Managed Lapack Of Single.Schur Decompose Method
Definition
Assembly: Numerics.NET.SinglePrecision (in Numerics.NET.SinglePrecision.dll) Version: 9.0.1
Overload List
Schur |
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Schur |
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SchurDecompose(Char, Char, Func<Complex<Single>, Boolean>, Int32, Span<Complex<Single>>, Int32, Int32, Span<Complex<Single>>, Span<Complex<Single>>, Int32, Int32)
Computes for an N-by-N complex nonsymmetric matrix A, the
eigenvalues, the Schur form T, and, optionally, the matrix of Schur
vectors Z.
public override void SchurDecompose(
char jobvs,
char sort,
Func<Complex<float>, bool> select,
int n,
Span<Complex<float>> a,
int lda,
out int sdim,
Span<Complex<float>> w,
Span<Complex<float>> vs,
int ldvs,
out int info
)
Parameters
- jobvs Char
-
C# JOBVS is CHARACTER*1 = 'N': Schur vectors are not computed; = 'V': Schur vectors are computed.
- sort Char
-
C# SORT is CHARACTER*1 Specifies whether or not to order the eigenvalues on the diagonal of the Schur form. = 'N': Eigenvalues are not ordered: = 'S': Eigenvalues are ordered (see SELECT).
- select Func<Complex<Single>, Boolean>
-
C# SELECT is a LOGICAL FUNCTION of one COMPLEX*16 argument SELECT must be declared EXTERNAL in the calling subroutine. If SORT = 'S', SELECT is used to select eigenvalues to order to the top left of the Schur form. IF SORT = 'N', SELECT is not referenced. The eigenvalue W(j) is selected if SELECT(W(j)) is true.
- n Int32
-
C# N is INTEGER The order of the matrix A. N >= 0.
- a Span<Complex<Single>>
-
C# A is COMPLEX*16 array, dimension (LDA,N) On entry, the N-by-N matrix A. On exit, A has been overwritten by its Schur form T.
- lda Int32
-
C# LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
- sdim Int32
-
C# SDIM is INTEGER If SORT = 'N', SDIM = 0. If SORT = 'S', SDIM = number of eigenvalues for which SELECT is true.
- w Span<Complex<Single>>
-
C# W is COMPLEX*16 array, dimension (N) W contains the computed eigenvalues, in the same order that they appear on the diagonal of the output Schur form T.
- vs Span<Complex<Single>>
-
C# VS is COMPLEX*16 array, dimension (LDVS,N) If JOBVS = 'V', VS contains the unitary matrix Z of Schur vectors. If JOBVS = 'N', VS is not referenced.
- ldvs Int32
-
C# LDVS is INTEGER The leading dimension of the array VS. LDVS >= 1; if JOBVS = 'V', LDVS >= N.
- info Int32
-
C# INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = i, and i is <= N: the QR algorithm failed to compute all the eigenvalues; elements 1:ILO-1 and i+1:N of W contain those eigenvalues which have converged; if JOBVS = 'V', VS contains the matrix which reduces A to its partially converged Schur form. = N+1: the eigenvalues could not be reordered because some eigenvalues were too close to separate (the problem is very ill-conditioned); = N+2: after reordering, roundoff changed values of some complex eigenvalues so that leading eigenvalues in the Schur form no longer satisfy SELECT = .TRUE.. This could also be caused by underflow due to scaling.
Remarks
This gives the Schur factorization A = Z*T*(Z**H).
Optionally, it also orders the eigenvalues on the diagonal of the
Schur form so that selected eigenvalues are at the top left.
The leading columns of Z then form an orthonormal basis for the
invariant subspace corresponding to the selected eigenvalues.
A complex matrix is in Schur form if it is upper triangular.
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
SchurDecompose(Char, Char, Func<Single, Single, Boolean>, Int32, Span<Single>, Int32, Int32, Span<Single>, Span<Single>, Span<Single>, Int32, Int32)
Computes for an N-by-N real nonsymmetric matrix A, the
eigenvalues, the real Schur form T, and, optionally, the matrix of
Schur vectors Z.
public override void SchurDecompose(
char jobvs,
char sort,
Func<float, float, bool> select,
int n,
Span<float> a,
int lda,
out int sdim,
Span<float> wr,
Span<float> wi,
Span<float> vs,
int ldvs,
out int info
)
Parameters
- jobvs Char
-
C# JOBVS is CHARACTER*1 = 'N': Schur vectors are not computed; = 'V': Schur vectors are computed.
- sort Char
-
C# SORT is CHARACTER*1 Specifies whether or not to order the eigenvalues on the diagonal of the Schur form. = 'N': Eigenvalues are not ordered; = 'S': Eigenvalues are ordered (see SELECT).
- select Func<Single, Single, Boolean>
-
C# SELECT is a LOGICAL FUNCTION of two DOUBLE PRECISION arguments SELECT must be declared EXTERNAL in the calling subroutine. If SORT = 'S', SELECT is used to select eigenvalues to sort to the top left of the Schur form. If SORT = 'N', SELECT is not referenced. An eigenvalue WR(j)+sqrt(-1)*WI(j) is selected if SELECT(WR(j),WI(j)) is true; i.e., if either one of a complex conjugate pair of eigenvalues is selected, then both complex eigenvalues are selected. Note that a selected complex eigenvalue may no longer satisfy SELECT(WR(j),WI(j)) = .TRUE. after ordering, since ordering may change the value of complex eigenvalues (especially if the eigenvalue is ill-conditioned); in this case INFO is set to N+2 (see INFO below).
- n Int32
-
C# N is INTEGER The order of the matrix A. N >= 0.
- a Span<Single>
-
C# A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the N-by-N matrix A. On exit, A has been overwritten by its real Schur form T.
- lda Int32
-
C# LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
- sdim Int32
-
C# SDIM is INTEGER If SORT = 'N', SDIM = 0. If SORT = 'S', SDIM = number of eigenvalues (after sorting) for which SELECT is true. (Complex conjugate pairs for which SELECT is true for either eigenvalue count as 2.)
- wr Span<Single>
-
C# WR is DOUBLE PRECISION array, dimension (N)
- wi Span<Single>
-
C# WI is DOUBLE PRECISION array, dimension (N) WR and WI contain the real and imaginary parts, respectively, of the computed eigenvalues in the same order that they appear on the diagonal of the output Schur form T. Complex conjugate pairs of eigenvalues will appear consecutively with the eigenvalue having the positive imaginary part first.
- vs Span<Single>
-
C# VS is DOUBLE PRECISION array, dimension (LDVS,N) If JOBVS = 'V', VS contains the orthogonal matrix Z of Schur vectors. If JOBVS = 'N', VS is not referenced.
- ldvs Int32
-
C# LDVS is INTEGER The leading dimension of the array VS. LDVS >= 1; if JOBVS = 'V', LDVS >= N.
- info Int32
-
C# INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = i, and i is <= N: the QR algorithm failed to compute all the eigenvalues; elements 1:ILO-1 and i+1:N of WR and WI contain those eigenvalues which have converged; if JOBVS = 'V', VS contains the matrix which reduces A to its partially converged Schur form. = N+1: the eigenvalues could not be reordered because some eigenvalues were too close to separate (the problem is very ill-conditioned); = N+2: after reordering, roundoff changed values of some complex eigenvalues so that leading eigenvalues in the Schur form no longer satisfy SELECT=.TRUE. This could also be caused by underflow due to scaling.
Remarks
This gives the Schur factorization A = Z*T*(Z**T).
Optionally, it also orders the eigenvalues on the diagonal of the
real Schur form so that selected eigenvalues are at the top left.
The leading columns of Z then form an orthonormal basis for the
invariant subspace corresponding to the selected eigenvalues.
A matrix is in real Schur form if it is upper quasi-triangular with
1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in the
form
[ a b ]
[ c a ]
where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.