TESTING/EIG/sget23.f(3)

📦

version 3.12.1 · 2 versions

3.12.1 · arch rolling (latest)
3.12.0 · centos-stream 10, fedora 43, fedora 44

💖 NAME 💖

okay bestie, this page is from the Library Functions Manual and it's literally all about TESTING/EIG/sget23.f 💅

✨ SYNOPSIS ✨

Functions/Subroutines

   subroutine sget23 (comp, balanc, jtype, thresh, iseed, nounit, n, a,
       lda, h, wr, wi, wr1, wi1, vl, ldvl, vr, ldvr, lre, ldlre, rcondv,
       rcndv1, rcdvin, rconde, rcnde1, rcdein, scale, scale1, result, work,
       lwork, iwork, info)

SGET23

🌸 Function/Subroutine Documentation 🌸

subroutine sget23 (logical comp, character balanc, integer jtype, real thresh, integer, dimension( 4 ) iseed, integer nounit, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( lda, * ) h, real, dimension( * ) wr, real, dimension( * ) wi, real, dimension( * ) wr1, real, dimension( * ) wi1, real, dimension( ldvl, * ) vl, integer ldvl, real, dimension( ldvr, * ) vr, integer ldvr, real, 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, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer info)

   subroutine sget23 (logical comp, character balanc, integer jtype, real
       thresh, integer, dimension( 4 ) iseed, integer nounit, integer n, real,
       dimension( lda, * ) a, integer lda, real, dimension( lda, * ) h, real,
       dimension( * ) wr, real, dimension( * ) wi, real, dimension( * ) wr1,
       real, dimension( * ) wi1, real, dimension( ldvl, * ) vl, integer ldvl,
       real, dimension( ldvr, * ) vr, integer ldvr, real, 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, real,
       dimension( * ) work, integer lwork, integer, dimension( * ) iwork,
       integer info)

SGET23

this is the whole signature, no cap. every single argument is iconic in its own way 🫶

🎯 Purpose 🎯

okay so SGET23 checks the nonsymmetric eigenvalue problem driver SGEEVX. here's the tea:

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.

now the tests, bestie:

| A * VR - VR * W | / ( n |A| ulp ) here VR is the matrix of unit right eigenvectors. W is a block diagonal matrix, with a 1x1 block for each real eigenvalue and a 2x2 block for each complex conjugate pair. if eigenvalues j and j+1 are a complex conjugate pair, so WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the 2 x 2 block corresponding to the pair will be:

(  wr  wi  )
( -wi  wr  )

such a block multiplying an n x 2 matrix ( ur ui ) on the right will be the same as multiplying ur + i*ui by wr + i*wi.

| 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.
| |VR(i)| - 1 | / ulp and largest component real VR(i) denotes the i-th column of VR.
| |VL(i)| - 1 | / ulp and largest component real VL(i) denotes the i-th column of VL.
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.
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.
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.
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.
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.
|RCONDV - RCDVIN| / cond(RCONDV) RCONDV is the reciprocal right eigenvector condition number computed by SGEEVX 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.
|RCONDE - RCDEIN| / cond(RCONDE) RCONDE is the reciprocal eigenvalue condition number computed by SGEEVX 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 💅

okay now the parameters, one by one. no skipping, bestie.

COMP — LOGICAL. 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
BALANC — 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 — INTEGER. type of input matrix. used to label output if error occurs.
THRESH — REAL. a test will count as a fail 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.

bestie, THRESH must be at least zero, no cap. don't come at me with negative numbers 🙈

ISEED — 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 — INTEGER. the FORTRAN unit number for printing out error messages (e.g., if a routine returns INFO not equal to 0.)
N — INTEGER. the dimension of A. N must be at least 0.
A — REAL array, dimension (LDA,N). used to hold the matrix whose eigenvalues are to be computed.
LDA — INTEGER. the leading dimension of A, and H. LDA must be at least 1 and at least N.
H — REAL array, dimension (LDA,N). another copy of the test matrix A, modified by SGEEVX.
WR — REAL array, dimension (N).
WI — 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.
WR1 — REAL array, dimension (N).
WI1 — REAL array, dimension (N). like WR, WI, these arrays contain the eigenvalues of A, but those computed when SGEEVX only computes a partial eigendecomposition, i.e. not the eigenvalues and left and right eigenvectors.
VL — REAL array, dimension (LDVL,N). VL holds the computed left eigenvectors.
LDVL — INTEGER. leading dimension of VL. must be at least max(1,N).
VR — REAL array, dimension (LDVR,N). VR holds the computed right eigenvectors.
LDVR — INTEGER. leading dimension of VR. must be at least max(1,N).
LRE — REAL array, dimension (LDLRE,N). LRE holds the computed right or left eigenvectors.
LDLRE — INTEGER. leading dimension of LRE. must be at least max(1,N).
RCONDV — REAL array, dimension (N). RCONDV holds the computed reciprocal condition numbers for eigenvectors.
RCNDV1 — REAL array, dimension (N). RCNDV1 holds more computed reciprocal condition numbers for eigenvectors.
RCDVIN — REAL array, dimension (N). when COMP = .TRUE. RCDVIN holds the precomputed reciprocal condition numbers for eigenvectors to be compared with RCONDV.
RCONDE — REAL array, dimension (N). RCONDE holds the computed reciprocal condition numbers for eigenvalues.
RCNDE1 — REAL array, dimension (N). RCNDE1 holds more computed reciprocal condition numbers for eigenvalues.
RCDEIN — REAL array, dimension (N). when COMP = .TRUE. RCDEIN holds the precomputed reciprocal condition numbers for eigenvalues to be compared with RCONDE.
SCALE —
SCALE — it’s a REAL array, dimension (N). It holds the info describing the balancing of the matrix. 🫶
SCALE1 — also a REAL array, dimension (N), and it holds information describing balancing of the matrix. ✨
RESULT — a REAL array, dimension (11). These are the values computed by the 11 tests described above, and they’re currently limited to 1/ulp, to avoid overflow. 💅
WORK — a REAL array, dimension (LWORK). 🧚
LWORK — INTEGER. This is the number of entries in WORK. It must be at least 3*N, and 6*N+N**2 if tests 9, 10 or 11 are to be performed. 🔥
IWORK — an INTEGER array, dimension (2*N). 🌸
INFO — INTEGER. The vibe check goes like this:
- If 0, successful exit. ✅
- If <0, input parameter -INFO had an incorrect value. 😭
- If >0, SGEEVX 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 373 of file sget23.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

💖 Source/version check, bestie: LAPACK Version 3.12.0, page TESTING/EIG/sget23.f(3) — and the footer’s date isn’t separately listed here, so no invented date, periodt. Stay iconic! ✨

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms