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EXPM

Purpose:

Calculates the matrix exponential.

Syntax:

EXPM(a)

Returns:

A square matrix.

Example:

W1: ravel({1,2,3,4}, 2)

W2: expm(w1)

produces the following matrix in W2:

{{51.968956, 112.104847},

 {74.736565, 164.073803}} 

Example:

W1: ravel(1..9, 3)

W2: expm(w1)

W3: logm(w2)

W1 == {{1, 4, 7},

       {2, 5, 8},

       {3, 6, 9}}

W2 == {{1118906.699, 2533881.042, 3948856.384},

       {1374815.063, 3113415.031, 4852013.000},

       {1630724.426, 3692947.021, 5755170.615}}

W3 == {{1, 4, 7},

       {2, 5, 8},

       {3, 6, 9}}

demonstrating EXPM and LOGM are inverse functions.

Remarks:

EXPM(A) returns a matrix X such that logm(X) == A.

If DADiSP/MatrixXL is available, the algorithm in [1] is used to significantly optimize EXPM, else a 7th order Padé approximation algorithm of [2] is used to calculate the matrix exponential.

See FUNM to compute the general matrix function.

See Also:

DADiSP/MatrixXL

EXP

FUNM

LOGM

SQRTM

References: