TESTING/EIG/cget23.f(3)

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version 3.12.1 · 3 versions
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💅 TESTING/EIG/cget23.f — from the Library Functions Manual ✨

okay so bestie, buckle up, we're reading a Fortran manpage together and honestly? it's kind of iconic. this is TESTING/EIG/cget23.f, and it lives in the library functions manual like it owns the place 🎀

✨ NAME ✨

TESTING/EIG/cget23.f — that's it, that's the name, no notes 💅

🌸 SYNOPSIS 🌸

Functions/Subroutines

the whole squad of arguments, one subroutine, zero chill:

subroutine cget23 (comp, isrt, balanc, jtype, thresh, iseed, nounit, n,
    a, lda, h, w, w1, vl, ldvl, vr, ldvr, lre, ldlre, rcondv, rcndv1,
    rcdvin, rconde, rcnde1, rcdein, scale, scale1, result, work, lwork,
    rwork, info)

CGET23 — say it with your chest 👑

🦋 Function/Subroutine Documentation 🦋

the full signature, in all its glory 💖

subroutine cget23 (logical comp, integer isrt, character balanc, integer
    jtype, real thresh, integer, dimension( 4 ) iseed, integer nounit,
    integer n, complex, dimension( lda, * ) a, integer lda, complex,
    dimension( lda, * ) h, complex, dimension( * ) w, complex, dimension( *
    ) w1, complex, dimension( ldvl, * ) vl, integer ldvl, complex,
    dimension( ldvr, * ) vr, integer ldvr, complex, dimension( ldlre, * )
    lre, integer ldlre, real, dimension( * ) rcondv, real, dimension( * )
    rcndv1, real, dimension( * ) rcdvin, real, dimension( * ) rconde, real,
    dimension( * ) rcnde1, real, dimension( * ) rcdein, real, dimension( * )
    scale, real, dimension( * ) scale1, real, dimension( 11 ) result,
    complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork,
    integer info)

CGET23 ✨ (yes it says it twice, we love a routine that knows its own name 💅)

🧚 Purpose 🧚

💖 bestie listen: CGET23 checks the nonsymmetric eigenvalue problem driver CGEEVX. that's the whole assignment.

if COMP = .FALSE., the first 8 of the following tests get performed on the input matrix A, and also test 9 if LWORK is sufficiently large. if COMP is .TRUE., all 11 tests get performed. no skipping, no shortcuts, all eleven 😤

  1. | A * VR - VR * W | / ( n |A| ulp )

here VR is the matrix of unit right eigenvectors. W is a diagonal matrix with diagonal entries W(j).

  1. | A**H * VL - VL * W**H | / ( n |A| ulp )

here VL is the matrix of unit left eigenvectors, A**H is the conjugate transpose of A, and W is as above.

  1. | |VR(i)| - 1 | / ulp and largest component real

VR(i) denotes the i-th column of VR.

  1. | |VL(i)| - 1 | / ulp and largest component real

VL(i) denotes the i-th column of VL.

  1. 0 if W(full) = W(partial), 1/ulp otherwise

W(full) denotes the eigenvalues computed when VR, VL, RCONDV and RCONDE are also computed, and W(partial) denotes the eigenvalues computed when only some of VR, VL, RCONDV, and RCONDE are computed.

  1. 0 if VR(full) = VR(partial), 1/ulp otherwise

VR(full) denotes the right eigenvectors computed when VL, RCONDV and RCONDE are computed, and VR(partial) denotes the result when only some of VL and RCONDV are computed.

  1. 0 if VL(full) = VL(partial), 1/ulp otherwise

VL(full) denotes the left eigenvectors computed when VR, RCONDV and RCONDE are computed, and VL(partial) denotes the result when only some of VR and RCONDV are computed.

  1. 0 if SCALE, ILO, IHI, ABNRM (full) = SCALE, ILO, IHI, ABNRM (partial), 1/ulp otherwise

SCALE, ILO, IHI and ABNRM describe how the matrix is balanced. (full) is when VR, VL, RCONDE and RCONDV are also computed, and (partial) is when some are not computed.

  1. 0 if RCONDV(full) = RCONDV(partial), 1/ulp otherwise

RCONDV(full) denotes the reciprocal condition numbers of the right eigenvectors computed when VR, VL and RCONDE are also computed. RCONDV(partial) denotes the reciprocal condition numbers when only some of VR, VL and RCONDE are computed.

  1. |RCONDV - RCDVIN| / cond(RCONDV)

RCONDV is the reciprocal right eigenvector condition number computed by CGEEVX 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.

  1. |RCONDE - RCDEIN| / cond(RCONDE)

RCONDE is the reciprocal eigenvalue condition number computed by CGEEVX 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.

🎀 Parameters 🎀

COMP 💖

COMP is LOGICAL.

it 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

ISRT 🦋

ISRT is INTEGER.

if COMP = .TRUE., ISRT indicates in how the eigenvalues corresponding to values in RCDVIN and RCDEIN are ordered:

  • = 0 means the eigenvalues are sorted by increasing real part
  • = 1 means the eigenvalues are sorted by increasing imaginary part

if COMP = .FALSE., ISRT is not referenced. (it's just vibing in the corner 🫶)

BALANC 🌸

BALANC is CHARACTER.

it describes the balancing option to be tested:

  • = 'N' for no permuting or diagonal scaling
  • = 'P' for permuting but no diagonal scaling
  • = 'S' for no permuting but diagonal scaling
  • = 'B' for permuting and diagonal scaling

JTYPE 👑

JTYPE is INTEGER.

type of input matrix. used to label output if an error occurs. bestie's just a name tag 🏷️

THRESH 🔥

THRESH is REAL.

a test will count as failing if the value, 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. no negative threshold shenanigans, that's not the vibe 💀

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 an error occurs.

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 COMPLEX 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 COMPLEX array, dimension (LDA,N).

another copy of the test matrix A, modified by CGEEVX. she's been through things 💅

W ✨

W is COMPLEX array, dimension (N).

contains the eigenvalues of A.

W1 🦋

W1 is COMPLEX array, dimension (N).

like W, this array contains the eigenvalues of A, but those computed when CGEEVX only computes a partial eigendecomposition, i.e. not the eigenvalues and left and right eigenvectors.

VL 🌸

VL is COMPLEX array, dimension (LDVL,N).

VL holds the computed left eigenvectors.

LDVL 🫶

LDVL is INTEGER.

leading dimension of VL. must be at least max(1,N).

VR 🔥

VR is COMPLEX array, dimension (LDVR,N).

VR holds the computed right eigenvectors.

LDVR 😭

LDVR is INTEGER.

leading dimension of VR. must be at least max(1,N).

LRE 👑

LRE is COMPLEX array, dimension (LDLRE,N).

LRE holds the computed right or left eigenvectors.

LDLRE 🌈

LDLRE is INTEGER.

leading dimension of LRE. must be at least max(1,N).

RCONDV ⭐

RCONDV is REAL array, dimension (N).

RCONDV holds the computed reciprocal condition numbers for eigenvectors.

RCNDV1 💜

RCNDV1 is REAL array, dimension (N).

RCNDV1 holds more computed reciprocal condition numbers for eigenvectors. (yes, "more" — there's always more 💀)

RCDVIN 🎀

RCDVIN is REAL array, dimension (N).

when COMP = .TRUE., RCDVIN holds the precomputed reciprocal condition numbers for eigenvectors to be compared with RCONDV.

RCONDE 🧚

RCONDE is REAL array, dimension (N).

RCONDE holds the computed reciprocal condition numbers for eigenvalues.

RCNDE1 🌸

RCNDE1 is REAL array, dimension (N).

RCNDE1 holds more computed reciprocal condition numbers for eigenvalues.

RCDEIN 🍓

RCDEIN is REAL array, dimension (N).

when COMP = .TRUE., RCDEIN holds the precomputed reciprocal condition numbers for eigenvalues to be compared with RCONDE.

SCALE 🔥

SCALE is REAL array, dimension (N).

holds information describing balancing of matrix.

SCALE1 ✨

SCALE1 is REAL array, dimension (N).

holds information describing balancing of matrix. (twins 💅)

RESULT… 👀

and that's exactly where the page we've got runs out bestie — RESULT is up next, so hold that thought 🫶

  • RESULT — a REAL array, dimension (11) 💅 these are the values computed by the 11 tests described above, and rn they're capped at 1/ulp so nothing overflows and ruins the vibe. no cap, overflow is NOT the move 😭
  • WORK — a COMPLEX array, dimension (LWORK) ✨ your workspace bestie, she's complex and she's here to work 🫶
  • LWORK — an INTEGER 👑 the number of entries in WORK. This must be at least 2*N, and 2*N+N**2 if tests 9, 10 or 11 are to be performed. so like… if you're doing the extra tests, size her up accordingly, iykyk 💀
  • RWORK — a REAL array, dimension (2*N) 🌸 real ones only, and there's 2*N of them 🎀
  • INFO — an INTEGER ⭐ the whole mood report:
    • If 0, successful exit. slay 💖
    • If <0, input parameter -INFO had an incorrect value. not me forgetting to check the args 🙈
    • If >0, CGEEVX returned an error code, the absolute value of which is returned. so yeah, that's a real error, not a drill 😭🔥

✨ Author ✨

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.
Definition at line 363 of file cget23.f. 🎀

👑 Author (the Doxygen one) 👑

Generated automatically by Doxygen for LAPACK from the source code. the robots wrote this part, bestie 🤖✨

okay bestie that's the whole page 💖 this lil beauty comes from LAPACK Version 3.12.0, file TESTING/EIG/cget23.f(3) — go off and test those eigenbaddies ✨👑🦋

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