TESTING/EIG/zget23.f(3)

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version 3.12.1 · 3 versions
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💅 TESTING/EIG/zget23.f(3) — Library Functions Manual, bestie edition 💅

okay so this is the glow-up of the ZGET23 page, and yes it’s giving “eigenvalue checker with main character energy.” 💖

🌸 NAME 🌸

TESTING/EIG/zget23.f

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine zget23 (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)

ZGET23 — that’s the function we’re hyping up. 💅

🌈 Function/Subroutine Documentation 🌈

subroutine zget23 (logical comp, integer isrt, character balanc, integer
    jtype, double precision thresh, integer, dimension( 4 ) iseed, integer
    nounit, integer n, complex*16, dimension( lda, * ) a, integer lda,
    complex*16, dimension( lda, * ) h, complex*16, dimension( * ) w,
    complex*16, dimension( * ) w1, complex*16, dimension( ldvl, * ) vl,
    integer ldvl, complex*16, dimension( ldvr, * ) vr, integer ldvr,
    complex*16, dimension( ldlre, * ) lre, integer ldlre, double precision,
    dimension( * ) rcondv, double precision, dimension( * ) rcndv1, double
    precision, dimension( * ) rcdvin, double precision, dimension( * )
    rconde, double precision, dimension( * ) rcnde1, double precision,
    dimension( * ) rcdein, double precision, dimension( * ) scale, double
    precision, dimension( * ) scale1, double precision, dimension( 11 )
    result, complex*16, dimension( * ) work, integer lwork, double
    precision, dimension( * ) rwork, integer info)

ZGET23 — again, iconic. 👑

🎯 Purpose 🎯

okay so ZGET23 checks the nonsymmetric eigenvalue problem driver CGEEVX. Here’s the vibe check, bestie:

If COMP = .FALSE., the first 8 of the following tests will be performed on the input matrix A, and also test 9 if LWORK is sufficiently large. If COMP is .TRUE. all 11 tests will be performed.

  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 ZGEEVX 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 ZGEEVX 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 DOUBLE PRECISION.
original-text moment: “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.

  • 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*16 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*16 array, dimension (LDA,N). Another copy of the test matrix A, modified by ZGEEVX.
  • W — W is COMPLEX*16 array, dimension (N). Contains the eigenvalues of A.
  • W1 — W1 is COMPLEX*16 array, dimension (N). Like W, this array contains the eigenvalues of A, but those computed when ZGEEVX only computes a partial eigendecomposition, i.e. not the eigenvalues and left and right eigenvectors.
  • VL — VL is COMPLEX*16 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*16 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*16 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 DOUBLE PRECISION array, dimension (N). RCONDV holds the computed reciprocal condition numbers for eigenvectors.
  • RCNDV1 — RCNDV1 is DOUBLE PRECISION array, dimension (N). RCNDV1 holds more computed reciprocal condition numbers for eigenvectors.
  • RCDVIN — RCDVIN is DOUBLE PRECISION array, dimension (N). When COMP = .TRUE. RCDVIN holds the precomputed reciprocal condition numbers for eigenvectors to be compared with RCONDV.
  • RCONDE — RCONDE is DOUBLE PRECISION array, dimension (N). RCONDE holds the computed reciprocal condition numbers for eigenvalues.
  • RCNDE1 — RCNDE1 is DOUBLE PRECISION array, dimension (N). RCNDE1 holds more computed reciprocal condition numbers for eigenvalues.
  • RCDEIN — RCDEIN is DOUBLE PRECISION array, dimension (N). When COMP = .TRUE. RCDEIN holds the precomputed reciprocal condition numbers for eigenvalues to be compared with RCONDE.
  • SCALE — the original chunk ends right here at the SCALE heading, bestie, so this is the part 1 cutoff; the description continues in part 2. 🫶
  • SCALE — DOUBLE PRECISION array, dimension (N). Holds information describing balancing of matrix. 🫶
  • SCALE1 — DOUBLE PRECISION array, dimension (N). Holds information describing balancing of matrix. Yes, bestie, it’s the twin — same deets, same energy. 💅
  • RESULT — DOUBLE PRECISION array, dimension (11). The values computed by the 11 tests described above. RN those values are limited to 1/ulp, to avoid overflow. 😭✨
  • WORK — COMPLEX*16 array, dimension (LWORK). Scratch space, periodt. 🎀
  • LWORK — 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. No cap, bestie. 🔥
  • RWORK — DOUBLE PRECISION array, dimension (2*N). 🌸
  • INFO — INTEGER. If 0, successful exit. If <0, input parameter -INFO had an incorrect value. If >0, ZGEEVX 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 zget23.f.

🧚 Author

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