CGET23(3)

📦 version 3.12.0, in opensuse-leap 16.0

CGET23(3) 💅✨

okay so this page is from the Library Functions Manual, and it's all about CGET23 — a LAPACK test routine with main character energy. bestie, we're checking the nonsymmetric eigenvalue problem driver CGEEVX. no cap, it's giving linear algebra detective work 🔍💖

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/cget23.f

🌈 SYNOPSIS 🌈

🧚 Functions/Subroutines 🧚

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

🦋 Function/Subroutine Documentation 🦋

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

🎯 Purpose 🎯

okay so CGET23 checks the nonsymmetric eigenvalue problem driver CGEEVX. If COMP = .FALSE., the first 8 of the following tests are performed on the input matrix A, and test 9 is also run if LWORK is sufficiently large. If COMP is .TRUE., all 11 tests are performed. periodt 💅

  1. Test 1 — formula:
| 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. Test 2 — formula:
| 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. Test 3 — formula:
| |VR(i)| - 1 | / ulp and largest component real

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

  1. Test 4 — formula:
| |VL(i)| - 1 | / ulp and largest component real

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

  1. Test 5 — 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. Test 6 — 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. Test 7 — 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. Test 8 — this vibe:
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. Test 9 — 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. Test 10 — formula:
|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. Test 11 — formula:
|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. 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
  • 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.

  • BALANC — BALANC is CHARACTER. 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 error occurs.
  • THRESH — THRESH is REAL. 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.
  • 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.
  • 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.
  • 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.
  • 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.

RESULT

  • RESULT — this one's a REAL array, dimension (11) and it's lowkey the whole point of the function: it holds the values computed by the 11 tests we described up above. Heads up though — the values are currently limited to 1/ulp, to avoid overflow. So if you're out here expecting huge spicy numbers, bestie, no cap, you're getting capped at 1/ulp and that's just how it is 💅
  • WORK — WORK is COMPLEX array, dimension (LWORK). The scratch space. The vibes holder. 🫶
  • LWORK — LWORK is INTEGER, and it's literally just the number of entries in WORK. But listen, there's a minimum, and the minimum is not a suggestion:
It must be at least 2*N, and it must be 2*N+N**2 if tests 9, 10, or 11 are going to be performed. So if you're running the later tests and you skimped on LWORK? That's a you problem, and it's giving "I didn't read the docs." 🙈
  • RWORK — RWORK is REAL array, dimension (2*N). Real-valued workspace, size 2*N, keep it moving ✨
  • INFO — INFO is INTEGER, our favorite little status reporter, and here's the tea:
    • If 0, successful exit. Slay. Periodt. 👑
    • If <0, input parameter -INFO had an incorrect value. (Yes, the parameter number is the absolute value — classic LAPACK iykyk.)
    • If >0, CGEEVX 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 363 of file cget23.f.

🖨️ Author

Generated automatically by Doxygen for LAPACK from the source code. Not a real person, just a very enthusiastic documentation printer that decided it also counts as an author 😭 honestly? iconic behavior.

And that's the whole page, bestie — you made it to the end 🎀 This little gem is from LAPACK, Version 3.12.0, and it lives at that path up top in the footer (the .../IG/cget23.f(3) one — you know the vibe). Go forth, pass LWORK correctly, and don't let INFO catch you slippin' 🌈💜

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