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change ag08bd docstring sections to numpydoc style
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@KybernetikJo
KybernetikJo committed Aug 26, 2023
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143 changes: 74 additions & 69 deletions slycot/analysis.py
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Expand Up @@ -1903,75 +1903,80 @@ def ag08bd(l,n,m,p,A,E,B,C,D,equil='N',tol=0.0,ldwork=None):
and left Kronecker indices, and the multiplicities of infinite
eigenvalues.
Required arguments:
l : input int
The number of rows of matrices A, B, and E. l >= 0.
n : input int
The number of columns of matrices A, E, and C. n >= 0.
m : input int
The number of columns of matrix B. m >= 0.
p : input int
The number of rows of matrix C. p >= 0.
A : rank-2 array('d') with bounds (l,n)
The leading l-by-n part of this array must
contain the state dynamics matrix A of the system.
E : rank-2 array('d') with bounds (l,n)
The leading l-by-n part of this array must
contain the descriptor matrix E of the system.
B : rank-2 array('d') with bounds (l,m)
The leading l-by-m part of this array must
contain the input/state matrix B of the system.
C : rank-2 array('d') with bounds (p,n)
The leading p-by-n part of this array must
contain the state/output matrix C of the system.
D : rank-2 array('d') with bounds (p,m)
The leading p-by-m part of this array must contain the
direct transmission matrix D of the system.
Optional arguments:
equil := 'N' input string(len=1)
Specifies whether the user wishes to balance the system
matrix as follows:
= 'S': Perform balancing (scaling);
= 'N': Do not perform balancing.
tol := 0 input float
A tolerance used in rank decisions to determine the
effective rank, which is defined as the order of the
largest leading (or trailing) triangular submatrix in the
QR (or RQ) factorization with column (or row) pivoting
whose estimated condition number is less than 1/TOL.
If the user sets TOL <= 0, then default tolerances are
used instead, as follows: TOLDEF = L*N*EPS in TG01FD
(to determine the rank of E) and TOLDEF = (L+P)*(N+M)*EPS
in the rest, where EPS is the machine precision
(see LAPACK Library routine DLAMCH). TOL < 1.
ldwork : input int
The length of the cache array.
ldwork >= max( 4*(l,n), ldw ), if equil = 'S',
ldwork >= ldw, if equil = 'N', where
ldw = max(l+p,m+n)*(m+n) + max(1,5*max(l+p,m+n)).
For optimum performance ldwork should be larger.
Return objects:
Af : rank-2 array('d')
the leading NFZ-by-NFZ part of this array
contains the matrix Af of the reduced pencil.
Ef : rank-2 array('d')
the leading NFZ-by-NFZ part of this array
contains the matrix Ef of the reduced pencil.
nrank : output int
The normal rank of the system pencil.
niz : output int
The number of infinite zeros.
infz : rank-1 array('i')
The leading DINFZ elements of infz contain information
on the infinite elementary divisors as follows:
the system has infz(i) infinite elementary divisors of
degree i in the Smith form, where i = 1,2,...,DINFZ.
kronr : rank-1 array('i')
The leading NKROR elements of this array contain the
right Kronecker (column) indices.
infe : rank-1 array('i')
The leading NINFE elements of infe contain the
multiplicities of infinite eigenvalues.
Parameters
----------
l : int
The number of rows of matrices A, B, and E. l >= 0.
n : int
The number of columns of matrices A, E, and C. n >= 0.
m : int
The number of columns of matrix B. m >= 0.
p : int
The number of rows of matrix C. p >= 0.
A : (l, n) array_like
The leading l-by-n part of this array must
contain the state dynamics matrix A of the system.
E : (l, n) array_like
The leading l-by-n part of this array must
contain the descriptor matrix E of the system.
B : (l, m) array_like
The leading l-by-m part of this array must
contain the input/state matrix B of the system.
C : (p, n) array_like
The leading p-by-n part of this array must
contain the state/output matrix C of the system.
D : (p, m) array_like
The leading p-by-m part of this array must contain the
direct transmission matrix D of the system.
equil : {'S', 'N'}, optional
Specifies whether the user wishes to balance the system
matrix as follows:
= 'S': Perform balancing (scaling);
= 'N': Do not perform balancing.
Default is `N`
tol : float, optional
A tolerance used in rank decisions to determine the
effective rank, which is defined as the order of the
largest leading (or trailing) triangular submatrix in the
QR (or RQ) factorization with column (or row) pivoting
whose estimated condition number is less than 1/TOL.
If the user sets TOL <= 0, then default tolerances are
used instead, as follows: TOLDEF = L*N*EPS in TG01FD
(to determine the rank of E) and TOLDEF = (L+P)*(N+M)*EPS
in the rest, where EPS is the machine precision
(see LAPACK Library routine DLAMCH). TOL < 1.
Default is 0.
ldwork : int, optional
The length of the cache array.
ldwork >= max( 4*(l,n), ldw ), if equil = 'S',
ldwork >= ldw, if equil = 'N', where
ldw = max(l+p,m+n)*(m+n) + max(1,5*max(l+p,m+n)).
For optimum performance ldwork should be larger.
Default is None.
Returns
-------
Af : (nfz, nfz) ndarray
the leading NFZ-by-NFZ part of this array
contains the matrix Af of the reduced pencil.
Ef : (nfz, nfz) ndarray
the leading NFZ-by-NFZ part of this array
contains the matrix Ef of the reduced pencil.
nrank : int
The normal rank of the system pencil.
niz : int
The number of infinite zeros.
infz : (n+1) ndarray
The leading DINFZ elements of infz contain information
on the infinite elementary divisors as follows:
the system has infz(i) infinite elementary divisors of
degree i in the Smith form, where i = 1,2,...,DINFZ.
kronr : (n+m+1) ndarray
The leading NKROR elements of this array contain the
right Kronecker (column) indices.
infe : (1+min(l+p,n+m)) ndarray
The leading NINFE elements of infe contain the
multiplicities of infinite eigenvalues.
"""
hidden = ' (hidden by the wrapper)'
arg_list = ['equil', 'l', 'n', 'm', 'p',
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