utils_math_m Module

Checks if two arrays are elementwise close within tolerance

Swaps two arrays

Returns the scalar triple product a.(b x c)

Arguments

Return Value real(kind=rp)

Returns the determinant of an (N x N) matrix, where N = 2, 3, or 4.

Arguments

Return Value real(kind=rp)

Returns the trace of a square matrix

Arguments

Return Value real(kind=rp)

Checks if two floating point numbers of type double are close within tolerance.

Arguments

Return Value logical

Checks if two rank-1 floating point arrays of type double are close within tolerance.

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Return Value logical

Checks if two rank-2 floating point arrays of type double are close within tolerance.

Arguments

Return Value logical

Checks if two rank-3 floating point arrays of type double are close within tolerance.

Arguments

Return Value logical

Calculates the quadratic form x^T A x, where A is an n x n matrix and x is a vector of length n

Arguments

Return Value real(kind=rp)

Arguments

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Calculates the cross product between two 3-element vectors

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Calculates the cross product matrix of a 3-element vector. The cross product matrix A of a is defined as a x b = A . b, where b is another 3-element vector.

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Calculates the outer product of two vectors, $c_{ij} = a_i b_j$.

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Returns the vector triple product d = a x (b x c)

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Normalizes a vector in-place. If the magnitude of the vector is nearly zero, no normalization takes place and the vector is returned as is with a warning message.

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Generates evenly spaced numbers over a specified interval. Both end points are included. If start < finish, the returned step size (if step is present) will be negative.

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Generates numbers spaced evenly on a log scale. In linear space, the sequence starts at base ** start (base to the power of start) and ends with base ** stop

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Creates an identity matrix of size n x n.

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Returns the diagonal elements of a square matrix.

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Adds a square matrix and its transpose in place: $A_{ij} = A_{ij } + A_{ji}$

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Calculates the difference of a square matrix and its transpose in place: $A_{ij} = A_{ij } - A_{ji}$

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Multiplies a matrix with its transpose: $\mathbf{\mathrm{B}} = \mathbf{\mathrm{A}} \cdot \mathbf{\mathrm{A}}^T$

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Orthogonalizes a set of vectors in-place using Gram-Schmidt orthonormalization

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Inverts a 3x3 matrix.

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Calculates the eigenvalues of a 3 x 3 real symmetric matrix. The eigenvalues calculated are in decreasing order. Only the diagonal and lower triangular part of the matrix is accessed.

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Author

Joachim Kopp

Date

2006

Calculates the eigenvalues of a symmetric 3x3 matrix A using Cardano's analytical algorithm. Only the diagonal and upper triangular parts of A are accessed. The access is read-only.

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