TESTING/EIG/sget24.f(3)

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version 3.12.1 · 3 versions
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🌸 NAME 🌸

okay so bestie, this page is the manual entry for TESTING/EIG/sget24.f(3) — yes, that’s the file path and the section number, and we’re keeping it exactly like that 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

Here’s the subroutine synopsis, copied exactly so you can trust it, no cap:

subroutine sget24 (comp, jtype, thresh, iseed, nounit, n, a, lda, h, ht,
    wr, wi, wrt, wit, wrtmp, witmp, vs, ldvs, vs1, rcdein, rcdvin,
    nslct, islct, result, work, lwork, iwork, bwork, info)
  • SGET24 — that’s the all-caps name from the synopsis, right there, iconic and untouched 🫶

💅 Function/Subroutine Documentation 💅

   subroutine sget24 (logical comp, integer jtype, real thresh, integer,
       dimension( 4 ) iseed, integer nounit, integer n, real, dimension( lda, *
       ) a, integer lda, real, dimension( lda, * ) h, real, dimension( lda, * )
       ht, real, dimension( * ) wr, real, dimension( * ) wi, real, dimension( *
       ) wrt, real, dimension( * ) wit, real, dimension( * ) wrtmp, real,
       dimension( * ) witmp, real, dimension( ldvs, * ) vs, integer ldvs, real,
       dimension( ldvs, * ) vs1, real rcdein, real rcdvin, integer nslct,
       integer, dimension( * ) islct, real, dimension( 17 ) result, real,
       dimension( * ) work, integer lwork, integer, dimension( * ) iwork,
       logical, dimension( * ) bwork, integer info)
       SGET24

🎯 Purpose 🎯

Bestie, SGET24 checks the nonsymmetric eigenvalue (Schur form) problem expert driver SGEESX. Like, it's the vibe check for that whole situation. 💖

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 RCDV computed.
  • (15) — if RCDV the same no matter if VS and/or RCDE computed.
  • (16) — |RCONDE - RCDEIN| / cond(RCONDE)

RCONDE is the reciprocal average eigenvalue condition number computed by SGEESX 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 SGEESX 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.

🌸 Parameters 🌸

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

JTYPE

JTYPE is INTEGER. Type of input matrix. Used to label output if error occurs.

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.

THRESH

THRESH is REAL.

A test will count as if the , 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.

Yeah, bestie, the source has a tiny gap in that sentence — we are not inventing words, we're keeping it 100. 💅

NOUNIT

NOUNIT is INTEGER. The FORTRAN unit number for printing out error messages (e.g., if a routine returns INFO not equal to 0.)

N

N is INTEGER. The dimension of A. N must be at least 0.

A

A is REAL array, dimension (LDA, N). Used to hold the matrix whose eigenvalues are to be computed.

LDA

LDA is INTEGER. The leading dimension of A, and H. LDA must be at least 1 and at least N.

H

H is REAL array, dimension (LDA, N). Another copy of the test matrix A, modified by SGEESX.

HT

HT is REAL array, dimension (LDA, N). Yet another copy of the test matrix A, modified by SGEESX.

WR

WR is REAL array, dimension (N).

WI

WI is REAL 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.

WRT

WRT is REAL array, dimension (N).

WIT

WIT is REAL array, dimension (N).

Like WR, WI, these arrays contain the eigenvalues of A, but those computed when SGEESX only computes a partial eigendecomposition, i.e. not Schur vectors.

WRTMP

WRTMP is REAL array, dimension (N).

WITMP

WITMP is REAL array, dimension (N).

Like WR, WI, these arrays contain the eigenvalues of A, but sorted by increasing real part.

VS

VS is REAL array, dimension (LDVS, N). VS holds the computed Schur vectors.

LDVS

LDVS is INTEGER. Leading dimension of VS. Must be at least max(1, N).

VS1

VS1 is REAL array, dimension (LDVS, N). VS1 holds another copy of the computed Schur vectors.

RCDEIN

RCDEIN is REAL. When COMP = .TRUE. RCDEIN holds the precomputed reciprocal condition number for the average of selected eigenvalues.

RCDVIN

RCDVIN is REAL. When COMP = .TRUE. RCDVIN holds the precomputed reciprocal condition number for the selected right invariant subspace.

NSLCT

NSLCT is INTEGER. When COMP = .TRUE. the number of selected eigenvalues corresponding to the precomputed values RCDEIN and RCDVIN.

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.

RESULT

RESULT is REAL array, dimension (17).

The values computed by the 17 tests described above. The values are currently limited to 1/ulp, to avoid overflow.

WORK

WORK is REAL array, dimension (LWORK).

LWORK

LWORK is INTEGER. The number of entries in WORK to be passed to SGEESX. This must be at least 3*N, and N+N**2 if tests 14--16 are to be performed.

IWORK

IWORK is INTEGER array, dimension (N*N).

BWORK

BWORK is LOGICAL array, dimension (N).

INFO

INFO is INTEGER.

If 0, successful exit.

If <0, input parameter -INFO had an incorrect value.

If >0, SGEESX returned an error code, the absolute value of which is returned.

👑 Author 👑

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Definition at line 339 of file sget24.f.

🫶 Author 🫶

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