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Instant-use add-on functions for the Wolfram Language
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Compute the sign and natural logarithm of the determinant of an array in Python using the NumPy linear algebra package
ResourceFunction["NumPySignLogDet"][array] computes the sign and natural logarithm of the determinant of array in Python using the package NumPy. | |
ResourceFunction["NumPySignLogDet"][array,session] uses the specified running ExternalSessionObject session. |
Compute the sign and natural logarithm of the determinant of a matrix in NumPy:
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The determinant:
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Or using the built-in Wolfram Language function:
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Compute the sign and natural logarithm of the determinant of a real-valued matrix:
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Sparse array:
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NumericArray object:
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Complex-valued array:
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A tensor representing a list of matrices:
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Compare with the built-in Det:
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Use a singular matrix:
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Compare:
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Large matrix:
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Compare:
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Make several calls to NumPySignLogDet in the same external session:
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End the session:
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For real matrices, NumPySignLogDet returns the signs as -1 or 1 depending on whether the determinant is negative or positive:
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The sign is zero if the determinant is 0:
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For complex matrices, the signs are complex numbers with absolute values of 1:
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Or complex zero for singular matrices:
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NumPySignLogDet can give more accurate results than the resource function NumPyDet for small determinants:
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And determinants with large absolute values:
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NumPySignLogDet may still give inaccurate results since it computes with machine precision:
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Automatic conversion of the input array to a NumericArray object can fail:
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Convert the array to a NumericArray before passing it to NumPySignLogDet:
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A call to NumPySignLogDet on an arbitrary precision array fails:
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Convert the array to a NumericArray before passing it to NumPySignLogDet:
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Or use the machine-precision array:
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The logarithm value returned by NumPySignLogDet may be too small to compute the determinant with machine precision:
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Raise precision to get an estimate of the determinant:
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Compare:
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