SGET23(3)

📦 version 3.12.0, in opensuse-leap 16.0

🦋 SGET23(3) — Library Functions Manual 🦋

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/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 💅

   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

SGET23

🌸 Purpose 🌸

Okay bestie, SGET23 checks the nonsymmetric eigenvalue problem driver SGEEVX. 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. Periodt. 💅

Here’s the test lineup, no cap:

  1. Test 1 — formula:
| 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.

  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 — formula:
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 — formula:
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 — formula:
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 — formula:
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 — formula:
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 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.

  1. Test 11 — formula:
|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 🫶

  • 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
  • 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 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 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 SGEEVX.
  • 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.
  • WR1 — WR1 is REAL array, dimension (N)
  • WI1 — WI1 is 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 — VL is REAL 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 REAL 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 REAL 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 — RCDEIN is a REAL array, dimension (N). When COMP = .TRUE., RCDEIN holds the precomputed reciprocal condition numbers for eigenvalues to be compared with RCONDE. precomputed and ready to serve ✨
  • SCALE — SCALE is a REAL array, dimension (N). Holds information describing balancing of matrix. matrix-balancing lore 💅
  • SCALE1 — SCALE1 is a REAL array, dimension (N). Holds information describing balancing of matrix. same energy, different name 🦋
  • RESULT — RESULT is a REAL array, dimension (11). The values computed by the 11 tests described above. The values are currently limited to 1/ulp, to avoid overflow. 11 tests, 11 little receipts 🧾✨
  • WORK — WORK is a REAL array, dimension (LWORK). the workspace bestie 🫶
  • LWORK — LWORK is an INTEGER. The number of entries in WORK. This must be at least 3*N, and 6*N+N**2 if tests 9, 10 or 11 are to be performed. do not skimp on LWORK, fr fr 😭
  • IWORK — IWORK is an INTEGER array, dimension (2*N). integer squad 🎀
  • INFO — INFO is an INTEGER. 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. read the exit code, bestie 👑

👑 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.

and that’s the whole page, bestie 💖 footer sign-off: LAPACK Version 3.12.0, source /home/abui...IG/sget23.f(3) — the line you pasted doesn’t have a separate date on it, so no invented date here, periodt 💅

📦 where this page comes from