The recently released Multiprecision Computing Toolbox version 3.3.2 introduces multiple new routines and features for advanced numerical computing in arbitrary precision.
- Matrix functions, including logarithm, square root, exponential, trigonometric, and a general matrix function
funm % Evaluate general matrix function expm % Matrix exponential sqrtm % Matrix square root logm % Matrix logarithm sinm % Matrix sine cosm % Matrix cosine sinhm % Matrix hyperbolic sine coshm % Matrix hyperbolic cosine
- Special cases of an “economy sized” SVD decomposition
[U,S,V] = svd(X,0) [U,S,V] = svd(X,'econ')
- Kernel(null space) matrices, and matrices in Hessenberg form
null % Null space hess % Hessenberg form of matrix
- The formatted conversion of multiprecision entities into a string, and to standard data types
num2str % Convert number to string cast % Cast variable to different data type double % Convert to double precision int16 % Convert to 16-bit signed integer int32 % Convert to 32-bit signed integer int64 % Convert to 64-bit signed integer int8 % Convert to 8-bit signed integer single % Convert to single precision uint16 % Convert to 16-bit unsigned integer uint32 % Convert to 32-bit unsigned integer uint64 % Convert to 64-bit unsigned integer uint8 % Convert to 8-bit unsigned integer
- Logical Operations
all % Determine whether all array elements are nonzero or true any % Determine whether any array elements are nonzero not % Find logical NOT of array or scalar input xor % Logical exclusive-OR
Examples:
>> mp.Digits(50); % Matrix Logarithm >> X = mp.rand(5); >> norm(X - expm(logm(X)),1) 1.4833924403864679909085701388241692669212380232102e-54 % Null Space of Matrix >> X = mp.rand(3,5); >> norm(X*null(X),1) 8.6664199965605403870371093638563522224156087802478e-56 % Hessenberg Form of Matrix >> X = mp.rand(10); >> [P,H] = hess(X); >> norm(X - P*H*P',1) 3.3951974810054822928039499037225474000757620280265e-54
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