bsnputils module¶
Contains various numpy
utility programs.
Note
if the math looks strange in the documentation, just reload the page.
BivariatePolynomial
: a minimal class for bivariate polynomialsouter_bivar
: make aBivariatePolynomial
from twoPolynomial
objectscheck_vector
,check_matrix
,check_vector_or_matrix
,check_square
,check_tensor
: check an array and return its shapegrid_function
: apply a function on a lattice gridgenerate_RNG_streams
: generate a number of random number streams (for parallelizations)ecdf, inv_ecdf
: the empirical cdf of a sample and its inversenprepeat_col, nprepeat_row
: repeat a column or a rownpmaxabs
: maximum absolute value of the elements of an arrayrice_stderr
: the Rice local standard errors of a random variablebs_sqrt_pdmatrix
: square root of a posuitve definite matrixnplog
,npexp, npxlogx
: \(C^2\) extensions ofnp.log
,np.exp
, and \(x\log x\), with first two derivativesnppow
: \(a^b\) for arrays, with first two derivativesnppad_beg_zeros
,nppad_end_zeros
,nppad2_end_zeros
: pad the beginning or the end of an array with 0bsgrid, make_lexico_grid
: construct grid arraysgauleg, gauher
: nodes and weights of Gauss-Legendre and Gauss-Hermite polynomialsgaussian_expectation
: uses Gauss-Hermite to compute \(Ef(X)\) for \(X=N(0,1)\)legendre_polynomials
: evaluates the Legendre polynomialsquantile_transform
: returns the quantiles of values in an arrayprint_quantiles
: prints requested quantiles of an arrayset_elements_abovebelow_diagonal
: sets all elements of the given matrix above or below the diagonal to a specified scalar value.find_row_single_nonzero
: find a row that has at most one nonzero element in a matrixbring_row_up
,bring_col_left
: bring a row up, or a column leftmake_lower_tri
: make a square matrix lower triangular, if possible
BivariatePolynomial
¶
A class for bivariate polynomials as a list of Polynomial
objects, with a minimal interface:
- construct from a matrix of coefficients
- add, subtract, multiply (with a constant and with a
BivariatePolynomial
) - evaluate \(p(x, y)\) when x, y are at most vectors (and have the same shape if both vectors)
Source code in bs_python_utils/bsnputils.py
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|
__init__(coeffs)
¶
coeffs: a (deg1+1, deg2+2)
matrix
Source code in bs_python_utils/bsnputils.py
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|
bring_col_left(m, old_col, new_col)
¶
bring a column of a matrix to a column on the left of it
Parameters:
Name | Type | Description | Default |
---|---|---|---|
m |
ndarray
|
a Numpy matrix |
required |
old_col |
int
|
the original index of the column |
required |
new_col |
int
|
the destination index of the column |
required |
Returns:
Type | Description |
---|---|
ndarray
|
a matrix of the same shape with column |
ndarray
|
brought to the |
Source code in bs_python_utils/bsnputils.py
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|
bring_row_up(m, old_row, new_row)
¶
bring a row of a matrix to a higher row
Parameters:
Name | Type | Description | Default |
---|---|---|---|
m |
ndarray
|
a Numpy matrix |
required |
old_row |
int
|
the original index of the row |
required |
new_row |
int
|
the destination index of the row |
required |
Returns:
Type | Description |
---|---|
ndarray
|
a matrix of the same shape with row |
ndarray
|
|
Source code in bs_python_utils/bsnputils.py
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|
bs_sqrt_pdmatrix(m)
¶
square root of a positive definite matrix
Parameters:
Name | Type | Description | Default |
---|---|---|---|
m |
ndarray
|
a positive definite matrix |
required |
Returns:
Type | Description |
---|---|
ndarray
|
the square root of the matrix. |
Source code in bs_python_utils/bsnputils.py
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|
bsgrid(v, w)
¶
make a two-dimensional matrix of all pairs of elements of the vectors v
and w
Parameters:
Name | Type | Description | Default |
---|---|---|---|
v |
ndarray
|
basis vector, size m |
required |
w |
ndarray
|
basis vector, size n |
required |
Returns:
Type | Description |
---|---|
ndarray
|
an array of shape |
Examples:
>>> v = np.array([1,2,3])
>>> w = np.array([4,5])
>>> bsgrid(v, w)
array([[1, 4],
[1, 5],
[2, 4],
[2, 5],
[3, 4],
[3, 5]])
Source code in bs_python_utils/bsnputils.py
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|
check_matrix(x, fun_name=None)
¶
test that x
is a matrix; aborts otherwise
Parameters:
Name | Type | Description | Default |
---|---|---|---|
x |
Any
|
a matrix, we hope |
required |
fun_name |
str | None
|
name of the calling function |
None
|
Returns:
Type | Description |
---|---|
tuple[int, int]
|
the shape if successful |
Source code in bs_python_utils/bsnputils.py
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|
check_square(A, fun_name=None)
¶
test that an object used in fun_name
is a square matrix
Parameters:
Name | Type | Description | Default |
---|---|---|---|
A |
Any
|
square matrix, we hope |
required |
fun_name |
str | None
|
the name of the calling function |
None
|
Returns:
Type | Description |
---|---|
int
|
the number of rows and columns of |
Source code in bs_python_utils/bsnputils.py
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|
check_tensor(x, n_dims, fun_name=None)
¶
test that x
is an n_dims
dimensional array; aborts otherwise
Parameters:
Name | Type | Description | Default |
---|---|---|---|
x |
Any
|
an |
required |
fun_name |
str | None
|
name of the calling function |
None
|
Returns:
Type | Description |
---|---|
tuple[int, ...]
|
the shape if successful |
Source code in bs_python_utils/bsnputils.py
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|
check_vector(v, fun_name=None)
¶
test that v
is a vector; aborts otherwise
Parameters:
Name | Type | Description | Default |
---|---|---|---|
v |
Any
|
a vector, we hope |
required |
fun_name |
str | None
|
name of the calling function |
None
|
Returns:
Type | Description |
---|---|
int
|
the size if successful. |
Source code in bs_python_utils/bsnputils.py
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|
check_vector_or_matrix(x, fun_name=None)
¶
test that x
is a vector or a matrix; aborts otherwise
Parameters:
Name | Type | Description | Default |
---|---|---|---|
x |
Any
|
a vector or matrix, we hope |
required |
fun_name |
str | None
|
name of the calling function |
None
|
Returns:
Type | Description |
---|---|
int
|
the number of dimensions of |
Source code in bs_python_utils/bsnputils.py
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|
ecdf(x)
¶
Evaluate the empirical cdf at each point in sample
Parameters:
Name | Type | Description | Default |
---|---|---|---|
x |
ndarray
|
1-dim array |
required |
Returns:
Type | Description |
---|---|
ndarray
|
A 1-dim array |
Source code in bs_python_utils/bsnputils.py
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|
find_row_single_nonzero(m)
¶
find a row that has at most one nonzero element in a matrix
Parameters:
Name | Type | Description | Default |
---|---|---|---|
m |
ndarray
|
a matrix |
required |
Returns:
Type | Description |
---|---|
tuple[int, int] | None
|
the indices of the first such row, and of the column where the nonzero element is |
tuple[int, int] | None
|
(if that row is identically zero, return 0 for the column index) |
tuple[int, int] | None
|
or |
Source code in bs_python_utils/bsnputils.py
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|
gauher(n)
¶
nodes and weights for Gauss-Hermite integration
Parameters:
Name | Type | Description | Default |
---|---|---|---|
n |
int
|
number of nodes |
required |
Returns:
Type | Description |
---|---|
TwoArrays
|
array of |
Source code in bs_python_utils/bsnputils.py
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|
gauleg(n)
¶
nodes and weights for Gauss-Legendre integration \int_{-1}^1 f(x)dx
Parameters:
Name | Type | Description | Default |
---|---|---|---|
n |
int
|
number of nodes |
required |
Returns:
Type | Description |
---|---|
TwoArrays
|
array of |
Source code in bs_python_utils/bsnputils.py
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|
gaussian_expectation(f, x, w, n=16, vectorized=False, pars=None)
¶
computes the expectation of a function of an N(0,1)
random variable
using Gauss-Hermite with n nodes
the nodes and weights can be provided, if available
Parameters:
Name | Type | Description | Default |
---|---|---|---|
f |
Callable
|
a scalar or array function of a scalar or array variable and possibly other parameters |
required |
vectorized |
bool
|
if True, the function accepts an array as argument |
False
|
pars |
Iterable | None
|
parameters for |
None
|
n |
int
|
number of nodes |
16
|
x |
ndarray | None
|
locations of the nodes |
required |
w |
ndarray | None
|
their weights |
required |
Returns:
Type | Description |
---|---|
ndarray | float
|
the expectation of |
Source code in bs_python_utils/bsnputils.py
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|
generate_RNG_streams(nsim, initial_seed=13091962)
¶
return nsim
random number generators
Parameters:
Name | Type | Description | Default |
---|---|---|---|
nsim |
int
|
number of RNGs we want |
required |
initial_seed |
int
|
any large integer |
13091962
|
Returns:
Type | Description |
---|---|
list[Generator]
|
|
Examples:
>>> streams = generate_RNG_streams(10, 575856896)
>>> x = streams[i].normal(scale=s, size=(nmarkets, nproducts))
Source code in bs_python_utils/bsnputils.py
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|
grid_function(fun, x_points, y_points)
¶
apply a function f(x, y)
on a lattice grid
Parameters:
Name | Type | Description | Default |
---|---|---|---|
fun |
Callable[[ndarray, ndarray], ndarray]
|
should return a matrix |
required |
x_points |
ndarray
|
an |
required |
y_points |
ndarray
|
an |
required |
Returns:
Type | Description |
---|---|
ndarray
|
the |
Source code in bs_python_utils/bsnputils.py
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|
inv_ecdf(v, q)
¶
Evaluate the empirical q
-quantiles of the sample v
in a way that is consistent with ecdf
.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
v |
ndarray
|
1-dim array |
required |
q |
ndarray | float
|
1-dim array |
required |
Returns:
Type | Description |
---|---|
ndarray | float
|
A 1-dim array |
Source code in bs_python_utils/bsnputils.py
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|
legendre_polynomials(x, max_deg, a=-1.0, b=1.0, no_constant=False)
¶
evaluates the Legendre polynomials over x
in the interval \([a, b]\)
Parameters:
Name | Type | Description | Default |
---|---|---|---|
x |
ndarray
|
the points where the polynomials are to be evaluated |
required |
max_deg |
int
|
the maximum degree |
required |
a |
float
|
the start of the interval, classically -1 |
-1.0
|
b |
float
|
the end of the interval, classically 1 |
1.0
|
no_constant |
bool
|
if True, delete the constant polynomial |
False
|
Returns:
Type | Description |
---|---|
ndarray
|
an array of |
Source code in bs_python_utils/bsnputils.py
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|
make_lexico_grid(arr)
¶
1 |
|
eq 2$.
1 2 3 4 5 |
|
Source code in bs_python_utils/bsnputils.py
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|
make_lower_tri(m)
¶
make a square matrix lower triangular, if possible
Parameters:
Name | Type | Description | Default |
---|---|---|---|
m |
ndarray
|
a Numpy square matrix |
required |
Returns:
Type | Description |
---|---|
tuple[ndarray, list[int], list[int]] | None
|
if permuting rows and columns can make |
tuple[ndarray, list[int], list[int]] | None
|
and the row and column permutations used |
tuple[ndarray, list[int], list[int]] | None
|
else we return |
Source code in bs_python_utils/bsnputils.py
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|
npexp(arr, bigx=50.0, lowx=-50.0, deriv=0, verbose=False)
¶
\(C^2\) extension of \(\exp(a)\) above bigx
and below lowx
,
perhaps with derivatives
Parameters:
Name | Type | Description | Default |
---|---|---|---|
arr |
ndarray
|
any Numpy array |
required |
bigx |
float
|
upper bound |
50.0
|
lowx |
float
|
lower bound |
-50.0
|
deriv |
int
|
if 1, compute derivative, if 2, second derivative |
0
|
verbose |
bool
|
prints debugging info |
False
|
Returns:
Type | Description |
---|---|
ndarray | TwoArrays | ThreeArrays
|
\(\exp(a)\) \(C^2\)-extended above |
ndarray | TwoArrays | ThreeArrays
|
perhaps with derivatives |
Source code in bs_python_utils/bsnputils.py
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|
nplog(arr, eps=1e-30, deriv=0, verbose=False)
¶
\(C^2\) extension of \(\ln(a)\) below eps
, perhaps with derivatives
Parameters:
Name | Type | Description | Default |
---|---|---|---|
arr |
ndarray
|
any Numpy array |
required |
eps |
float
|
lower bound |
1e-30
|
deriv |
int
|
if 1, compute derivative, if 2, second derivative |
0
|
verbose |
bool
|
prints debugging info |
False
|
Returns:
Type | Description |
---|---|
ndarray | TwoArrays | ThreeArrays
|
\(\ln(a)\) \(C^2\)-extended below |
Source code in bs_python_utils/bsnputils.py
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|
npmaxabs(arr)
¶
maximum absolute value in an array
Parameters:
Name | Type | Description | Default |
---|---|---|---|
arr |
ndarray
|
any Numpy array |
required |
Returns:
Type | Description |
---|---|
float
|
the largest element in absolute value |
Source code in bs_python_utils/bsnputils.py
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|
nppad2_end_zeros(mat, m, n)
¶
pad the ends of a 2-dim array with zeros to increase its size to (m,n)
, if needed
Parameters:
Name | Type | Description | Default |
---|---|---|---|
mat |
ndarray
|
2-dim array |
required |
m |
int
|
number of rows requested |
required |
n |
int
|
number of columns requested |
required |
Returns:
Type | Description |
---|---|
ndarray
|
padded array, where needed |
Source code in bs_python_utils/bsnputils.py
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|
nppad_beg_zeros(v, n)
¶
pad the beginning of a 1-dim array with zeros to increase its size to n
, if needed
Parameters:
Name | Type | Description | Default |
---|---|---|---|
v |
ndarray
|
1-dim array of size |
required |
n |
int
|
size requested |
required |
Returns:
Type | Description |
---|---|
ndarray
|
padded array if |
Source code in bs_python_utils/bsnputils.py
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|
nppad_end_zeros(v, n)
¶
pad the end of a 1-dim array with zeros to increase its size to n
, if needed
Parameters:
Name | Type | Description | Default |
---|---|---|---|
v |
ndarray
|
1-dim array of size |
required |
n |
int
|
size requested |
required |
Returns:
Type | Description |
---|---|
ndarray
|
padded array if |
Source code in bs_python_utils/bsnputils.py
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|
nppow(a, b, deriv=0)
¶
evaluates a**b element-by-element, perhaps with derivatives
Parameters:
Name | Type | Description | Default |
---|---|---|---|
a |
ndarray
|
an array |
required |
b |
int | float | ndarray
|
if an array, should have the same shape as |
required |
deriv |
int
|
if 1, compute derivative, if 2, second derivative |
0
|
Returns:
Type | Description |
---|---|
ndarray | ThreeArrays | SixArrays
|
an array of the same shape as |
Source code in bs_python_utils/bsnputils.py
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|
nprepeat_col(v, n)
¶
create a matrix with n
columns equal to v
Parameters:
Name | Type | Description | Default |
---|---|---|---|
v |
ndarray
|
a 1-dim array of size |
required |
n |
int
|
the number of columns requested |
required |
Returns:
Type | Description |
---|---|
ndarray
|
a 2-dim array of shape |
Source code in bs_python_utils/bsnputils.py
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|
nprepeat_row(v, m)
¶
create a matrix with m
rows equal to v
Parameters:
Name | Type | Description | Default |
---|---|---|---|
v |
ndarray
|
a 1-dim array of size |
required |
m |
int
|
the number of rows requested |
required |
Returns:
Type | Description |
---|---|
ndarray
|
a 2-dim array of shape |
Source code in bs_python_utils/bsnputils.py
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|
npxlogx(arr, eps=1e-30, deriv=0, verbose=False)
¶
\(C^2\) extension of \(a\ln(a)\) below eps
, perhaps with derivatives
Parameters:
Name | Type | Description | Default |
---|---|---|---|
arr |
ndarray
|
a Numpy array |
required |
eps |
float
|
lower bound |
1e-30
|
deriv |
int
|
if 1, compute derivative, if 2, second derivative |
0
|
verbose |
bool
|
prints debugging info |
False
|
Returns:
Type | Description |
---|---|
ndarray | TwoArrays | ThreeArrays
|
\(a\ln(a)\) \(C^2\)-extended below |
Source code in bs_python_utils/bsnputils.py
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|
outer_bivar(pol1, pol2)
¶
make a BivariatePolynomial
from the product of two Polynomial
objects
Parameters:
Name | Type | Description | Default |
---|---|---|---|
pol1 |
Polynomial
|
Polynomial in the first variable |
required |
pol2 |
Polynomial
|
Polynomial in the second variable |
required |
Returns:
Type | Description |
---|---|
BivariatePolynomial
|
a |
Source code in bs_python_utils/bsnputils.py
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|
print_quantiles(v, quantiles)
¶
print these quantiles of the array(s)
Parameters:
Name | Type | Description | Default |
---|---|---|---|
v |
ndarray | Iterable[ndarray]
|
a vector or an iterable of vectors |
required |
quantiles |
ndarray
|
quantiles in [0,1] |
required |
Returns:
Type | Description |
---|---|
ndarray
|
the corresponding quantiles as a vector or a matrix |
Source code in bs_python_utils/bsnputils.py
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|
quantile_transform(v)
¶
transform a vector of counts into the corresponding quantiles
Parameters:
Name | Type | Description | Default |
---|---|---|---|
v |
ndarray
|
a vector of counts |
required |
Returns:
Type | Description |
---|---|
ndarray
|
the corresponding quantiles |
Source code in bs_python_utils/bsnputils.py
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|
rice_stderr(y, x, is_sorted=False)
¶
computes the Rice local estimators of the standard error of y | x
Parameters:
Name | Type | Description | Default |
---|---|---|---|
y |
ndarray
|
vector of y-values |
required |
x |
ndarray
|
vector of x-values |
required |
is_sorted |
bool
|
set it to |
False
|
Returns:
Type | Description |
---|---|
ndarray | float
|
an array of the same size with the stderr(y | x) |
Source code in bs_python_utils/bsnputils.py
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set_elements_abovebelow_diagonal(matrix, scalar, location)
¶
Sets all elements of the given matrix above or below the diagonal to the specified scalar value.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
matrix |
ndarray
|
the input matrix; it must be square |
required |
scalar |
int | float
|
The scalar value to set the elements above or below the diagonal. |
required |
location |
str
|
'above', 'below', 'on_above', 'on_below'. |
required |
Returns:
Type | Description |
---|---|
ndarray
|
The updated matrix with elements above or below the diagonal set to the scalar value, |
ndarray
|
including the diagonal for the |
Source code in bs_python_utils/bsnputils.py
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