@@ -67,9 +67,9 @@ def ab01nd(n, m, A, B, jobz='N', tol=0, ldwork=None):
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the order of the matrix A. ``n > 0``.
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m : int
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The number of system inputs, or of columns of B. ``m > 0``.
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- A : (n,n) array_like
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+ A : (n, n) array_like
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The original state dynamics matrix A.
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- B : (n,m) array_like
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+ B : (n, m) array_like
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The input matrix B.
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jobz : {'N', 'F', 'I'}, optional
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Indicates whether the user wishes to accumulate in a matrix Z
@@ -92,12 +92,12 @@ def ab01nd(n, m, A, B, jobz='N', tol=0, ldwork=None):
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Returns
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-------
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- Ac : (n,n) ndarray
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+ Ac : (n, n) ndarray
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The leading ncont-by-ncont part contains the upper block
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Hessenberg state dynamics matrix Acont in Ac, given by Z'*A*Z,
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of a controllable realization for the original system. The
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elements below the first block-subdiagonal are set to zero.
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- Bc : (n,m) ndarray
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+ Bc : (n, m) ndarray
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The leading ncont-by-m part of this array contains the transformed
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input matrix Bcont in Bc, given by ``Z'*B``, with all elements but the
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first block set to zero.
@@ -164,16 +164,16 @@ def ab04md(type_t, n, m, p, A, B, C, D, alpha=1.0, beta=1.0, ldwork=None):
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p : int
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The number of rows of matrix C. It represents the dimension of
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the output vector. p > 0.
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- A : (n,n) array_like
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+ A : (n, n) array_like
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The leading n-by-n part of this array must contain the system state
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matrix A.
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- B : (n,m) array_like
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+ B : (n, m) array_like
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The leading n-by-m part of this array must contain the system input
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matrix B.
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- C : (p,n) array_like
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+ C : (p, n) array_like
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The leading p-by-n part of this array must contain the system output
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matrix C.
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- D : (p,m) array_like
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+ D : (p, m) array_like
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The leading p-by-m part of this array must contain the system direct
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transmission matrix D.
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alpha : double, optional
@@ -189,13 +189,13 @@ def ab04md(type_t, n, m, p, A, B, C, D, alpha=1.0, beta=1.0, ldwork=None):
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ldwork >= max(1, n), default is max(1, n)
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Returns
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-------
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- At : (n,n) ndarray
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+ At : (n, n) ndarray
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The state matrix At of the transformed system.
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- Bt : (n,m) ndarray
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+ Bt : (n, m) ndarray
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The input matrix Bt of the transformed system.
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- Ct : (p,n) ndarray
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+ Ct : (p, n) ndarray
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The output matrix Ct of the transformed system.
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- Dt : (p,m) ndarray
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+ Dt : (p, m) ndarray
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The transmission matrix Dt of the transformed system.
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Raises
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------
@@ -241,28 +241,28 @@ def ab05md(n1,m1,p1,n2,p2,A1,B1,C1,D1,A2,B2,C2,D2,uplo='U'):
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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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+ 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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+ 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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+ 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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+ 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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+ 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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+ 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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+ 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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+ 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
@@ -278,16 +278,16 @@ def ab05md(n1,m1,p1,n2,p2,A1,B1,C1,D1,A2,B2,C2,D2,uplo='U'):
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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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+ 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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+ 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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+ 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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+ 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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@@ -333,28 +333,28 @@ def ab05nd(n1,m1,p1,n2,A1,B1,C1,D1,A2,B2,C2,D2,alpha=1.0,ldwork=None):
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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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- A1 : (n1,n1) array_like
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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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+ 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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+ 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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+ 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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+ 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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+ 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 : (m1,n2) array_like
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+ C2 : (m1, n2) array_like
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The leading m1-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 : (m1,p1) array_like
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+ D2 : (m1, p1) array_like
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The leading m1-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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alpha : float, optional
@@ -373,16 +373,16 @@ def ab05nd(n1,m1,p1,n2,A1,B1,C1,D1,A2,B2,C2,D2,alpha=1.0,ldwork=None):
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The number of state variables (n1 + n2) in the connected system, i.e.
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the order of the matrix A, the number of rows of B and the number of
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columns of C.
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- A : (n1+n2,n1+n2) ndarray
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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 connected system.
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- B : (n1+n2,m1) ndarray
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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 connected system.
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- C : (p1,n1,n2) ndarray
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+ C : (p1, n1, n2) ndarray
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The leading p1-by-n part of this array contains the state/output
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matrix C for the connected system.
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- D : (p1,m1) ndarray
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+ D : (p1, m1) ndarray
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The leading p1-by-m1 part of this array contains the input/output
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matrix D for the connected system.
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@@ -419,19 +419,19 @@ def ab07nd(n,m,A,B,C,D,ldwork=None):
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Parameters
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----------
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n : int
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- The order of the state matrix A. n >= 0.
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+ The order of the state matrix A. n >= 0.
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m : int
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- The number of system inputs and outputs. m >= 0.
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- A : (n,n) array_like
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+ The number of system inputs and outputs. m >= 0.
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+ A : (n, n) array_like
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The leading n-by-n part of this array must contain the state matrix
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A of the original system.
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- B : (n,m) array_like
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+ B : (n, m) array_like
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The leading n-by-m part of this array must contain the input matrix
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B of the original system.
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- C : (m,n) array_like
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+ C : (m, n) array_like
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The leading m-by-n part of this array must contain the output matrix
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C of the original system.
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- D : (m,m) array_like
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+ D : (m, m) array_like
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The leading m-by-m part of this array must contain the feedthrough
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matrix D of the original system.
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ldwork : int, optional
@@ -440,16 +440,16 @@ def ab07nd(n,m,A,B,C,D,ldwork=None):
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Returns
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-------
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- Ai : (n,n) ndarray
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+ Ai : (n, n) ndarray
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The leading n-by-n part of this array contains the state matrix Ai
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of the inverse system.
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- Bi : (n,m) ndarray
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+ Bi : (n, m) ndarray
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The leading n-by-m part of this array contains the input matrix Bi
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of the inverse system.
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- Ci : (m,n) ndarray
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+ Ci : (m, n) ndarray
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The leading m-by-n part of this array contains the output matrix Ci
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of the inverse system.
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- Di : (m,m) ndarray
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+ Di : (m, m) ndarray
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The leading m-by-m part of this array contains the feedthrough
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matrix Di of the inverse system.
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rcond : float
@@ -707,11 +707,11 @@ def ab09ad(dico,job,equil,n,m,p,A,B,C,nr=None,tol=0,ldwork=None):
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Balance `B` or not `N`
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equil : {'S', 'N'}
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Scale `S` or not `N`
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- n : input int
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+ n : int
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The number of state variables. n >= 0.
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- m : input int
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+ m : int
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The number of system inputs. m >= 0.
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- p : input int
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+ p : int
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The number of system outputs. p >= 0.
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A : (n, n) array_like
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The leading n-by-n part of this array must contain the state
@@ -994,7 +994,7 @@ def ab09bd(dico,job,equil,n,m,p,A,B,C,D,nr=None,tol1=0,tol2=0,ldwork=None):
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nr is the desired order of
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the resulting reduced order system. 0 <= nr <= n.
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Default is None.
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- tol1 : double precision , optional
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+ tol1 : float , optional
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If ordsel = 'A', tol1 contains the tolerance for
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determining the order of reduced system.
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For model reduction, the recommended value is
@@ -1007,7 +1007,7 @@ def ab09bd(dico,job,equil,n,m,p,A,B,C,D,nr=None,tol1=0,tol2=0,ldwork=None):
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This value is used by default if tol1 <= 0 on entry.
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If ordsel = 'F', the value of tol1 is ignored.
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Default is `0.0`.
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- tol2 : double precision , optional
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+ tol2 : float , optional
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The tolerance for determining the order of a minimal
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realization of the given system. The recommended value is
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tol2 = n*eps*hnorm(A,B,C). This value is used by default
@@ -1148,7 +1148,7 @@ def ab09md(dico,job,equil,n,m,p,A,B,C,alpha=None,nr=None,tol=0,ldwork=None):
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On entry with ordsel = 'F', nr is the desired order of the
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resulting reduced order system. 0 <= nr <= n.
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Default is None.
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- tol : double precision , optional
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+ tol : float , optional
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If ordsel = 'A', tol contains the tolerance for
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determining the order of reduced system.
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For model reduction, the recommended value is
@@ -1322,7 +1322,7 @@ def ab09nd(dico,job,equil,n,m,p,A,B,C,D,alpha=None,nr=None,tol1=0,tol2=0,ldwork=
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nr is the desired order of
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the resulting reduced order system. 0 <= nr <= n.
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Default is None.
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- tol1 : double precision , optional
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+ tol1 : float , optional
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If ordsel = 'A', tol1 contains the tolerance for
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determining the order of reduced system.
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For model reduction, the recommended value is
@@ -1338,7 +1338,7 @@ def ab09nd(dico,job,equil,n,m,p,A,B,C,D,alpha=None,nr=None,tol1=0,tol2=0,ldwork=
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of the alpha-stable part.
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If ordsel = 'F', the value of tol1 is ignored.
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Default is `0.0`.
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- tol2 : double precision , optional
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+ tol2 : float , optional
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The tolerance for determining the order of a minimal
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realization of the alpha-stable part of the given system.
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The recommended value is tol2 = ns*eps*hnorm(As,Bs,Cs).
@@ -1670,7 +1670,7 @@ def ab13ed(n, A, tol = 9.0):
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----------
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n : int
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The order of the matrix A. ``n >= 0.``
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- A : (n,n) array_like
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+ A : (n, n) array_like
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The leading n-by-n part of this array must contain the matrix A.
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tol : float, optional
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Specifies the accuracy with which low and high approximate
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