keepdims, initial, where])Return the maximum along a given axis.
mean
([axis, dtype, out, keepdims, where])Returns the average of the array elements along given axis.
median
([axis])Compute the median along the specified axis.
min
([axis, out, keepdims, initial, where])Return the minimum along a given axis.
nansum
([axis, out, keepdims, initial, where])Deprecated since version 5.3.
newbyteorder
([new_order])Return the array with the same data viewed with a different byte order.
nonzero
()Return the indices of the elements that are nonzero.
override_unit
(unit[, parse_strict])Forcefully reset the unit of these data
pad
(pad_width, **kwargs)Pad this series to a new size
partition
(kth[, axis, kind, order])Rearranges the elements in the array in such a way that the value of the element in kth position is in the position it would be in a sorted array.
pcolormesh
(**kwargs)percentile
(percentile)Calculate a given spectral percentile for this
Spectrogram
.plot
([method, figsize, xscale])Plot the data for this
Spectrogram
prepend
(other[, inplace, pad, gap, resize])Connect another series onto the start of the current one.
prod
([axis, dtype, out, keepdims, initial, ...])Return the product of the array elements over the given axis
ptp
([axis, out, keepdims])Peak to peak (maximum  minimum) value along a given axis.
put
(indices, values[, mode])Set
a.flat[n] = values[n]
for alln
in indices.ratio
(operand)Calculate the ratio of this
Spectrogram
against a referenceravel
([order])Return a flattened array.
read
(source, *args, **kwargs)Read data into a
Spectrogram
repeat
(repeats[, axis])Repeat elements of an array.
reshape
(shape[, order])Returns an array containing the same data with a new shape.
resize
(new_shape[, refcheck])Change shape and size of array inplace.
round
([decimals, out])Return
a
with each element rounded to the given number of decimals.searchsorted
(v[, side, sorter])Find indices where elements of v should be inserted in a to maintain order.
setfield
(val, dtype[, offset])Put a value into a specified place in a field defined by a datatype.
setflags
([write, align, uic])Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY, respectively.
shift
(delta)Shift this
Series
forward on the Xaxis bydelta
sort
([axis, kind, order])Sort an array inplace.
squeeze
([axis])Remove axes of length one from
a
.std
([axis, dtype, out, ddof, keepdims, where])Returns the standard deviation of the array elements along given axis.
step
(**kwargs)Create a step plot of this series
sum
([axis, dtype, out, keepdims, initial, where])Return the sum of the array elements over the given axis.
swapaxes
(axis1, axis2)Return a view of the array with
axis1
andaxis2
interchanged.take
(indices[, axis, out, mode])Return an array formed from the elements of
a
at the given indices.to
(unit[, equivalencies, copy])Return a new
Quantity
object with the specified unit.to_string
([unit, precision, format, subfmt])Generate a string representation of the quantity and its unit.
to_value
([unit, equivalencies])The numerical value, possibly in a different unit.
tobytes
([order])Not implemented, use
.value.tobytes()
instead.tofile
(fid[, sep, format])Not implemented, use
.value.tofile()
instead.tolist
()Return the array as an
a.ndim
levels deep nested list of Python scalars.tostring
([order])Construct Python bytes containing the raw data bytes in the array.
trace
([offset, axis1, axis2, dtype, out])Return the sum along diagonals of the array.
transpose
(*axes)Returns a view of the array with axes transposed.
update
(other[, inplace])Update this series by appending new data from an other and dropping the same amount of data off the start.
value_at
(x, y)Return the value of this
Series
at the given(x, y)
coordinatesvar
([axis, dtype, out, ddof, keepdims, where])Returns the variance of the array elements, along given axis.
variance
([bins, low, high, nbins, log, ...])Calculate the
SpectralVariance
of thisSpectrogram
.view
([dtype][, type])New view of array with the same data.
write
(target, *args, **kwargs)Write this
Spectrogram
to a filezip
()zpk
(zeros, poles, gain[, analog])Filter this
Spectrogram
by applying a zeropolegain filterAttributes Documentation
 T¶
 band¶
Frequency band described by this
Spectrogram
 base¶
Base object if memory is from some other object.
Examples
The base of an array that owns its memory is None:
>>> x = np.array([1,2,3,4]) >>> x.base is None True
Slicing creates a view, whose memory is shared with x:
>>> y = x[2:] >>> y.base is x True
 cgs¶
Returns a copy of the current
Quantity
instance with CGS units. The value of the resulting object will be scaled.
 ctypes¶
An object to simplify the interaction of the array with the ctypes module.
This attribute creates an object that makes it easier to use arrays when calling shared libraries with the ctypes module. The returned object has, among others, data, shape, and strides attributes (see Notes below) which themselves return ctypes objects that can be used as arguments to a shared library.
See also
Notes
Below are the public attributes of this object which were documented in “Guide to NumPy” (we have omitted undocumented public attributes, as well as documented private attributes):
 _ctypes.data
A pointer to the memory area of the array as a Python integer. This memory area may contain data that is not aligned, or not in correct byteorder. The memory area may not even be writeable. The array flags and datatype of this array should be respected when passing this attribute to arbitrary Ccode to avoid trouble that can include Python crashing. User Beware! The value of this attribute is exactly the same as
self._array_interface_['data'][0]
.Note that unlike
data_as
, a reference will not be kept to the array: code likectypes.c_void_p((a + b).ctypes.data)
will result in a pointer to a deallocated array, and should be spelt(a + b).ctypes.data_as(ctypes.c_void_p)
 _ctypes.shape
(c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the Cinteger corresponding to
dtype('p')
on this platform (seec_intp
). This basetype could bectypes.c_int
,ctypes.c_long
, orctypes.c_longlong
depending on the platform. The ctypes array contains the shape of the underlying array.
 _ctypes.strides
(c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the same as for the shape attribute. This ctypes array contains the strides information from the underlying array. This strides information is important for showing how many bytes must be jumped to get to the next element in the array.
 _ctypes.data_as(obj)
Return the data pointer cast to a particular ctypes object. For example, calling
self._as_parameter_
is equivalent toself.data_as(ctypes.c_void_p)
. Perhaps you want to use the data as a pointer to a ctypes array of floatingpoint data:self.data_as(ctypes.POINTER(ctypes.c_double))
.The returned pointer will keep a reference to the array.
 _ctypes.shape_as(obj)
Return the shape tuple as an array of some other ctypes type. For example:
self.shape_as(ctypes.c_short)
.
 _ctypes.strides_as(obj)
Return the strides tuple as an array of some other ctypes type. For example:
self.strides_as(ctypes.c_longlong)
.
If the ctypes module is not available, then the ctypes attribute of array objects still returns something useful, but ctypes objects are not returned and errors may be raised instead. In particular, the object will still have the
as_parameter
attribute which will return an integer equal to the data attribute.Examples
>>> import ctypes >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32) >>> x array([[0, 1], [2, 3]], dtype=int32) >>> x.ctypes.data 31962608 # may vary >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)) <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents c_uint(0) >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents c_ulong(4294967296) >>> x.ctypes.shape <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary >>> x.ctypes.strides <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary
 data¶
Python buffer object pointing to the start of the array’s data.
 df¶
Frequency spacing of this
Spectrogram
 dt¶
Timespacing for this
Spectrogram
 dtype¶
Datatype of the array’s elements.
Warning
Setting
arr.dtype
is discouraged and may be deprecated in the future. Setting will replace thedtype
without modifying the memory (see alsondarray.view
andndarray.astype
).See also
ndarray.astype
Cast the values contained in the array to a new datatype.
ndarray.view
Create a view of the same data but a different datatype.
numpy.dtype
Examples
>>> x array([[0, 1], [2, 3]]) >>> x.dtype dtype('int32') >>> type(x.dtype) <type 'numpy.dtype'>
 epoch¶
Starting GPS epoch for this
Spectrogram
 equivalencies¶
A list of equivalencies that will be applied by default during unit conversions.
 f0¶
Starting frequency for this
Spectrogram
 flags¶
Information about the memory layout of the array.
Notes
The
flags
object can be accessed dictionarylike (as ina.flags['WRITEABLE']
), or by using lowercased attribute names (as ina.flags.writeable
). Short flag names are only supported in dictionary access.Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be changed by the user, via direct assignment to the attribute or dictionary entry, or by calling
ndarray.setflags
.The array flags cannot be set arbitrarily:
WRITEBACKIFCOPY can only be set
False
.ALIGNED can only be set
True
if the data is truly aligned.WRITEABLE can only be set
True
if the array owns its own memory or the ultimate owner of the memory exposes a writeable buffer interface or is a string.
Arrays can be both Cstyle and Fortranstyle contiguous simultaneously. This is clear for 1dimensional arrays, but can also be true for higher dimensional arrays.
Even for contiguous arrays a stride for a given dimension
arr.strides[dim]
may be arbitrary ifarr.shape[dim] == 1
or the array has no elements. It does not generally hold thatself.strides[1] == self.itemsize
for Cstyle contiguous arrays orself.strides[0] == self.itemsize
for Fortranstyle contiguous arrays is true. Attributes¶
 C_CONTIGUOUS (C)
The data is in a single, Cstyle contiguous segment.
 F_CONTIGUOUS (F)
The data is in a single, Fortranstyle contiguous segment.
 OWNDATA (O)
The array owns the memory it uses or borrows it from another object.
 WRITEABLE (W)
The data area can be written to. Setting this to False locks the data, making it readonly. A view (slice, etc.) inherits WRITEABLE from its base array at creation time, but a view of a writeable array may be subsequently locked while the base array remains writeable. (The opposite is not true, in that a view of a locked array may not be made writeable. However, currently, locking a base object does not lock any views that already reference it, so under that circumstance it is possible to alter the contents of a locked array via a previously created writeable view onto it.) Attempting to change a nonwriteable array raises a RuntimeError exception.
 ALIGNED (A)
The data and all elements are aligned appropriately for the hardware.
 WRITEBACKIFCOPY (X)
This array is a copy of some other array. The CAPI function PyArray_ResolveWritebackIfCopy must be called before deallocating to the base array will be updated with the contents of this array.
 FNC
F_CONTIGUOUS and not C_CONTIGUOUS.
 FORC
F_CONTIGUOUS or C_CONTIGUOUS (onesegment test).
 BEHAVED (B)
ALIGNED and WRITEABLE.
 CARRAY (CA)
BEHAVED and C_CONTIGUOUS.
 FARRAY (FA)
BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.
 flat¶
A 1D iterator over the Quantity array.
This returns a
QuantityIterator
instance, which behaves the same as theflatiter
instance returned byflat
, and is similar to, but not a subclass of, Python’s builtin iterator object.
 frequencies¶
Series of frequencies for this Spectrogram
 imag¶
The imaginary part of the array.
Examples
>>> x = np.sqrt([1+0j, 0+1j]) >>> x.imag array([ 0. , 0.70710678]) >>> x.imag.dtype dtype('float64')
 info¶
Container for meta information like name, description, format. This is required when the object is used as a mixin column within a table, but can be used as a general way to store meta information.
 isscalar¶
True if the
value
of this quantity is a scalar, or False if it is an arraylike object.Note
This is subtly different from
numpy.isscalar
in thatnumpy.isscalar
returns False for a zerodimensional array (e.g.np.array(1)
), while this is True for quantities, since quantities cannot represent true numpy scalars.
 itemsize¶
Length of one array element in bytes.
Examples
>>> x = np.array([1,2,3], dtype=np.float64) >>> x.itemsize 8 >>> x = np.array([1,2,3], dtype=np.complex128) >>> x.itemsize 16
 nbytes¶
Total bytes consumed by the elements of the array.
See also
sys.getsizeof
Memory consumed by the object itself without parents in case view. This does include memory consumed by nonelement attributes.
Notes
Does not include memory consumed by nonelement attributes of the array object.
Examples
>>> x = np.zeros((3,5,2), dtype=np.complex128) >>> x.nbytes 480 >>> np.prod(x.shape) * x.itemsize 480
 ndim¶
Number of array dimensions.
Examples
>>> x = np.array([1, 2, 3]) >>> x.ndim 1 >>> y = np.zeros((2, 3, 4)) >>> y.ndim 3
 real¶
The real part of the array.
See also
numpy.real
equivalent function
Examples
>>> x = np.sqrt([1+0j, 0+1j]) >>> x.real array([ 1. , 0.70710678]) >>> x.real.dtype dtype('float64')
 shape¶
Tuple of array dimensions.
The shape property is usually used to get the current shape of an array, but may also be used to reshape the array inplace by assigning a tuple of array dimensions to it. As with
numpy.reshape
, one of the new shape dimensions can be 1, in which case its value is inferred from the size of the array and the remaining dimensions. Reshaping an array inplace will fail if a copy is required.Warning
Setting
arr.shape
is discouraged and may be deprecated in the future. Usingndarray.reshape
is the preferred approach.See also
numpy.shape
Equivalent getter function.
numpy.reshape
Function similar to setting
shape
.ndarray.reshape
Method similar to setting
shape
.
Examples
>>> x = np.array([1, 2, 3, 4]) >>> x.shape (4,) >>> y = np.zeros((2, 3, 4)) >>> y.shape (2, 3, 4) >>> y.shape = (3, 8) >>> y array([[ 0., 0., 0., 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0., 0., 0., 0.]]) >>> y.shape = (3, 6) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: total size of new array must be unchanged >>> np.zeros((4,2))[::2].shape = (1,) Traceback (most recent call last): File "<stdin>", line 1, in <module> AttributeError: Incompatible shape for inplace modification. Use `.reshape()` to make a copy with the desired shape.
 si¶
Returns a copy of the current
Quantity
instance with SI units. The value of the resulting object will be scaled.
 size¶
Number of elements in the array.
Equal to
np.prod(a.shape)
, i.e., the product of the array’s dimensions.Notes
a.size
returns a standard arbitrary precision Python integer. This may not be the case with other methods of obtaining the same value (like the suggestednp.prod(a.shape)
, which returns an instance ofnp.int_
), and may be relevant if the value is used further in calculations that may overflow a fixed size integer type.Examples
>>> x = np.zeros((3, 5, 2), dtype=np.complex128) >>> x.size 30 >>> np.prod(x.shape) 30
 span¶
GPS [start, stop) span for this
Spectrogram
 strides¶
Tuple of bytes to step in each dimension when traversing an array.
The byte offset of element
(i[0], i[1], ..., i[n])
in an arraya
is:offset = sum(np.array(i) * a.strides)
A more detailed explanation of strides can be found in the “ndarray.rst” file in the NumPy reference guide.
Warning
Setting
arr.strides
is discouraged and may be deprecated in the future.numpy.lib.stride_tricks.as_strided
should be preferred to create a new view of the same data in a safer way.See also
Notes
Imagine an array of 32bit integers (each 4 bytes):
x = np.array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]], dtype=np.int32)
This array is stored in memory as 40 bytes, one after the other (known as a contiguous block of memory). The strides of an array tell us how many bytes we have to skip in memory to move to the next position along a certain axis. For example, we have to skip 4 bytes (1 value) to move to the next column, but 20 bytes (5 values) to get to the same position in the next row. As such, the strides for the array
x
will be(20, 4)
.Examples
>>> y = np.reshape(np.arange(2*3*4), (2,3,4)) >>> y array([[[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]], [[12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23]]]) >>> y.strides (48, 16, 4) >>> y[1,1,1] 17 >>> offset=sum(y.strides * np.array((1,1,1))) >>> offset/y.itemsize 17
>>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0) >>> x.strides (32, 4, 224, 1344) >>> i = np.array([3,5,2,2]) >>> offset = sum(i * x.strides) >>> x[3,5,2,2] 813 >>> offset / x.itemsize 813
 times¶
Series of GPS times for each sample
 value¶
The numerical value of this instance.
See also
to_value
Get the numerical value in a given unit.
Methods Documentation
 abs(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])[source]¶
Calculate the absolute value elementwise.
np.abs
is a shorthand for this function. Parameters¶
 xarray_like
Input array.
 outndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshlyallocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
 wherearray_like, optional
This condition is broadcast over the input. At locations where the condition is True, the
out
array will be set to the ufunc result. Elsewhere, theout
array will retain its original value. Note that if an uninitializedout
array is created via the defaultout=None
, locations within it where the condition is False will remain uninitialized. **kwargs
For other keywordonly arguments, see the ufunc docs.
 Returns¶
 absolutendarray
An ndarray containing the absolute value of each element in
. This is a scalar ifx
. For complex input,a + ib
, the absolute value isx
is a scalar.
Examples
>>> x = np.array([1.2, 1.2]) >>> np.absolute(x) array([ 1.2, 1.2]) >>> np.absolute(1.2 + 1j) 1.5620499351813308
Plot the function over
[10, 10]
:>>> import matplotlib.pyplot as plt
>>> x = np.linspace(start=10, stop=10, num=101) >>> plt.plot(x, np.absolute(x)) >>> plt.show()
(
png
)Plot the function over the complex plane:
>>> xx = x + 1j * x[:, np.newaxis] >>> plt.imshow(np.abs(xx), extent=[10, 10, 10, 10], cmap='gray') >>> plt.show()
(
png
)The
abs
function can be used as a shorthand fornp.absolute
on ndarrays.>>> x = np.array([1.2, 1.2]) >>> abs(x) array([1.2, 1.2])

all(axis=
None
, out=None
, keepdims=False
, *, where=True
)¶ Returns True if all elements evaluate to True.
Refer to
numpy.all
for full documentation.See also
numpy.all
equivalent function

any(axis=
None
, out=None
, keepdims=False
, *, where=True
)¶ Returns True if any of the elements of
a
evaluate to True.Refer to
numpy.any
for full documentation.See also
numpy.any
equivalent function

append(other, inplace=
True
, pad=None
, gap=None
, resize=True
)[source]¶ Connect another series onto the end of the current one.
 Parameters¶
 other
Series
another series of the same type to connect to this one
 inplace
bool
, optional perform operation inplace, modifying current series, otherwise copy data and return new series, default:
True
Warning
inplace
append bypasses the reference check innumpy.ndarray.resize
, so be carefully to only use this for arrays that haven’t been sharing their memory! pad
float
, optional value with which to pad discontiguous series, by default gaps will result in a
ValueError
. gap
str
, optional action to perform if there’s a gap between the other series and this one. One of
'raise'
 raise aValueError
'ignore'
 remove gap and join data'pad'
 pad gap with zeros
If
pad
is given and is notNone
, the default is'pad'
, otherwise'raise'
. Ifgap='pad'
is given, the default forpad
is0
. resize
bool
, optional resize this array to accommodate new data, otherwise shift the old data to the left (potentially falling off the start) and put the new data in at the end, default:
True
.
 other
 Returns¶
 series
Series
a new series containing joined data sets
 series

argmax(axis=
None
, out=None
, *, keepdims=False
)¶ Return indices of the maximum values along the given axis.
Refer to
numpy.argmax
for full documentation.See also
numpy.argmax
equivalent function

argmin(axis=
None
, out=None
, *, keepdims=False
)¶ Return indices of the minimum values along the given axis.
Refer to
numpy.argmin
for detailed documentation.See also
numpy.argmin
equivalent function

argpartition(kth, axis=
 1
, kind='introselect'
, order=None
)¶ Returns the indices that would partition this array.
Refer to
numpy.argpartition
for full documentation.New in version 1.8.0.
See also
numpy.argpartition
equivalent function

argsort(axis=
 1
, kind=None
, order=None
)¶ Returns the indices that would sort this array.
Refer to
numpy.argsort
for full documentation.See also
numpy.argsort
equivalent function

astype(dtype, order=
'K'
, casting='unsafe'
, subok=True
, copy=True
)¶ Copy of the array, cast to a specified type.
 Parameters¶
 dtypestr or dtype
Typecode or datatype to which the array is cast.
 order{‘C’, ‘F’, ‘A’, ‘K’}, optional
Controls the memory layout order of the result. ‘C’ means C order, ‘F’ means Fortran order, ‘A’ means ‘F’ order if all the arrays are Fortran contiguous, ‘C’ order otherwise, and ‘K’ means as close to the order the array elements appear in memory as possible. Default is ‘K’.
 casting{‘no’, ‘equiv’, ‘safe’, ‘same_kind’, ‘unsafe’}, optional
Controls what kind of data casting may occur. Defaults to ‘unsafe’ for backwards compatibility.
‘no’ means the data types should not be cast at all.
‘equiv’ means only byteorder changes are allowed.
‘safe’ means only casts which can preserve values are allowed.
‘same_kind’ means only safe casts or casts within a kind, like float64 to float32, are allowed.
‘unsafe’ means any data conversions may be done.
 subokbool, optional
If True, then subclasses will be passedthrough (default), otherwise the returned array will be forced to be a baseclass array.
 copybool, optional
By default, astype always returns a newly allocated array. If this is set to false, and the
dtype
,order
, andsubok
requirements are satisfied, the input array is returned instead of a copy.
 Returns¶
 Raises¶
 ComplexWarning
When casting from complex to float or int. To avoid this, one should use
a.real.astype(t)
.
Notes
Changed in version 1.17.0: Casting between a simple data type and a structured one is possible only for “unsafe” casting. Casting to multiple fields is allowed, but casting from multiple fields is not.
Changed in version 1.9.0: Casting from numeric to string types in ‘safe’ casting mode requires that the string dtype length is long enough to store the max integer/float value converted.
Examples
>>> x = np.array([1, 2, 2.5]) >>> x array([1. , 2. , 2.5])
>>> x.astype(int) array([1, 2, 2])

byteswap(inplace=
False
)¶ Swap the bytes of the array elements
Toggle between lowendian and bigendian data representation by returning a byteswapped array, optionally swapped inplace. Arrays of bytestrings are not swapped. The real and imaginary parts of a complex number are swapped individually.
 Parameters¶
 inplacebool, optional
If
True
, swap bytes inplace, default isFalse
.
 Returns¶
 outndarray
The byteswapped array. If
inplace
isTrue
, this is a view to self.
Examples
>>> A = np.array([1, 256, 8755], dtype=np.int16) >>> list(map(hex, A)) ['0x1', '0x100', '0x2233'] >>> A.byteswap(inplace=True) array([ 256, 1, 13090], dtype=int16) >>> list(map(hex, A)) ['0x100', '0x1', '0x3322']
Arrays of bytestrings are not swapped
>>> A = np.array([b'ceg', b'fac']) >>> A.byteswap() array([b'ceg', b'fac'], dtype='S3')
A.newbyteorder().byteswap()
produces an array with the same valuesbut different representation in memory
>>> A = np.array([1, 2, 3]) >>> A.view(np.uint8) array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0], dtype=uint8) >>> A.newbyteorder().byteswap(inplace=True) array([1, 2, 3]) >>> A.view(np.uint8) array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3], dtype=uint8)

choose(choices, out=
None
, mode='raise'
)¶ Use an index array to construct a new array from a set of choices.
Refer to
numpy.choose
for full documentation.See also
numpy.choose
equivalent function

clip(min=
None
, max=None
, out=None
, **kwargs)¶ Return an array whose values are limited to
[min, max]
. One of max or min must be given.Refer to
numpy.clip
for full documentation.See also
numpy.clip
equivalent function

compress(condition, axis=
None
, out=None
)¶ Return selected slices of this array along given axis.
Refer to
numpy.compress
for full documentation.See also
numpy.compress
equivalent function
 conj()¶
Complexconjugate all elements.
Refer to
numpy.conjugate
for full documentation.See also
numpy.conjugate
equivalent function
 conjugate()¶
Return the complex conjugate, elementwise.
Refer to
numpy.conjugate
for full documentation.See also
numpy.conjugate
equivalent function

copy(order=
'C'
)[source]¶ Return a copy of the array.
 Parameters¶
 order{‘C’, ‘F’, ‘A’, ‘K’}, optional
Controls the memory layout of the copy. ‘C’ means Corder, ‘F’ means Forder, ‘A’ means ‘F’ if
a
is Fortran contiguous, ‘C’ otherwise. ‘K’ means match the layout ofa
as closely as possible. (Note that this function andnumpy.copy()
are very similar but have different default values for their order= arguments, and this function always passes subclasses through.)
See also
numpy.copy
Similar function with different default behavior
numpy.copyto
Notes
This function is the preferred method for creating an array copy. The function
numpy.copy()
is similar, but it defaults to using order ‘K’, and will not pass subclasses through by default.Examples
>>> x = np.array([[1,2,3],[4,5,6]], order='F')
>>> y = x.copy()
>>> x.fill(0)
>>> x array([[0, 0, 0], [0, 0, 0]])
>>> y array([[1, 2, 3], [4, 5, 6]])
>>> y.flags['C_CONTIGUOUS'] True

crop(start=
None
, end=None
, copy=False
)[source]¶ Crop this series to the given xaxis extent.
Notes
If either
start
orend
are outside of the originalSeries
span, warnings will be printed and the limits will be restricted to thexspan
.

crop_frequencies(low=
None
, high=None
, copy=False
)[source]¶ Crop this
Spectrogram
to the specified frequencies Parameters¶
 low
float
lower frequency bound for cropped
Spectrogram
 high
float
upper frequency bound for cropped
Spectrogram
 copy
bool
if
False
return a view of the original data, otherwise create a fresh memory copy
 low
 Returns¶
 spec
Spectrogram
A new
Spectrogram
with a subset of data from the frequency axis
 spec

cumprod(axis=
None
, dtype=None
, out=None
)¶ Return the cumulative product of the elements along the given axis.
Refer to
numpy.cumprod
for full documentation.See also
numpy.cumprod
equivalent function

cumsum(axis=
None
, dtype=None
, out=None
)¶ Return the cumulative sum of the elements along the given axis.
Refer to
numpy.cumsum
for full documentation.See also
numpy.cumsum
equivalent function

decompose(bases=
[]
)¶ Generates a new
Quantity
with the units decomposed. Decomposed units have only irreducible units in them (seeastropy.units.UnitBase.decompose
). Parameters¶
 basessequence of
UnitBase
, optional The bases to decompose into. When not provided, decomposes down to any irreducible units. When provided, the decomposed result will only contain the given units. This will raises a
UnitsError
if it’s not possible to do so.
 basessequence of
 Returns¶
 newq
Quantity
A new object equal to this quantity with units decomposed.
 newq

diagonal(offset=
0
, axis1=0
, axis2=1
)¶ Return specified diagonals. In NumPy 1.9 the returned array is a readonly view instead of a copy as in previous NumPy versions. In a future version the readonly restriction will be removed.
Refer to
numpy.diagonal()
for full documentation.See also
numpy.diagonal
equivalent function

diff(n=
1
, axis= 1
)[source]¶ Calculate the nth order discrete difference along given axis.
The first order difference is given by
out[n] = a[n+1]  a[n]
along the given axis, higher order differences are calculated by usingdiff
recursively. Parameters¶
 nint, optional
The number of times values are differenced.
 axisint, optional
The axis along which the difference is taken, default is the last axis.
 Returns¶
 diff
Series
The
n
order differences. The shape of the output is the same as the input, except alongaxis
where the dimension is smaller byn
.
 diff
See also
numpy.diff
for documentation on the underlying method

dot(b, out=
None
)¶
 dump(file)¶
Not implemented, use
.value.dump()
instead.
 dumps()[source]¶
Returns the pickle of the array as a string. pickle.loads will convert the string back to an array.
 Parameters¶
 None

ediff1d(to_end=
None
, to_begin=None
)¶
 fill(value)¶
Fill the array with a scalar value.
 Parameters¶
 valuescalar
All elements of
a
will be assigned this value.
Examples
>>> a = np.array([1, 2]) >>> a.fill(0) >>> a array([0, 0]) >>> a = np.empty(2) >>> a.fill(1) >>> a array([1., 1.])
Fill expects a scalar value and always behaves the same as assigning to a single array element. The following is a rare example where this distinction is important:
>>> a = np.array([None, None], dtype=object) >>> a[0] = np.array(3) >>> a array([array(3), None], dtype=object) >>> a.fill(np.array(3)) >>> a array([array(3), array(3)], dtype=object)
Where other forms of assignments will unpack the array being assigned:
>>> a[...] = np.array(3) >>> a array([3, 3], dtype=object)
 filter(*filt, **kwargs)[source]¶
Apply the given filter to this
Spectrogram
. Parameters¶
 *filtfilter arguments
1, 2, 3, or 4 arguments defining the filter to be applied,
 analog
bool
, optional if
True
, filter definition will be converted from Hertz to Zdomain digital representation, default:False
 inplace
bool
, optional if
True
, this array will be overwritten with the filtered version, default:False
 Returns¶
 result
Spectrogram
the filtered version of the input
Spectrogram
, ifinplace=True
was given, this is just a reference to the modified input array
 result
 Raises¶
 ValueError
if
filt
arguments cannot be interpreted properly

flatten(order=
'C'
)[source]¶ Return a copy of the array collapsed into one dimension.
Any index information is removed as part of the flattening, and the result is returned as a
Quantity
array. Parameters¶
 order{‘C’, ‘F’, ‘A’, ‘K’}, optional
‘C’ means to flatten in rowmajor (Cstyle) order. ‘F’ means to flatten in columnmajor (Fortran style) order. ‘A’ means to flatten in columnmajor order if
a
is Fortran contiguous in memory, rowmajor order otherwise. ‘K’ means to flattena
in the order the elements occur in memory. The default is ‘C’.
 Returns¶
 y
Quantity
A copy of the input array, flattened to one dimension.
 y
Examples
>>> a = Array([[1,2], [3,4]], unit='m', name='Test') >>> a.flatten() <Quantity [1., 2., 3., 4.] m>
 classmethod from_spectra(*spectra, **kwargs)[source]¶
Build a new
Spectrogram
from a list of spectra. Parameters¶
 *spectra
any number of
FrequencySeries
series dt
float
,Quantity
, optional stride between given spectra
 Returns¶
 Spectrogram
a new
Spectrogram
from a vertical stacking of the spectra The new object takes the metadata from the first givenFrequencySeries
if not given explicitly
Notes
Each
FrequencySeries
passed to this constructor must be the same length.

getfield(dtype, offset=
0
)¶ Returns a field of the given array as a certain type.
A field is a view of the array data with a given datatype. The values in the view are determined by the given type and the offset into the current array in bytes. The offset needs to be such that the view dtype fits in the array dtype; for example an array of dtype complex128 has 16byte elements. If taking a view with a 32bit integer (4 bytes), the offset needs to be between 0 and 12 bytes.
 Parameters¶
 dtypestr or dtype
The data type of the view. The dtype size of the view can not be larger than that of the array itself.
 offsetint
Number of bytes to skip before beginning the element view.
Examples
>>> x = np.diag([1.+1.j]*2) >>> x[1, 1] = 2 + 4.j >>> x array([[1.+1.j, 0.+0.j], [0.+0.j, 2.+4.j]]) >>> x.getfield(np.float64) array([[1., 0.], [0., 2.]])
By choosing an offset of 8 bytes we can select the complex part of the array for our view:
>>> x.getfield(np.float64, offset=8) array([[1., 0.], [0., 4.]])
 inject(other)[source]¶
Add two compatible
Series
along their shared xaxis values. Parameters¶
 other
Series
a
Series
whose xindex intersects withself.xindex
 other
 Returns¶
 out
Series
the sum of
self
andother
along their shared xaxis values
 out
 Raises¶
 ValueError
if
self
andother
have incompatible units or xindex intervals
Notes
If
other.xindex
andself.xindex
do not intersect, this method will return a copy ofself
. If the series have uniformly offset indices, this method will raise a warning.If
self.xindex
is an array of timestamps, and ifother.xspan
is not a subset ofself.xspan
, thenother
will be cropped before being adding toself
.Users who wish to taper or window their
Series
should do so before passing it to this method. SeeTimeSeries.taper()
andplanck()
for more information.

insert(obj, values, axis=
None
)¶ Insert values along the given axis before the given indices and return a new
Quantity
object.This is a thin wrapper around the
numpy.insert
function. Parameters¶
 objint, slice or sequence of int
Object that defines the index or indices before which
values
is inserted. valuesarraylike
Values to insert. If the type of
values
is different from that of quantity,values
is converted to the matching type.values
should be shaped so that it can be broadcast appropriately The unit ofvalues
must be consistent with this quantity. axisint, optional
Axis along which to insert
values
. Ifaxis
is None then the quantity array is flattened before insertion.
 Returns¶
 out
Quantity
A copy of quantity with
values
inserted. Note that the insertion does not occur inplace: a new quantity array is returned.
 out
Examples
>>> import astropy.units as u >>> q = [1, 2] * u.m >>> q.insert(0, 50 * u.cm) <Quantity [ 0.5, 1., 2.] m>
>>> q = [[1, 2], [3, 4]] * u.m >>> q.insert(1, [10, 20] * u.m, axis=0) <Quantity [[ 1., 2.], [ 10., 20.], [ 3., 4.]] m>
>>> q.insert(1, 10 * u.m, axis=1) <Quantity [[ 1., 10., 2.], [ 3., 10., 4.]] m>
 is_compatible(other)[source]¶
Check whether this series and other have compatible metadata
This method tests that the
sample size
, and theunit
match.

is_contiguous(other, tol=
3.814697265625e06
)[source]¶ Check whether other is contiguous with self.
 Parameters¶
 other
Series
,numpy.ndarray
another series of the same type to test for contiguity
 tol
float
, optional the numerical tolerance of the test
 other
 Returns¶
 1
if
other
is contiguous with this series, i.e. would attach seamlessly onto the end
 1
if
other
is anticontiguous with this seires, i.e. would attach seamlessly onto the start
 0
if
other
is completely discontiguous with thie series
Notes
if a raw
numpy.ndarray
is passed as other, with no metadata, then the contiguity check will always pass
 item(*args)¶
Copy an element of an array to a scalar Quantity and return it.
Like
item()
except that it always returns aQuantity
, not a Python scalar.
 itemset(*args)¶
Insert scalar into an array (scalar is cast to array’s dtype, if possible)
There must be at least 1 argument, and define the last argument as item. Then,
a.itemset(*args)
is equivalent to but faster thana[args] = item
. The item should be a scalar value andargs
must select a single item in the arraya
. Parameters¶
 *argsArguments
If one argument: a scalar, only used in case
a
is of size 1. If two arguments: the last argument is the value to be set and must be a scalar, the first argument specifies a single array element location. It is either an int or a tuple.
Notes
Compared to indexing syntax,
itemset
provides some speed increase for placing a scalar into a particular location in anndarray
, if you must do this. However, generally this is discouraged: among other problems, it complicates the appearance of the code. Also, when usingitemset
(anditem
) inside a loop, be sure to assign the methods to a local variable to avoid the attribute lookup at each loop iteration.Examples
>>> np.random.seed(123) >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[2, 2, 6], [1, 3, 6], [1, 0, 1]]) >>> x.itemset(4, 0) >>> x.itemset((2, 2), 9) >>> x array([[2, 2, 6], [1, 0, 6], [1, 0, 9]])
 max(axis=None, out=None, keepdims=False, initial=<no value>, where=True)¶
Return the maximum along a given axis.
Refer to
numpy.amax
for full documentation.See also
numpy.amax
equivalent function

mean(axis=
None
, dtype=None
, out=None
, keepdims=False
, *, where=True
)¶ Returns the average of the array elements along given axis.
Refer to
numpy.mean
for full documentation.See also
numpy.mean
equivalent function

median(axis=
None
, **kwargs)[source]¶ Compute the median along the specified axis.
Returns the median of the array elements.
 Parameters¶
 aarray_like
Input array or object that can be converted to an array.
 axis{int, sequence of int, None}, optional
Axis or axes along which the medians are computed. The default is to compute the median along a flattened version of the array. A sequence of axes is supported since version 1.9.0.
 outndarray, optional
Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type (of the output) will be cast if necessary.
 overwrite_inputbool, optional
If True, then allow use of memory of input array
a
for calculations. The input array will be modified by the call tomedian
. This will save memory when you do not need to preserve the contents of the input array. Treat the input as undefined, but it will probably be fully or partially sorted. Default is False. Ifoverwrite_input
isTrue
anda
is not already anndarray
, an error will be raised. keepdimsbool, optional
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original
arr
.New in version 1.9.0.
 Returns¶
 medianndarray
A new array holding the result. If the input contains integers or floats smaller than
float64
, then the output datatype isnp.float64
. Otherwise, the datatype of the output is the same as that of the input. Ifout
is specified, that array is returned instead.
See also
Notes
Given a vector
V
of lengthN
, the median ofV
is the middle value of a sorted copy ofV
,V_sorted
 i e.,V_sorted[(N1)/2]
, whenN
is odd, and the average of the two middle values ofV_sorted
whenN
is even.Examples
>>> a = np.array([[10, 7, 4], [3, 2, 1]]) >>> a array([[10, 7, 4], [ 3, 2, 1]]) >>> np.median(a) 3.5 >>> np.median(a, axis=0) array([6.5, 4.5, 2.5]) >>> np.median(a, axis=1) array([7., 2.]) >>> m = np.median(a, axis=0) >>> out = np.zeros_like(m) >>> np.median(a, axis=0, out=m) array([6.5, 4.5, 2.5]) >>> m array([6.5, 4.5, 2.5]) >>> b = a.copy() >>> np.median(b, axis=1, overwrite_input=True) array([7., 2.]) >>> assert not np.all(a==b) >>> b = a.copy() >>> np.median(b, axis=None, overwrite_input=True) 3.5 >>> assert not np.all(a==b)
 min(axis=None, out=None, keepdims=False, initial=<no value>, where=True)¶
Return the minimum along a given axis.
Refer to
numpy.amin
for full documentation.See also
numpy.amin
equivalent function

nansum(axis=
None
, out=None
, keepdims=False
, *, initial=None
, where=True
)¶ Deprecated since version 5.3: The nansum method is deprecated and may be removed in a future version. Use np.nansum instead.

newbyteorder(new_order=
'S'
, /)¶ Return the array with the same data viewed with a different byte order.
Equivalent to:
arr.view(arr.dtype.newbytorder(new_order))
Changes are also made in all fields and subarrays of the array data type.
 Parameters¶
 new_orderstring, optional
Byte order to force; a value from the byte order specifications below.
new_order
codes can be any of:‘S’  swap dtype from current to opposite endian
{‘<’, ‘little’}  little endian
{‘>’, ‘big’}  big endian
{‘=’, ‘native’}  native order, equivalent to
sys.byteorder
{‘’, ‘I’}  ignore (no change to byte order)
The default value (‘S’) results in swapping the current byte order.
 Returns¶
 new_arrarray
New array object with the dtype reflecting given change to the byte order.
 nonzero()¶
Return the indices of the elements that are nonzero.
Refer to
numpy.nonzero
for full documentation.See also
numpy.nonzero
equivalent function

override_unit(unit, parse_strict=
'raise'
)[source]¶ Forcefully reset the unit of these data
Use of this method is discouraged in favour of
to()
, which performs accurate conversions from one unit to another. The method should really only be used when the original unit of the array is plain wrong.
 pad(pad_width, **kwargs)[source]¶
Pad this series to a new size
See also
numpy.pad
for details on the underlying functionality

partition(kth, axis=
 1
, kind='introselect'
, order=None
)¶ Rearranges the elements in the array in such a way that the value of the element in kth position is in the position it would be in a sorted array. All elements smaller than the kth element are moved before this element and all equal or greater are moved behind it. The ordering of the elements in the two partitions is undefined.
New in version 1.8.0.
 Parameters¶
 kthint or sequence of ints
Element index to partition by. The kth element value will be in its final sorted position and all smaller elements will be moved before it and all equal or greater elements behind it. The order of all elements in the partitions is undefined. If provided with a sequence of kth it will partition all elements indexed by kth of them into their sorted position at once.
Deprecated since version 1.22.0: Passing booleans as index is deprecated.
 axisint, optional
Axis along which to sort. Default is 1, which means sort along the last axis.
 kind{‘introselect’}, optional
Selection algorithm. Default is ‘introselect’.
 orderstr or list of str, optional
When
a
is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need to be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.
See also
numpy.partition
Return a partitioned copy of an array.
argpartition
Indirect partition.
sort
Full sort.
Notes
See
np.partition
for notes on the different algorithms.Examples
>>> a = np.array([3, 4, 2, 1]) >>> a.partition(3) >>> a array([2, 1, 3, 4])
>>> a.partition((1, 3)) >>> a array([1, 2, 3, 4])
 percentile(percentile)[source]¶
Calculate a given spectral percentile for this
Spectrogram
. Parameters¶
 percentile
float
percentile (0  100) of the bins to compute
 percentile
 Returns¶
 spectrum
FrequencySeries
the given percentile
FrequencySeries
calculated from thisSpectralVaraicence
 spectrum

plot(method=
'pcolormesh'
, figsize=(12, 6)
, xscale='autogps'
, **kwargs)[source]¶ Plot the data for this
Spectrogram
 Parameters¶
 method
str
, optional which plotting method to use to render this spectrogram, either
'pcolormesh'
(default) or'imshow'
 figsize
tuple
offloat
, optional (width, height)
(inches) of the output figure xscale
str
, optional the Xaxis scale
 **kwargs
all keyword arguments are passed along to underlying functions, see below for references
 method
 Returns¶
 plot
Plot
the
Plot
containing the data
 plot
See also
matplotlib.pyplot.figure
for documentation of keyword arguments used to create the figure
matplotlib.figure.Figure.add_subplot
for documentation of keyword arguments used to create the axes
gwpy.plot.Axes.imshow
gwpy.plot.Axes.pcolormesh
for documentation of keyword arguments used in rendering the
Spectrogram
data

prepend(other, inplace=
True
, pad=None
, gap=None
, resize=True
)[source]¶ Connect another series onto the start of the current one.
 Parameters¶
 other
Series
another series of the same type as this one
 inplace
bool
, optional perform operation inplace, modifying current series, otherwise copy data and return new series, default:
True
Warning
inplace
prepend bypasses the reference check innumpy.ndarray.resize
, so be carefully to only use this for arrays that haven’t been sharing their memory! pad
float
, optional value with which to pad discontiguous series, by default gaps will result in a
ValueError
. gap
str
, optional action to perform if there’s a gap between the other series and this one. One of
'raise'
 raise aValueError
'ignore'
 remove gap and join data'pad'
 pad gap with zeros
If
pad
is given and is notNone
, the default is'pad'
, otherwise'raise'
. resize
bool
, optional resize this array to accommodate new data, otherwise shift the old data to the left (potentially falling off the start) and put the new data in at the end, default:
True
.
 other
 Returns¶
 series
TimeSeries
timeseries containing joined data sets
 series

prod(axis=
None
, dtype=None
, out=None
, keepdims=False
, initial=1
, where=True
)¶ Return the product of the array elements over the given axis
Refer to
numpy.prod
for full documentation.See also
numpy.prod
equivalent function

ptp(axis=
None
, out=None
, keepdims=False
)¶ Peak to peak (maximum  minimum) value along a given axis.
Refer to
numpy.ptp
for full documentation.See also
numpy.ptp
equivalent function

put(indices, values, mode=
'raise'
)¶ Set
a.flat[n] = values[n]
for alln
in indices.Refer to
numpy.put
for full documentation.See also
numpy.put
equivalent function
 ratio(operand)[source]¶
Calculate the ratio of this
Spectrogram
against a reference Parameters¶
 operand
str
,FrequencySeries
,Quantity
a
FrequencySeries
orQuantity
to weight against, or one of'mean'
: weight against the mean of each spectrum in this Spectrogram'median'
: weight against the median of each spectrum in this Spectrogram
 operand
 Returns¶
 spectrogram
Spectrogram
a new
Spectrogram
 spectrogram
 Raises¶
 ValueError
if
operand
is given as astr
that isn’t supported
 ravel([order])¶
Return a flattened array.
Refer to
numpy.ravel
for full documentation.See also
numpy.ravel
equivalent function
ndarray.flat
a flat iterator on the array.
 classmethod read(source, *args, **kwargs)[source]¶
Read data into a
Spectrogram
Arguments and keywords depend on the output format, see the online documentation for full details for each format, the parameters below are common to most formats.
 Parameters¶
 source
str
,list
Source of data, any of the following:
 *args
Other arguments are (in general) specific to the given
format
. format
str
, optional Source format identifier. If not given, the format will be detected if possible. See below for list of acceptable formats.
 **kwargs
Other keywords are (in general) specific to the given
format
.
 source
 Returns¶
 specgram
Spectrogram
 specgram
Notes
The available builtin formats are:
Format
Read
Write
Autoidentify
hdf5
Yes
No
No

repeat(repeats, axis=
None
)¶ Repeat elements of an array.
Refer to
numpy.repeat
for full documentation.See also
numpy.repeat
equivalent function

reshape(shape, order=
'C'
)¶ Returns an array containing the same data with a new shape.
Refer to
numpy.reshape
for full documentation.See also
numpy.reshape
equivalent function
Notes
Unlike the free function
numpy.reshape
, this method onndarray
allows the elements of the shape parameter to be passed in as separate arguments. For example,a.reshape(10, 11)
is equivalent toa.reshape((10, 11))
.

resize(new_shape, refcheck=
True
)¶ Change shape and size of array inplace.
 Parameters¶
 new_shapetuple of ints, or
n
ints Shape of resized array.
 refcheckbool, optional
If False, reference count will not be checked. Default is True.
 new_shapetuple of ints, or
 Returns¶
 None
 Raises¶
 ValueError
If
a
does not own its own data or references or views to it exist, and the data memory must be changed. PyPy only: will always raise if the data memory must be changed, since there is no reliable way to determine if references or views to it exist. SystemError
If the
order
keyword argument is specified. This behaviour is a bug in NumPy.
See also
resize
Return a new array with the specified shape.
Notes
This reallocates space for the data area if necessary.
Only contiguous arrays (data elements consecutive in memory) can be resized.
The purpose of the reference count check is to make sure you do not use this array as a buffer for another Python object and then reallocate the memory. However, reference counts can increase in other ways so if you are sure that you have not shared the memory for this array with another Python object, then you may safely set
refcheck
to False.Examples
Shrinking an array: array is flattened (in the order that the data are stored in memory), resized, and reshaped:
>>> a = np.array([[0, 1], [2, 3]], order='C') >>> a.resize((2, 1)) >>> a array([[0], [1]])
>>> a = np.array([[0, 1], [2, 3]], order='F') >>> a.resize((2, 1)) >>> a array([[0], [2]])
Enlarging an array: as above, but missing entries are filled with zeros:
>>> b = np.array([[0, 1], [2, 3]]) >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple >>> b array([[0, 1, 2], [3, 0, 0]])
Referencing an array prevents resizing…
>>> c = a >>> a.resize((1, 1)) Traceback (most recent call last): ... ValueError: cannot resize an array that references or is referenced ...
Unless
refcheck
is False:>>> a.resize((1, 1), refcheck=False) >>> a array([[0]]) >>> c array([[0]])

round(decimals=
0
, out=None
)¶ Return
a
with each element rounded to the given number of decimals.Refer to
numpy.around
for full documentation.See also
numpy.around
equivalent function

searchsorted(v, side=
'left'
, sorter=None
)¶ Find indices where elements of v should be inserted in a to maintain order.
For full documentation, see
numpy.searchsorted
See also
numpy.searchsorted
equivalent function

setfield(val, dtype, offset=
0
)¶ Put a value into a specified place in a field defined by a datatype.
Place
val
intoa
’s field defined bydtype
and beginningoffset
bytes into the field. Parameters¶
 valobject
Value to be placed in field.
 dtypedtype object
Datatype of the field in which to place
val
. offsetint, optional
The number of bytes into the field at which to place
val
.
 Returns¶
 None
See also
Examples
>>> x = np.eye(3) >>> x.getfield(np.float64) array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]) >>> x.setfield(3, np.int32) >>> x.getfield(np.int32) array([[3, 3, 3], [3, 3, 3], [3, 3, 3]], dtype=int32) >>> x array([[1.0e+000, 1.5e323, 1.5e323], [1.5e323, 1.0e+000, 1.5e323], [1.5e323, 1.5e323, 1.0e+000]]) >>> x.setfield(np.eye(3), np.int32) >>> x array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]])

setflags(write=
None
, align=None
, uic=None
)¶ Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY, respectively.
These Booleanvalued flags affect how numpy interprets the memory area used by
a
(see Notes below). The ALIGNED flag can only be set to True if the data is actually aligned according to the type. The WRITEBACKIFCOPY and flag can never be set to True. The flag WRITEABLE can only be set to True if the array owns its own memory, or the ultimate owner of the memory exposes a writeable buffer interface, or is a string. (The exception for string is made so that unpickling can be done without copying memory.) Parameters¶
 writebool, optional
Describes whether or not
a
can be written to. alignbool, optional
Describes whether or not
a
is aligned properly for its type. uicbool, optional
Describes whether or not
a
is a copy of another “base” array.
Notes
Array flags provide information about how the memory area used for the array is to be interpreted. There are 7 Boolean flags in use, only four of which can be changed by the user: WRITEBACKIFCOPY, WRITEABLE, and ALIGNED.
WRITEABLE (W) the data area can be written to;
ALIGNED (A) the data and strides are aligned appropriately for the hardware (as determined by the compiler);
WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced by .base). When the CAPI function PyArray_ResolveWritebackIfCopy is called, the base array will be updated with the contents of this array.
All flags can be accessed using the single (upper case) letter as well as the full name.
Examples
>>> y = np.array([[3, 1, 7], ... [2, 0, 0], ... [8, 5, 9]]) >>> y array([[3, 1, 7], [2, 0, 0], [8, 5, 9]]) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : True ALIGNED : True WRITEBACKIFCOPY : False >>> y.setflags(write=0, align=0) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : False ALIGNED : False WRITEBACKIFCOPY : False >>> y.setflags(uic=1) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: cannot set WRITEBACKIFCOPY flag to True
 shift(delta)[source]¶
Shift this
Series
forward on the Xaxis bydelta
This modifies the series inplace.
 Parameters¶
Examples
>>> from gwpy.types import Series >>> a = Series([1, 2, 3, 4, 5], x0=0, dx=1, xunit='m') >>> print(a.x0) 0.0 m >>> a.shift(5) >>> print(a.x0) 5.0 m >>> a.shift('1 km') 995.0 m

sort(axis=
 1
, kind=None
, order=None
)¶ Sort an array inplace. Refer to
numpy.sort
for full documentation. Parameters¶
 axisint, optional
Axis along which to sort. Default is 1, which means sort along the last axis.
 kind{‘quicksort’, ‘mergesort’, ‘heapsort’, ‘stable’}, optional
Sorting algorithm. The default is ‘quicksort’. Note that both ‘stable’ and ‘mergesort’ use timsort under the covers and, in general, the actual implementation will vary with datatype. The ‘mergesort’ option is retained for backwards compatibility.
Changed in version 1.15.0: The ‘stable’ option was added.
 orderstr or list of str, optional
When
a
is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.
See also
numpy.sort
Return a sorted copy of an array.
numpy.argsort
Indirect sort.
numpy.lexsort
Indirect stable sort on multiple keys.
numpy.searchsorted
Find elements in sorted array.
numpy.partition
Partial sort.
Notes
See
numpy.sort
for notes on the different sorting algorithms.Examples
>>> a = np.array([[1,4], [3,1]]) >>> a.sort(axis=1) >>> a array([[1, 4], [1, 3]]) >>> a.sort(axis=0) >>> a array([[1, 3], [1, 4]])
Use the
order
keyword to specify a field to use when sorting a structured array:>>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)]) >>> a.sort(order='y') >>> a array([(b'c', 1), (b'a', 2)], dtype=[('x', 'S1'), ('y', '<i8')])

squeeze(axis=
None
)¶ Remove axes of length one from
a
.Refer to
numpy.squeeze
for full documentation.See also
numpy.squeeze
equivalent function

std(axis=
None
, dtype=None
, out=None
, ddof=0
, keepdims=False
, *, where=True
)¶ Returns the standard deviation of the array elements along given axis.
Refer to
numpy.std
for full documentation.See also
numpy.std
equivalent function

sum(axis=
None
, dtype=None
, out=None
, keepdims=False
, initial=0
, where=True
)¶ Return the sum of the array elements over the given axis.
Refer to
numpy.sum
for full documentation.See also
numpy.sum
equivalent function
 swapaxes(axis1, axis2)¶
Return a view of the array with
axis1
andaxis2
interchanged.Refer to
numpy.swapaxes
for full documentation.See also
numpy.swapaxes
equivalent function

take(indices, axis=
None
, out=None
, mode='raise'
)¶ Return an array formed from the elements of
a
at the given indices.Refer to
numpy.take
for full documentation.See also
numpy.take
equivalent function

to(unit, equivalencies=
[]
, copy=True
)¶ Return a new
Quantity
object with the specified unit. Parameters¶
 unitunitlike
An object that represents the unit to convert to. Must be an
UnitBase
object or a string parseable by theunits
package. equivalencieslist of tuple
A list of equivalence pairs to try if the units are not directly convertible. See Equivalencies. If not provided or
[]
, class default equivalencies will be used (none forQuantity
, but may be set for subclasses) IfNone
, no equivalencies will be applied at all, not even any set globally or within a context. copybool, optional
If
True
(default), then the value is copied. Otherwise, a copy will only be made if necessary.
See also
to_value
get the numerical value in a given unit.

to_string(unit=
None
, precision=None
, format=None
, subfmt=None
)¶ Generate a string representation of the quantity and its unit.
The behavior of this function can be altered via the
numpy.set_printoptions
function and its various keywords. The exception to this is thethreshold
keyword, which is controlled via the[units.quantity]
configuration itemlatex_array_threshold
. This is treated separately because the numpy default of 1000 is too big for most browsers to handle. Parameters¶
 unitunitlike, optional
Specifies the unit. If not provided, the unit used to initialize the quantity will be used.
 precisionnumber, optional
The level of decimal precision. If
None
, or not provided, it will be determined from NumPy print options. formatstr, optional
The format of the result. If not provided, an unadorned string is returned. Supported values are:
‘latex’: Return a LaTeXformatted string
‘latex_inline’: Return a LaTeXformatted string that uses negative exponents instead of fractions
 subfmtstr, optional
Subformat of the result. For the moment, only used for
format='latex'
andformat='latex_inline'
. Supported values are:‘inline’: Use
$ ... $
as delimiters.‘display’: Use
$\displaystyle ... $
as delimiters.
 Returns¶
 str
A string with the contents of this Quantity

to_value(unit=
None
, equivalencies=[]
)¶ The numerical value, possibly in a different unit.
 Parameters¶
 unitunitlike, optional
The unit in which the value should be given. If not given or
None
, use the current unit. equivalencieslist of tuple, optional
A list of equivalence pairs to try if the units are not directly convertible (see Equivalencies). If not provided or
[]
, class default equivalencies will be used (none forQuantity
, but may be set for subclasses). IfNone
, no equivalencies will be applied at all, not even any set globally or within a context.
 Returns¶
 valuendarray or scalar
The value in the units specified. For arrays, this will be a view of the data if no unit conversion was necessary.
See also
to
Get a new instance in a different unit.

tobytes(order=
'C'
)¶ Not implemented, use
.value.tobytes()
instead.

tofile(fid, sep=
''
, format='%s'
)¶ Not implemented, use
.value.tofile()
instead.
 tolist()¶
Return the array as an
a.ndim
levels deep nested list of Python scalars.Return a copy of the array data as a (nested) Python list. Data items are converted to the nearest compatible builtin Python type, via the
item
function.If
a.ndim
is 0, then since the depth of the nested list is 0, it will not be a list at all, but a simple Python scalar. Parameters¶
 none
 Returns¶
 yobject, or list of object, or list of list of object, or …
The possibly nested list of array elements.
Notes
The array may be recreated via
a = np.array(a.tolist())
, although this may sometimes lose precision.Examples
For a 1D array,
a.tolist()
is almost the same aslist(a)
, except thattolist
changes numpy scalars to Python scalars:>>> a = np.uint32([1, 2]) >>> a_list = list(a) >>> a_list [1, 2] >>> type(a_list[0]) <class 'numpy.uint32'> >>> a_tolist = a.tolist() >>> a_tolist [1, 2] >>> type(a_tolist[0]) <class 'int'>
Additionally, for a 2D array,
tolist
applies recursively:>>> a = np.array([[1, 2], [3, 4]]) >>> list(a) [array([1, 2]), array([3, 4])] >>> a.tolist() [[1, 2], [3, 4]]
The base case for this recursion is a 0D array:
>>> a = np.array(1) >>> list(a) Traceback (most recent call last): ... TypeError: iteration over a 0d array >>> a.tolist() 1

tostring(order=
'C'
)[source]¶ Construct Python bytes containing the raw data bytes in the array.
Constructs Python bytes showing a copy of the raw contents of data memory. The bytes object is produced in Corder by default. This behavior is controlled by the
order
parameter.New in version 1.9.0.
 Parameters¶
 order{‘C’, ‘F’, ‘A’}, optional
Controls the memory layout of the bytes object. ‘C’ means Corder, ‘F’ means Forder, ‘A’ (short for Any) means ‘F’ if
a
is Fortran contiguous, ‘C’ otherwise. Default is ‘C’.
 Returns¶
 sbytes
Python bytes exhibiting a copy of
a
’s raw data.
See also
frombuffer
Inverse of this operation, construct a 1dimensional array from Python bytes.
Examples
>>> x = np.array([[0, 1], [2, 3]], dtype='<u2') >>> x.tobytes() b'\x00\x00\x01\x00\x02\x00\x03\x00' >>> x.tobytes('C') == x.tobytes() True >>> x.tobytes('F') b'\x00\x00\x02\x00\x01\x00\x03\x00'

trace(offset=
0
, axis1=0
, axis2=1
, dtype=None
, out=None
)¶ Return the sum along diagonals of the array.
Refer to
numpy.trace
for full documentation.See also
numpy.trace
equivalent function
 transpose(*axes)¶
Returns a view of the array with axes transposed.
Refer to
numpy.transpose
for full documentation. Parameters¶
 axesNone, tuple of ints, or
n
ints None or no argument: reverses the order of the axes.
tuple of ints:
i
in thej
th place in the tuple means that the array’si
th axis becomes the transposed array’sj
th axis.n
ints: same as an ntuple of the same ints (this form is intended simply as a “convenience” alternative to the tuple form).
 axesNone, tuple of ints, or
 Returns¶
 pndarray
View of the array with its axes suitably permuted.
See also
transpose
Equivalent function.
ndarray.T
Array property returning the array transposed.
ndarray.reshape
Give a new shape to an array without changing its data.
Examples
>>> a = np.array([[1, 2], [3, 4]]) >>> a array([[1, 2], [3, 4]]) >>> a.transpose() array([[1, 3], [2, 4]]) >>> a.transpose((1, 0)) array([[1, 3], [2, 4]]) >>> a.transpose(1, 0) array([[1, 3], [2, 4]])
>>> a = np.array([1, 2, 3, 4]) >>> a array([1, 2, 3, 4]) >>> a.transpose() array([1, 2, 3, 4])

update(other, inplace=
True
)[source]¶ Update this series by appending new data from an other and dropping the same amount of data off the start.
This is a convenience method that just calls
append
withresize=False
.

var(axis=
None
, dtype=None
, out=None
, ddof=0
, keepdims=False
, *, where=True
)¶ Returns the variance of the array elements, along given axis.
Refer to
numpy.var
for full documentation.See also
numpy.var
equivalent function

variance(bins=
None
, low=None
, high=None
, nbins=500
, log=False
, norm=False
, density=False
)[source]¶ Calculate the
SpectralVariance
of thisSpectrogram
. Parameters¶
 bins
ndarray
, optional, defaultNone
array of histogram bin edges, including the rightmost edge
 low
float
, optional, default:None
left edge of lowest amplitude bin, only read if
bins
is not given high
float
, optional, default:None
right edge of highest amplitude bin, only read if
bins
is not given nbins
int
, optional, default:500
number of bins to generate, only read if
bins
is not given log
bool
, optional, default:False
calculate amplitude bins over a logarithmic scale, only read if
bins
is not given norm
bool
, optional, default:False
normalise bin counts to a unit sum
 density
bool
, optional, default:False
normalise bin counts to a unit integral
 bins
 Returns¶
 specvar
SpectralVariance
2Darray of spectral frequencyamplitude counts
 specvar
See also
numpy.histogram
for details on specifying bins and weights
 view([dtype][, type])¶
New view of array with the same data.
Note
Passing None for
dtype
is different from omitting the parameter, since the former invokesdtype(None)
which is an alias fordtype('float_')
. Parameters¶
 dtypedatatype or ndarray subclass, optional
Datatype descriptor of the returned view, e.g., float32 or int16. Omitting it results in the view having the same datatype as
a
. This argument can also be specified as an ndarray subclass, which then specifies the type of the returned object (this is equivalent to setting thetype
parameter). typePython type, optional
Type of the returned view, e.g., ndarray or matrix. Again, omission of the parameter results in type preservation.
Notes
a.view()
is used two different ways:a.view(some_dtype)
ora.view(dtype=some_dtype)
constructs a view of the array’s memory with a different datatype. This can cause a reinterpretation of the bytes of memory.a.view(ndarray_subclass)
ora.view(type=ndarray_subclass)
just returns an instance ofndarray_subclass
that looks at the same array (same shape, dtype, etc.) This does not cause a reinterpretation of the memory.For
a.view(some_dtype)
, ifsome_dtype
has a different number of bytes per entry than the previous dtype (for example, converting a regular array to a structured array), then the last axis ofa
must be contiguous. This axis will be resized in the result.Changed in version 1.23.0: Only the last axis needs to be contiguous. Previously, the entire array had to be Ccontiguous.
Examples
>>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)])
Viewing array data using a different type and dtype:
>>> y = x.view(dtype=np.int16, type=np.matrix) >>> y matrix([[513]], dtype=int16) >>> print(type(y)) <class 'numpy.matrix'>
Creating a view on a structured array so it can be used in calculations
>>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)]) >>> xv = x.view(dtype=np.int8).reshape(1,2) >>> xv array([[1, 2], [3, 4]], dtype=int8) >>> xv.mean(0) array([2., 3.])
Making changes to the view changes the underlying array
>>> xv[0,1] = 20 >>> x array([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')])
Using a view to convert an array to a recarray:
>>> z = x.view(np.recarray) >>> z.a array([1, 3], dtype=int8)
Views share data:
>>> x[0] = (9, 10) >>> z[0] (9, 10)
Views that change the dtype size (bytes per entry) should normally be avoided on arrays defined by slices, transposes, fortranordering, etc.:
>>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16) >>> y = x[:, ::2] >>> y array([[1, 3], [4, 6]], dtype=int16) >>> y.view(dtype=[('width', np.int16), ('length', np.int16)]) Traceback (most recent call last): ... ValueError: To change to a dtype of a different size, the last axis must be contiguous >>> z = y.copy() >>> z.view(dtype=[('width', np.int16), ('length', np.int16)]) array([[(1, 3)], [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])
However, views that change dtype are totally fine for arrays with a contiguous last axis, even if the rest of the axes are not Ccontiguous:
>>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4) >>> x.transpose(1, 0, 2).view(np.int16) array([[[ 256, 770], [3340, 3854]], [[1284, 1798], [4368, 4882]], [[2312, 2826], [5396, 5910]]], dtype=int16)
 write(target, *args, **kwargs)[source]¶
Write this
Spectrogram
to a fileArguments and keywords depend on the output format, see the online documentation for full details for each format, the parameters below are common to most formats.
 Parameters¶
Notes
The available builtin formats are:
Format
Read
Write
Autoidentify
hdf5
Yes
Yes
No
 zip()[source]¶
Zip the
xindex
andvalue
arrays of thisSeries
 Returns¶
 stacked2d
numpy.ndarray
The array formed by stacking the the
xindex
andvalue
of this series
 stacked2d
Examples
>>> a = Series([0, 2, 4, 6, 8], xindex=[5, 4, 3, 2, 1]) >>> a.zip() array([[5., 0.], [4., 2.], [3., 4.], [2., 6.], [1., 8.]])

zpk(zeros, poles, gain, analog=
True
)[source]¶ Filter this
Spectrogram
by applying a zeropolegain filter Parameters¶
 Returns¶
 specgram
Spectrogram
the frequencydomain filtered version of the input data
 specgram
See also
Spectrogram.filter
for details on how a digital ZPKformat filter is applied
Examples
To apply a zpk filter with file poles at 100 Hz, and five zeros at 1 Hz (giving an overall DC gain of 1e10):
>>> data2 = data.zpk([100]*5, [1]*5, 1e10)