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change ab05md docstring sections to numpydoc style
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‎slycot/analysis.py‎

Lines changed: 72 additions & 64 deletions
Original file line numberDiff line numberDiff line change
@@ -144,76 +144,84 @@ def ab01nd(n, m, A, B, jobz='N', tol=0, ldwork=None):
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Z = None
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return Ac, Bc, ncont, indcon, nblk, Z, tau
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def ab05md(n1,m1,p1,n2,p2,A1,B1,C1,D1,A2,B2,C2,D2,uplo='U'):
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""" n,a,b,c,d = ab05md(n1,m1,p1,n2,p2,a1,b1,c1,d1,a2,b2,c2,d2,[uplo])
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To obtain the state-space model (A,B,C,D) for the cascaded
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inter-connection of two systems, each given in state-space form.
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Required arguments:
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n1 : input int
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The number of state variables in the first system, i.e. the order
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of the matrix A1. n1 > 0.
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m1 : input int
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The number of input variables for the first system. m1 > 0.
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p1 : input int
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The number of output variables from the first system and the number
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of input variables for the second system. p1 > 0.
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n2 : input int
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The number of state variables in the second system, i.e. the order
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of the matrix A2. n2 > 0.
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p2 : input int
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The number of output variables from the second system. p2 > 0.
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A1 : input rank-2 array('d') with bounds (n1,n1)
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The leading n1-by-n1 part of this array must contain the state
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transition matrix A1 for the first system.
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B1 : input rank-2 array('d') with bounds (n1,m1)
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The leading n1-by-m1 part of this array must contain the input/state
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matrix B1 for the first system.
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C1 : input rank-2 array('d') with bounds (p1,n1)
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The leading p1-by-n1 part of this array must contain the state/output
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matrix C1 for the first system.
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D1 : input rank-2 array('d') with bounds (p1,m1)
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The leading p1-by-m1 part of this array must contain the input/output
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matrix D1 for the first system.
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A2 : input rank-2 array('d') with bounds (n2,n2)
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The leading n2-by-n2 part of this array must contain the state
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transition matrix A2 for the second system.
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B2 : input rank-2 array('d') with bounds (n2,p1)
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The leading n2-by-p1 part of this array must contain the input/state
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matrix B2 for the second system.
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C2 : input rank-2 array('d') with bounds (p2,n2)
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The leading p2-by-n2 part of this array must contain the state/output
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matrix C2 for the second system.
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D2 : input rank-2 array('d') with bounds (p2,p1)
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The leading p2-by-p1 part of this array must contain the input/output
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matrix D2 for the second system.
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Optional arguments:
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uplo := 'U' input string(len=1)
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Indicates whether the user wishes to obtain the matrix A in
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the upper or lower block diagonal form, as follows:
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= 'U': Obtain A in the upper block diagonal form;
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= 'L': Obtain A in the lower block diagonal form.
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Return objects:
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n : int
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The number of state variables (n1 + n2) in the resulting system,
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i.e. the order of the matrix A, the number of rows of B and
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the number of columns of C.
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A : rank-2 array('d') with bounds (n1+n2,n1+n2)
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The leading N-by-N part of this array contains the state transition
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matrix A for the cascaded system.
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B : rank-2 array('d') with bounds (n1+n2,m1)
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The leading n-by-m1 part of this array contains the input/state
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matrix B for the cascaded system.
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C : rank-2 array('d') with bounds (p2,n1+n2)
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The leading p2-by-n part of this array contains the state/output
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matrix C for the cascaded system.
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D : rank-2 array('d') with bounds (p2,m1)
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The leading p2-by-m1 part of this array contains the input/output
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matrix D for the cascaded system.
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Notes:
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Parameters
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----------
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n1 : int
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The number of state variables in the first system, i.e. the order
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of the matrix A1. n1 > 0.
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m1 : int
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The number of input variables for the first system. m1 > 0.
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p1 : int
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The number of output variables from the first system and the number
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of input variables for the second system. p1 > 0.
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n2 : int
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The number of state variables in the second system, i.e. the order
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of the matrix A2. n2 > 0.
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p2 : int
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The number of output variables from the second system. p2 > 0.
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A1 : (n1,n1) array_like
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The leading n1-by-n1 part of this array must contain the state
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transition matrix A1 for the first system.
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B1 : (n1,m1) array_like
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The leading n1-by-m1 part of this array must contain the input/state
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matrix B1 for the first system.
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C1 : (p1,n1) array_like
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The leading p1-by-n1 part of this array must contain the state/output
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matrix C1 for the first system.
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D1 : (p1,m1) array_like
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The leading p1-by-m1 part of this array must contain the input/output
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matrix D1 for the first system.
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A2 : (n2,n2) array_like
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The leading n2-by-n2 part of this array must contain the state
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transition matrix A2 for the second system.
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B2 : (n2,p1) array_like
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The leading n2-by-p1 part of this array must contain the input/state
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matrix B2 for the second system.
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C2 : (p2,n2) array_like
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The leading p2-by-n2 part of this array must contain the state/output
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matrix C2 for the second system.
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D2 : (p2,p1) array_like
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The leading p2-by-p1 part of this array must contain the input/output
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matrix D2 for the second system.
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uplo : {'U', 'L'}, optional
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Indicates whether the user wishes to obtain the matrix A in
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the upper or lower block diagonal form, as follows:
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= 'U': Obtain A in the upper block diagonal form;
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= 'L': Obtain A in the lower block diagonal form.
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Default is `U`.
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Returns
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-------
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n : int
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The number of state variables (n1 + n2) in the resulting system,
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i.e. the order of the matrix A, the number of rows of B and
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the number of columns of C.
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A : (n1+n2,n1+n2) ndarray
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The leading N-by-N part of this array contains the state transition
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matrix A for the cascaded system.
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B : (n1+n2,m1) ndarray
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The leading n-by-m1 part of this array contains the input/state
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matrix B for the cascaded system.
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C : (p2,n1+n2) ndarray
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The leading p2-by-n part of this array contains the state/output
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matrix C for the cascaded system.
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D : (p2,m1) ndarray
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The leading p2-by-m1 part of this array contains the input/output
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matrix D for the cascaded system.
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Raises
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------
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SlycotParameterError
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:info = -i: the i-th argument had an illegal value
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Notes
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-----
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The implemented methods rely on accuracy enhancing square-root or
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balancing-free square-root techniques.
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The algorithms require less than 30N^3 floating point operations.

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