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`a`: Shall be a rank-2 `real` or `complex` array containing the data. It is an `intent(in)` argument.
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`order` (optional): Shall be a non-negative `integer` value specifying the order of the Pade approximation. By default `order=10`. It is an `intent(in)` argument.
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`err` (optional): Shall be a `type(linalg_state_type)` value. This is an `intent(out)` argument.
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### Return value
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The returned array `E` contains the Pade approximation of \(\exp(A)\).
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If `A` is non-square or `order` is negative, it raises a `LINALG_VALUE_ERROR`.
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If `err` is not present, exceptions trigger an `error stop`.
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