Numpy: use with multiprecision data types

Numpy: general use with multiprecision data types

• Numpy array creation from shape or value
  • Conversion from integer, float or complex array
    • npm.t()
  • Ones on the diagonal and zeros elsewhere: numpy.eye
    • npm.eye()
  • Identity array: numpy.identity
    • npm.identity()
  • Array of ones: numpy.ones
    • npm.ones()
  • Array of ones: numpy.ones_like
    • npm.ones_like()
  • Array of zeros: numpy.zeros
    • npm.zeros()
  • Array of zeros: numpy.zeros_like
    • npm.zeros_like()
  • Array of constant: numpy.full
    • npm.full()
  • Array of constant: numpy.full_like
    • npm.full_like()
  • Array with ones at and below the given diagonal and zeros elsewhere: numpy.tri
    • npm.tri()
• Numpy array creation from existing data
  • Array from object: numpy.array
    • npm.array()
  • Array from object: numpy.asarray
    • npm.asarray()
  • Array from object: numpy.asanyarray
    • npm.asanyarray()
  • Array from data in a text or binary file: numpy.fromfile
    • npm.fromfile()
  • Array from a function: numpy.fromfunction
    • npm.fromfunction()
  • Array from an iterable object: numpy.fromiter
    • npm.fromiter()
  • Array from text data in a string: numpy.fromstring
    • npm.fromstring()
  • Array from text data in a formatted file: numpy.loadtxt
    • npm.loadtxt()
  • Array from text data in a text file (can handle missing values): numpy.genfromtxt
    • npm.genfromtxt()
• Building special arrays for numerical work
  • Evenly spaced values within a given interval: numpy.arange
    • npm.arange()
  • Evenly spaced values within a given interval: numpy.linspace
    • npm.linspace()
  • Evenly spaced values on a log scale: numpy.logspace
    • npm.logspace()
  • Evenly spaced values on a log scale (a geometric progression): numpy.geomspace
    • npm.geomspace()
  • Extract a diagonal or construct a diagonal array: numpy.diag
    • npm.diag()
  • Extract specified diagonals: numpy.diagonal
    • npm.diagonal()
  • Two-dimensional array with the flattened input as a diagonal: numpy.diagflat
    • npm.diagflat()
  • Lower triangle of an array: numpy.tril
    • npm.tril()
  • Upper triangle of an array: numpy.triu
    • npm.triu()
  • Vandermonde matrix.: numpy.vander
    • npm.vander()
• Numpy indexing
  • Single element indexing
  • Slicing and striding
  • Dimensional indexing tools
  • Broadcasting Overview
  • General Broadcasting Rules
  • Broadcastable arrays
  • Assigning values to indexed arrays
• Numpy basic array manipulation routines
  • Copy values from one array to another: numpy.copyto
    • npm.copyto()
  • Get the shape of an array: numpy.shape
    • npm.shape()
  • Reshape an array without changing its data: numpy.reshape
    • npm.reshape()
  • Get a contiguous flattened array: numpy.ravel
    • npm.ravel()
  • 1-D iterator over the array: ndarry.flat
    • ndarry.flat()
  • Get a copy of the array collapsed into one dimension: ndarry.flatten
    • ndarry.flatten()
• Numpy array manipulation: Transpose-like operations
  • Move axes of an array to new positions: numpy.flatten
    • npm.moveaxis()
  • Interchange two axes of an array: numpy.swapaxes
    • npm.swapaxes()
  • Get an array with axes transposed: numpy.transpose
    • npm.transpose()
• Numpy array manipulation: Changing number of dimensions
  • Convert inputs to arrays with at least one dimension: numpy.atleast_1d
    • npm.atleast_1d()
  • Convert inputs to arrays with at least two dimensions: numpy.atleast_2d
    • npm.atleast_2d()
  • Convert inputs to arrays with at least two dimensions: numpy.atleast_3d
    • npm.atleast_3d()
  • Broadcast an array to a new shape: numpy.broadcast_to
    • npm.broadcast_to()
  • Broadcast any number of arrays against each other: numpy.broadcast_arrays
    • npm.broadcast_arrays()
  • Expand the shape of an array: numpy.expand_dims
    • npm.expand_dims()
  • Remove axes of length one from an array: numpy.squeeze
    • npm.squeeze()
• Numpy array manipulation: Joining arrays
  • Join a sequence of arrays along an existing axis: numpy.concatenate
    • npm.concatenate()
  • Join a sequence of arrays along an existing axis: numpy.stack
    • npm.stack()
  • Assemble an nd-array from nested lists of blocks: numpy.block
    • npm.block()
  • Stack arrays in sequence vertically (row wise): numpy.vstack
    • npm.vstack()
  • Stack arrays in sequence horizontally (column wise): numpy.hstack
    • npm.hstack()
  • Stack arrays in sequence depth wise (along third axis): numpy.dstack
    • npm.dstack()
  • Stack 1-D arrays as columns into a 2-D array: numpy.column_stack
    • npm.column_stack()
• Numpy array manipulation: Splitting and tiling arrays
  • Split an array into multiple sub-arrays as views: numpy.split
    • npm.split()
  • Split an array into multiple sub-arrays: numpy.array_split
    • npm.array_split()
  • Split array into multiple sub-arrays along the 3rd axis (depth): numpy.dsplit
    • npm.dsplit()
  • Split an array into multiple sub-arrays horizontally (column-wise): numpy.hsplit
    • npm.hsplit()
  • Split an array into multiple sub-arrays vertically (row-wise): numpy.vsplit
    • npm.vsplit()
  • Construct an array by repeating a given array: numpy.tile
    • npm.tile()
  • Repeat each element of an array after themselves: numpy.repeat
    • npm.repeat()
• Numpy array manipulation: Adding and removing elements
  • Pad an array: numpy.pad
    • npm.pad()
  • Return a new array with sub-arrays along an axis deleted: numpy.delete
    • npm.delete()
  • Insert values along the given axis before the given indices: numpy.insert
    • npm.insert()
  • Append values to the end of an array: numpy.append
    • npm.append()
  • Trim zeros from a 1-D array: numpy.trim_zeros
    • npm.trim_zeros()
  • Find the unique elements of an array: numpy.unique
    • npm.unique()
• Numpy array manipulation: Rearranging elements
  • Reverse the order of elements in an array along the given axis: numpy.flip
    • npm.flip()
  • Reverse the order of elements along axis 1 (left/right): numpy.fliplr
    • npm.fliplr()
  • Reverse the order of elements along axis 0 (up/down): numpy.flipud
    • npm.flipud()
  • Roll array elements along a given axis: numpy.roll
    • npm.roll()
  • Rotate an array by 90 degrees: numpy.rot90
    • npm.rot90()
• Numpy array manipulation: Sorting
  • Sorted copy of an array: numpy.sort
    • npm.sort()
  • Indirect stable sort using a sequence of keys: numpy.lexsort
    • npm.lexsort()
  • Indices that would sort an array: numpy.argsort
    • npm.argsort()
  • Matching 1d index and data slices: numpy.take_along_axis
    • npm.take_along_axis()
  • Sorting a complex array: numpy.sort_complex
    • npm.sort_complex()
• Numpy array manipulation: Searching
  • Indices of the maximum values along an axis: numpy.argmax
    • npm.argmax()
  • Get indices of the minimum values along an axis: numpy.argmin
    • npm.argmin()
  • Find the indices of array elements that are non-zero, grouped by element: numpy.argwhere
    • npm.argwhere()
  • Get the indices of array elements that are non-zero: numpy.nonzero
    • npm.nonzero()
  • Return elements depending on a condition: numpy.where
    • npm.where()
  • Return an array drawn from elements in choicelist, depending on a condition: numpy.select
    • npm.select()
• Numpy mathematical functions: Sums, products, differences
  • Product of array elements: numpy.prod
    • npm.prod()
  • Sum of array elements: numpy.sum
    • npm.sum()
  • Cumulative product of array elements: numpy.cumprod
    • npm.cumprod()
  • Cumulative sum of array elements: numpy.cumsum
    • npm.cumsum()
  • N-th discrete difference: numpy.diff
    • npm.diff()
  • Differences between consecutive elements: numpy.ediff1d
    • npm.ediff1d()
  • Gradient of an N-dimensional array: numpy.gradient
    • npm.gradient()
  • Trapezoidal rule: numpy.trapezoid
    • npm.trapezoid()
• Numpy mathematical functions: Extrema Finding
  • Element-wise maximum of array elements: numpy.maximum
    • npm.maximum()
  • Element-wise minimum of array elements: numpy.minimum
    • npm.minimum()
  • Maximum of an array or maximum along an axis: numpy.max
    • npm.max()
  • Minimum of an array or maximum along an axis: numpy.min
    • npm.min()
• Numpy mathematical functions: Arithmetic operations, elementwise
  • Numerical positive, element-wise: numpy.positive
    • npm.positive()
  • Numerical negative, element-wise: numpy.negative
    • npm.negative()
  • Add arguments element-wise: numpy.add
    • npm.add()
  • Subtract arguments element-wise: numpy.subtract
    • npm.subtract()
  • Multiply arguments element-wise: numpy.multiply
    • npm.multiply()
  • Divide arguments element-wise: numpy.divide
    • npm.divide()
  • Floor-divide arguments element-wise: numpy.floor_divide
    • npm.floor_divide()
  • Element-wise remainder of division: numpy.remainder
    • npm.remainder()
  • Element-wise square: numpy.square
    • npm.square()
  • Element-wise reciprocal: numpy.reciprocal
    • npm.reciprocal()
• Numpy mathematical functions: Averages and variances
  • Median of the array elements.: numpy.median
    • npm.median()
  • Average of the array elements.: numpy.average
    • npm.average()
  • Arithmetic mean: numpy.mean
    • npm.mean()
  • Variance: numpy.var
    • npm.var()
• Numpy mathematical functions: Matrix and vector products
  • Dot product: numpy.dot
    • npm.dot()
  • Dot product of two vectors: numpy.vdot
    • npm.vdot()
  • Inner product of two arrays: numpy.inner
    • npm.inner()
  • Outer product of two vectors: numpy.outer
    • npm.outer()
  • Matrix product of two arrays: numpy.matmul
    • npm.matmul()
  • Tensor dot product: numpy.matmul
    • npm.tensordot()
  • Einstein summation: numpy.einsum
    • npm.einsum()
  • Kronecker product: numpy.kron
    • npm.kron()
  • Discrete, linear convolution: numpy.convolve
    • npm.convolve()
• Numpy logical functions: Truth value testing
  • Test whether all array elements evaluate to True.: numpy.all, ctx.all
    • npm.all()
  • Test whether any array element evaluates to True: numpy.any, ctx.any
    • npm.any()
  • Logical AND: numpy.logical_and, ctx.logical_and
    • npm.logical_and()
  • Logical OR: numpy.logical_or, ctx.logical_or
    • npm.logical_or()
  • Logical XOR: numpy.logical_xor, ctx.logical_xor
    • npm.logical_xor()
  • Testing array equality: numpy.array_equal, ctx.array_equal
    • npm.array_equal()
  • Testing array array_equivalence: numpy.array_equiv, ctx.array_equiv
    • npm.array_equiv()
  • Truth value of (x1 > x2) element-wise: numpy.greater, ctx.greater
    • npm.greater()
  • Truth value of (x1 >= x2) element-wise: numpy.greater_equal, ctx.greater_equal
    • npm.greater_equal()
  • Truth value of (x1 < x2) element-wise: numpy.less, ctx.less
    • npm.less()
  • Truth value of (x1 <= x2) element-wise: numpy.less_equal, ctx.less_equal
    • npm.less_equal()
  • Truth value of (x1 == x2) element-wise: numpy.equal, ctx.equal
    • npm.equal()
  • Truth value of (x1 != x2) element-wise: numpy.equal, ctx.equal
    • npm.not_equal()
• Numpy mathematical functions: Integer and fractional
  • Floor of the input, element-wise.: numpy.floor, ctx.floor
    • npm.floor()
  • Ceiling of the input, element-wise.: numpy.ceil, ctx.ceil
    • npm.ceil()
  • Truncated value of the input, element-wise.: numpy.trunc, ctx.trunc
    • npm.trunc()
  • Fix value of the input, element-wise.: numpy.fix, ctx.fix
    • npm.fix()
• Numpy mathematical functions: Miscellaneous
  • Random Generator
  • Vectorization of a function: numpy.vectorize
    • npm.vectorize()
• Summary and examples: Numpy utility functions
  • Exact mathematical constants
  • Complex components
  • Array contents
  • Array type testing
  • Using tolerances
  • Clipping (limiting) the values in an array.
• Arithmetic operations with scalars and iterables
  • fadd: Addition using a custom precision and rounding mode
    • ctx.fadd()
  • fsub: Subtraction using a custom precision and rounding mode
    • ctx.fsub()
  • fneg: Negation of a number using a custom precision and rounding mode
    • ctx.fneg()
  • fmul: Multiplication using a custom precision and rounding mode
    • ctx.fmul()
  • fdiv: Division using a custom precision and rounding mode
    • ctx.fdiv()
  • fsum: Sum of a finite number of terms
    • ctx.fsum()
  • fprod: Product of a finite number of factors
    • ctx.fprod()
  • fdot: Dot product
    • ctx.fdot()
• Numerical transformations and descriptive statistics
  • Centering of a matrix
    • mat.centered()
  • Standardization of a matrix
    • mat.standardized()
  • Trace
    • mat.trace()
  • Squared Norm
    • mat.squaredNorm()
  • Euclidian Norm
    • mat.Norm()
  • Covariance matrix
    • mat.covariance_matrix()
  • Correlation matrix
    • mat.correlation()
  • Summary statistic
    • mat.summary()
  • Vector norm of a matrix
    • ctx.norm()
  • Matrix norm
    • ctx.mnorm()
• Standard decompositions and linear solving
  • Cholesky decomposition
    • ctx.cholesky()
  • Cholesky decomposition, solve
    • ctx.cholesky_solve()
  • Matrix LU factorization
    • ctx.lu()
  • Determinant of a matrix, using LU decomposition
    • ctx.det()
  • Inverse of a matrix, using the LU factorization
    • ctx.inverse()
  • Linear equations: LU solve
    • ctx.lu_solve()
  • Linear equations: residual of LU solve
    • ctx.residual()
  • ??? LU improve solution
    • improve_solution()
  • mpmath: LU condition number
    • ctx.cond()
  • QR factorization
    • ctx.qr()
  • QR solve
    • ctx.qr_solve()
• Singular Value and Eigen decompositions
  • Real singular value decomposition of a matrix A
    • ctx.svd_r()
  • Complex singular value decomposition of a matrix A
    • ctx.svd_c()
  • mpmath: Singular value decomposition of a matrix A (real or complex)
    • ctx.svd()
  • Eigenvalue problem for a real symmetric square matrix A
    • ctx.eigsy()
  • Eigenvalue problem for a complex hermitian square matrix A
    • ctx.eighe()
  • mpmath: Eigenvalue problem for a selfadjoint square matrix A
    • ctx.eigh()
  • mpmath: tridiag_sym
    • r_sy_tridiag()
  • mpmath tridiag_her
    • c_he_tridiag_0()
  • mpmath: tridiag_eigen_sym
    • tridiag_eigen()
  • Eigensystem decomposition of a matrix A (real or complex)
    • ctx.eig()
  • Sorting Eigenvalues
    • ctx.eig_sort()
  • mpmath: Hessenberg decomposition of a matrix A (real or complex)
    • ctx.hessenberg()
  • Schur decomposition of a matrix A (real or complex)
    • ctx.schur()
• Analytic functions of a matrix
  • Matrix Exponential
    • ctx.expm()
  • Matrix Sine
    • ctx.sinm()
  • Matrix Cosine
    • ctx.cosm()
    • cosm_()
  • Matrix Hyperbolic Sine
    • ctx.sinhm()
  • Matrix Hyperbolic Cosine
    • ctx.coshm()
  • Matrix Square Root
    • ctx.sqrtm()
  • Matrix Logarithm
    • ctx.logm()
  • Matrix power
    • ctx.powm()
• Discrete Fourier transform (DFT)
  • Overview
  • One-dimensional discrete Fourier Transform (fft)
    • ctx.fft()
  • One-dimensional inverse discrete Fourier Transform (ifft)
    • ctx.ifft()
  • One-dimensional discrete Fourier Transform for real input (rfft)
    • ctx.rfft()
  • One-dimensional inverse discrete Fourier Transform of rfft (irfft)
    • ctx.irfft()
  • FFT of a signal that has Hermitian symmetry, i.e., a real spectrum (hfft)
    • ctx.hfft()
  • Inverse FFT of a signal that has Hermitian symmetry (ihfft)
    • ctx.ihfft()
  • Discrete Fourier Transform sample frequencies (fftfreq)
    • ctx.fftfreq()
  • Discrete Fourier Transform sample frequencies for usage with rfft, irfft (rfftfreq)
    • ctx.rfftfreq()
• Flint/Functions for matrices
  • Matrix multiplication: special options for FMPQ, ARB, ACB
    • ArbMatTimes()
  • Determinant (incl. special options for FMPQ, ARB, ACB)
    • mat.Det()
  • Inverse (incl. special options for FMPQ, ARB, ACB)
    • mat.Inverse()
  • Solve (incl. special options for FMPQ, ARB, ACB)
    • mat.Solve()
    • mat.ArbSolve()
    • mat.FmpzSolve()
    • mat.FmpzSolveFflu()
    • mat.FmpzSolveCramer()
    • mat.FmpzSolveDixon()
  • Matrix Exponential
    • mat.ApcExpm()
  • Matrix Sine
    • mat.ApcSinm()
  • Matrix Cosine
    • mat.ApcCosm()
  • Matrix Hyperbolic Sine
    • mat.ApcSinhm()
  • Matrix Hyperbolic Cosine
    • mat.ApcCoshm()
  • Characteristic polynomial
    • mat.ApcCharpoly()
  • Calculating eigenvalues via characteristic polynomials
  • Eigenvalue enclosure (Rump)
    • mat.ApcEigEnclosureRump()
  • Eigenvalues, step by setp
    • mat.ApcEigSimple()
  • Eigenvalues, multiple
    • mat.ApcEigMultiple()