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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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| subroutine dget24 | ( | logical | COMP, |
| integer | JTYPE, | ||
| double precision | THRESH, | ||
| integer, dimension( 4 ) | ISEED, | ||
| integer | NOUNIT, | ||
| integer | N, | ||
| double precision, dimension( lda, * ) | A, | ||
| integer | LDA, | ||
| double precision, dimension( lda, * ) | H, | ||
| double precision, dimension( lda, * ) | HT, | ||
| double precision, dimension( * ) | WR, | ||
| double precision, dimension( * ) | WI, | ||
| double precision, dimension( * ) | WRT, | ||
| double precision, dimension( * ) | WIT, | ||
| double precision, dimension( * ) | WRTMP, | ||
| double precision, dimension( * ) | WITMP, | ||
| double precision, dimension( ldvs, * ) | VS, | ||
| integer | LDVS, | ||
| double precision, dimension( ldvs, * ) | VS1, | ||
| double precision | RCDEIN, | ||
| double precision | RCDVIN, | ||
| integer | NSLCT, | ||
| integer, dimension( * ) | ISLCT, | ||
| double precision, dimension( 17 ) | RESULT, | ||
| double precision, dimension( * ) | WORK, | ||
| integer | LWORK, | ||
| integer, dimension( * ) | IWORK, | ||
| logical, dimension( * ) | BWORK, | ||
| integer | INFO | ||
| ) |
DGET24
DGET24 checks the nonsymmetric eigenvalue (Schur form) problem
expert driver DGEESX.
If COMP = .FALSE., the first 13 of the following tests will be
be performed on the input matrix A, and also tests 14 and 15
if LWORK is sufficiently large.
If COMP = .TRUE., all 17 test will be performed.
(1) 0 if T is in Schur form, 1/ulp otherwise
(no sorting of eigenvalues)
(2) | A - VS T VS' | / ( n |A| ulp )
Here VS is the matrix of Schur eigenvectors, and T is in Schur
form (no sorting of eigenvalues).
(3) | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues).
(4) 0 if WR+sqrt(-1)*WI are eigenvalues of T
1/ulp otherwise
(no sorting of eigenvalues)
(5) 0 if T(with VS) = T(without VS),
1/ulp otherwise
(no sorting of eigenvalues)
(6) 0 if eigenvalues(with VS) = eigenvalues(without VS),
1/ulp otherwise
(no sorting of eigenvalues)
(7) 0 if T is in Schur form, 1/ulp otherwise
(with sorting of eigenvalues)
(8) | A - VS T VS' | / ( n |A| ulp )
Here VS is the matrix of Schur eigenvectors, and T is in Schur
form (with sorting of eigenvalues).
(9) | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues).
(10) 0 if WR+sqrt(-1)*WI are eigenvalues of T
1/ulp otherwise
If workspace sufficient, also compare WR, WI with and
without reciprocal condition numbers
(with sorting of eigenvalues)
(11) 0 if T(with VS) = T(without VS),
1/ulp otherwise
If workspace sufficient, also compare T with and without
reciprocal condition numbers
(with sorting of eigenvalues)
(12) 0 if eigenvalues(with VS) = eigenvalues(without VS),
1/ulp otherwise
If workspace sufficient, also compare VS with and without
reciprocal condition numbers
(with sorting of eigenvalues)
(13) if sorting worked and SDIM is the number of
eigenvalues which were SELECTed
If workspace sufficient, also compare SDIM with and
without reciprocal condition numbers
(14) if RCONDE the same no matter if VS and/or RCONDV computed
(15) if RCONDV the same no matter if VS and/or RCONDE computed
(16) |RCONDE - RCDEIN| / cond(RCONDE)
RCONDE is the reciprocal average eigenvalue condition number
computed by DGEESX and RCDEIN (the precomputed true value)
is supplied as input. cond(RCONDE) is the condition number
of RCONDE, and takes errors in computing RCONDE into account,
so that the resulting quantity should be O(ULP). cond(RCONDE)
is essentially given by norm(A)/RCONDV.
(17) |RCONDV - RCDVIN| / cond(RCONDV)
RCONDV is the reciprocal right invariant subspace condition
number computed by DGEESX and RCDVIN (the precomputed true
value) is supplied as input. cond(RCONDV) is the condition
number of RCONDV, and takes errors in computing RCONDV into
account, so that the resulting quantity should be O(ULP).
cond(RCONDV) is essentially given by norm(A)/RCONDE. | [in] | COMP | COMP is LOGICAL
COMP describes which input tests to perform:
= .FALSE. if the computed condition numbers are not to
be tested against RCDVIN and RCDEIN
= .TRUE. if they are to be compared |
| [in] | JTYPE | JTYPE is INTEGER
Type of input matrix. Used to label output if error occurs. |
| [in] | ISEED | ISEED is INTEGER array, dimension (4)
If COMP = .FALSE., the random number generator seed
used to produce matrix.
If COMP = .TRUE., ISEED(1) = the number of the example.
Used to label output if error occurs. |
| [in] | THRESH | THRESH is DOUBLE PRECISION
A test will count as "failed" if the "error", computed as
described above, exceeds THRESH. Note that the error
is scaled to be O(1), so THRESH should be a reasonably
small multiple of 1, e.g., 10 or 100. In particular,
it should not depend on the precision (single vs. double)
or the size of the matrix. It must be at least zero. |
| [in] | NOUNIT | NOUNIT is INTEGER
The FORTRAN unit number for printing out error messages
(e.g., if a routine returns INFO not equal to 0.) |
| [in] | N | N is INTEGER
The dimension of A. N must be at least 0. |
| [in,out] | A | A is DOUBLE PRECISION array, dimension (LDA, N)
Used to hold the matrix whose eigenvalues are to be
computed. |
| [in] | LDA | LDA is INTEGER
The leading dimension of A, and H. LDA must be at
least 1 and at least N. |
| [out] | H | H is DOUBLE PRECISION array, dimension (LDA, N)
Another copy of the test matrix A, modified by DGEESX. |
| [out] | HT | HT is DOUBLE PRECISION array, dimension (LDA, N)
Yet another copy of the test matrix A, modified by DGEESX. |
| [out] | WR | WR is DOUBLE PRECISION array, dimension (N) |
| [out] | WI | WI is DOUBLE PRECISION array, dimension (N)
The real and imaginary parts of the eigenvalues of A.
On exit, WR + WI*i are the eigenvalues of the matrix in A. |
| [out] | WRT | WRT is DOUBLE PRECISION array, dimension (N) |
| [out] | WIT | WIT is DOUBLE PRECISION array, dimension (N)
Like WR, WI, these arrays contain the eigenvalues of A,
but those computed when DGEESX only computes a partial
eigendecomposition, i.e. not Schur vectors |
| [out] | WRTMP | WRTMP is DOUBLE PRECISION array, dimension (N) |
| [out] | WITMP | WITMP is DOUBLE PRECISION array, dimension (N)
Like WR, WI, these arrays contain the eigenvalues of A,
but sorted by increasing real part. |
| [out] | VS | VS is DOUBLE PRECISION array, dimension (LDVS, N)
VS holds the computed Schur vectors. |
| [in] | LDVS | LDVS is INTEGER
Leading dimension of VS. Must be at least max(1, N). |
| [out] | VS1 | VS1 is DOUBLE PRECISION array, dimension (LDVS, N)
VS1 holds another copy of the computed Schur vectors. |
| [in] | RCDEIN | RCDEIN is DOUBLE PRECISION
When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
condition number for the average of selected eigenvalues. |
| [in] | RCDVIN | RCDVIN is DOUBLE PRECISION
When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
condition number for the selected right invariant subspace. |
| [in] | NSLCT | NSLCT is INTEGER
When COMP = .TRUE. the number of selected eigenvalues
corresponding to the precomputed values RCDEIN and RCDVIN. |
| [in] | ISLCT | ISLCT is INTEGER array, dimension (NSLCT)
When COMP = .TRUE. ISLCT selects the eigenvalues of the
input matrix corresponding to the precomputed values RCDEIN
and RCDVIN. For I=1, ... ,NSLCT, if ISLCT(I) = J, then the
eigenvalue with the J-th largest real part is selected.
Not referenced if COMP = .FALSE. |
| [out] | RESULT | RESULT is DOUBLE PRECISION array, dimension (17)
The values computed by the 17 tests described above.
The values are currently limited to 1/ulp, to avoid
overflow. |
| [out] | WORK | WORK is DOUBLE PRECISION array, dimension (LWORK) |
| [in] | LWORK | LWORK is INTEGER
The number of entries in WORK to be passed to DGEESX. This
must be at least 3*N, and N+N**2 if tests 14--16 are to
be performed. |
| [out] | IWORK | IWORK is INTEGER array, dimension (N*N) |
| [out] | BWORK | BWORK is LOGICAL array, dimension (N) |
| [out] | INFO | INFO is INTEGER
If 0, successful exit.
If <0, input parameter -INFO had an incorrect value.
If >0, DGEESX returned an error code, the absolute
value of which is returned. |
1.9.4