@@ -58,9 +58,10 @@ def sb01bd(n,m,np,alpha,A,B,w,dico,tol=0.0,ldwork=None):
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:= 'C': continuous-time system;
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:= 'D': discrete-time system.
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tol : float, optional
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- The absolute tolerance level below which the elements of A or B are
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- considered zero (used for controllability tests).
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- If tol <= 0 the default value is used.
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+ The absolute tolerance level below which the elements of A or B are
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+ considered zero (used for controllability tests).
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+ If tol <= 0 the default value is used.
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+ Default is `0.0`.
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ldwork : int, optional
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The length of the cache array. The default value is
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max(1,5*m,5*n,2*n+4*m), for optimum performance it should be larger.
@@ -128,7 +129,6 @@ def sb01bd(n,m,np,alpha,A,B,w,dico,tol=0.0,ldwork=None):
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Example
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-------
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-
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>>> import numpy as np
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>>> import slycot
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>>> A = np.array([[0, 1, 0], [0, 0, 1], [-2, 1, 3]])
@@ -281,8 +281,6 @@ def sb02md(n,A,G,Q,dico,hinv='D',uplo='U',scal='N',sort='S',ldwork=None):
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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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SlycotArithmeticError
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:info = 1:
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Matrix A is (numerically) singular in discrete-
@@ -304,7 +302,6 @@ def sb02md(n,A,G,Q,dico,hinv='D',uplo='U',scal='N',sort='S',ldwork=None):
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Example
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-------
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-
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>>> import numpy as np
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>>> import slycot
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>>> A = np.array([[0, 1], [0, 0]])
@@ -622,7 +619,6 @@ def sb02od(n,m,A,B,Q,R,dico,p=None,L=None,fact='N',uplo='U',sort='S',tol=0.0,ldw
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Example
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-------
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-
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>>> import numpy as np
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>>> import slycot
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>>> A = np.array([[0, 1], [0, 0]])
@@ -707,7 +703,7 @@ def sb03md57(A, U=None, C=None,
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C : (n, n) array_like
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If job = 'X' or 'B', this array must contain the symmetric matrix C.
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If job = 'S', C is not referenced.
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- dico : {'C', 'D'}
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+ dico : {'C', 'D'}, optional
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Specifies the equation from which X is to be determined as follows:
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:= 'C': Equation (1), continuous-time case;
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:= 'D': Equation (2), discrete-time case.
@@ -905,7 +901,7 @@ def sb03od(n,m,A,Q,B,dico,fact='N',trans='N',ldwork=None):
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For optimum performance ldwork should sometimes be larger.
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Returns
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- _______
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+ -------
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U : (n, n) ndarray
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The leading n-by-n part of this array contains
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the upper triangular Cholesky factor U of the solution
@@ -1019,6 +1015,9 @@ def sb04md(n,m,A,B,C,ldwork=None):
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Matrix B
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C : (n, m) array_like
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Matrix C
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+ ldwork : int, optional
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+ The length of the array DWORK.
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+ Default is None.
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Returns
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-------
@@ -1068,6 +1067,9 @@ def sb04qd(n,m,A,B,C,ldwork=None):
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Matrix B
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C : (n, m) array_like
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Matrix C
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+ ldwork : int, optional
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+ The length of the array DWORK.
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+ Default is None.
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Returns
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-------
@@ -1743,9 +1745,9 @@ def sb10yd(discfl,flag,lendat,rfrdat,ifrdat,omega,n,tol,ldwork=None):
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n : int
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On entry, the desired order of the system to be fitted.
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n <= lendat-1.
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- tol : int, optional
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+ tol : int
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The length of the cache array.
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- ldwork : int
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+ ldwork : int, optional
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With None it will be automatically calculated.
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For details see SLICOT help.
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@@ -2206,6 +2208,7 @@ def sg02ad(dico,jobb,fact,uplo,jobl,scal,sort,acc,N,M,P,A,E,B,Q,R,L,ldwork=None,
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LDR >= MAX(1,M) if JOBB = 'B' and FACT = 'N' or 'C';
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LDR >= MAX(1,P) if JOBB = 'B' and FACT = 'D' or 'B';
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LDR >= 1 if JOBB = 'G'.
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+
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L : (n, M) array_like
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If JOBL = 'N' and JOBB = 'B', the leading N-by-M part of
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this array must contain the cross weighting matrix L.
@@ -2217,6 +2220,7 @@ def sg02ad(dico,jobb,fact,uplo,jobl,scal,sort,acc,N,M,P,A,E,B,Q,R,L,ldwork=None,
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LDWORK >= MAX(7*(2*N+1)+16,16*N), if JOBB = 'G';
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LDWORK >= MAX(7*(2*N+1)+16,16*N,2*N+M,3*M), if JOBB = 'B'.
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+
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For optimum performance LDWORK should be larger.
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Default: ``max(7*(2*n+1)+16,16*n)``
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tol : float, optional
@@ -2432,7 +2436,7 @@ def sg03bd(n,m,A,E,Q,Z,B,dico,fact='N',trans='N',ldwork=None):
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than one).
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Parameters
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- __________
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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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m : int
@@ -2495,11 +2499,13 @@ def sg03bd(n,m,A,E,Q,Z,B,dico,fact='N',trans='N',ldwork=None):
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on entry or not:
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:= 'N': Factorization is not supplied;
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:= 'F': Factorization is supplied.
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+ Default is 'N'.
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trans : {'N', 'T'}, optional
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Specifies whether the transposed equation is to be solved
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or not:
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:= 'N': op(A) = A, op(E) = E;
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:= 'T': op(A) = A**T, op(E) = E**T.
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+ Default is 'N'.
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ldwork : int, optional
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The dimension of the array dwork::
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@@ -2508,7 +2514,7 @@ def sg03bd(n,m,A,E,Q,Z,B,dico,fact='N',trans='N',ldwork=None):
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For good performance, ldwork should be larger.
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Returns
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- _______
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+ -------
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U : (n, n) ndarray
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The leading n-by-b part of this array contains
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the Cholesky factor U of the solution matrix X of the
@@ -2521,6 +2527,7 @@ def sg03bd(n,m,A,E,Q,Z,B,dico,fact='N',trans='N',ldwork=None):
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If INFO = 0, 3, 5, 6, or 7, then
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((j), j=1,...,n, are the
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eigenvalues of the matrix pencil A - lambda * E.
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+ Default is None.
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Raises
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------
@@ -2647,7 +2654,7 @@ def sb10fd(n,m,np,ncon,nmeas,gamma,A,B,C,D,tol=0.0,ldwork=None):
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whose reciprocal condition numbers are less than tol are
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not allowed. If tol <= 0, then a default value equal to
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sqrt(eps) is used, where eps is the relative machine
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- precision.
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+ precision. Default is `0.0`.
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ldwork : int, optional
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The dimension of the cache array::
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@@ -2683,7 +2690,7 @@ def sb10fd(n,m,np,ncon,nmeas,gamma,A,B,C,D,tol=0.0,ldwork=None):
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if the default (None) value is used, the size for good performance
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is automatically used, when ldwork is set to zero, the minimum
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- cache size will be used.
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+ cache size will be used. Default is None.
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Returns
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-------
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