TESTING/EIG/zchkee.F(3)

📦
version 3.12.0 · 3 versions
, in centos-stream 10, fedora 43, fedora 44

🌸 NAME 🌸

TESTING/EIG/zchkee.F — bestie, this is the LAPACK manual page for it, and it's a BIG one. Buckle up. 💖

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

  • program zchkee — aka ZCHKEE 🦋

💅 Function/Subroutine Documentation 💅

👑 program zchkee 👑

ZCHKEE ✨

🌈 Purpose 🌈

So ZCHKEE tests the COMPLEX*16 LAPACK subroutines for the matrix eigenvalue problem. Obsessed, honestly. The test paths in this version are:

  • NEP (Nonsymmetric Eigenvalue Problem) — tests ZGEHRD, ZUNGHR, ZHSEQR, ZTREVC, ZHSEIN, and ZUNMHR 🔥
  • SEP (Hermitian Eigenvalue Problem) — tests ZHETRD, ZUNGTR, ZSTEQR, ZSTERF, ZSTEIN, ZSTEDC, and the drivers ZHEEV(X), ZHBEV(X), ZHPEV(X), ZHEEVD, ZHBEVD, ZHPEVD 🌸
  • SVD (Singular Value Decomposition) — tests ZGEBRD, ZUNGBR, and ZBDSQR, plus the drivers ZGESVD, ZGESDD 💀
  • ZEV (Nonsymmetric Eigenvalue/eigenvector Driver) — tests ZGEEV
  • ZES (Nonsymmetric Schur form Driver) — tests ZGEES
  • ZVX (Nonsymmetric Eigenvalue/eigenvector Expert Driver) — tests ZGEEVX
  • ZSX (Nonsymmetric Schur form Expert Driver) — tests ZGEESX
  • ZGG (Generalized Nonsymmetric Eigenvalue Problem) — tests ZGGHD3, ZGGBAL, ZGGBAK, ZHGEQZ, and ZTGEVC
  • ZGS (Generalized Nonsymmetric Schur form Driver) — tests ZGGES
  • ZGV (Generalized Nonsymmetric Eigenvalue/eigenvector Driver) — tests ZGGEV
  • ZGX (Generalized Nonsymmetric Schur form Expert Driver) — tests ZGGESX
  • ZXV (Generalized Nonsymmetric Eigenvalue/eigenvector Expert Driver) — tests ZGGEVX
  • ZSG (Hermitian Generalized Eigenvalue Problem) — tests ZHEGST, ZHEGV, ZHEGVD, ZHEGVX, ZHPGST, ZHPGV, ZHPGVD, ZHPGVX, ZHBGST, ZHBGV, ZHBGVD, and ZHBGVX 🫶
  • ZHB (Hermitian Band Eigenvalue Problem) — tests ZHBTRD
  • ZBB (Band Singular Value Decomposition) — tests ZGBBRD
  • ZEC (Eigencondition estimation) — tests ZTRSYL, ZTREXC, ZTRSNA, and ZTRSEN
  • ZBL (Balancing a general matrix) — tests ZGEBAL
  • ZBK (Back transformation on a balanced matrix) — tests ZGEBAK
  • ZGL (Balancing a matrix pair) — tests ZGGBAL
  • ZGK (Back transformation on a matrix pair) — tests ZGGBAK
  • GLM (Generalized Linear Regression Model) — tests ZGGGLM
  • GQR (Generalized QR and RQ factorizations) — tests ZGGQRF and ZGGRQF
  • GSV (Generalized Singular Value Decomposition) — tests ZGGSVD, ZGGSVP, ZTGSJA, ZLAGS2, ZLAPLL, and ZLAPMT ⭐
  • CSD (CS decomposition) — tests ZUNCSD
  • LSE (Constrained Linear Least Squares) — tests ZGGLSE

okay so every test path has its own lil set of inputs, but the data sets for the driver routines xEV, xES, xVX, and xSX can be concatenated into a single input file. Not me being efficient. 💅 The first line of input should contain one of the 3-character path names in columns 1-3. The number of remaining lines depends on what's found on that first line.

The number of matrix types used in testing is often controllable from the input file. The number of matrix types for each path, and the test routine that describes them, is as follows:

Path name(s)  Types    Test routine

ZHS or NEP      21     ZCHKHS
ZST or SEP      21     ZCHKST (routines)
                18     ZDRVST (drivers)
ZBD or SVD      16     ZCHKBD (routines)
                 5     ZDRVBD (drivers)
ZEV             21     ZDRVEV
ZES             21     ZDRVES
ZVX             21     ZDRVVX
ZSX             21     ZDRVSX
ZGG             26     ZCHKGG (routines)
ZGS             26     ZDRGES
ZGX              5     ZDRGSX
ZGV             26     ZDRGEV
ZXV              2     ZDRGVX
ZSG             21     ZDRVSG
ZHB             15     ZCHKHB
ZBB             15     ZCHKBB
ZEC              -     ZCHKEC
ZBL              -     ZCHKBL
ZBK              -     ZCHKBK
ZGL              -     ZCHKGL
ZGK              -     ZCHKGK
GLM              8     ZCKGLM
GQR              8     ZCKGQR
GSV              8     ZCKGSV
CSD              3     ZCKCSD
LSE              8     ZCKLSE

🦋 NEP input file 🦋

  • line 2: NN, INTEGER — number of values of N.
  • line 3: NVAL, INTEGER array, dimension (NN) — the values for the matrix dimension N.
  • line 4: NPARMS, INTEGER — number of values of the parameters NB, NBMIN, NX, NS, and MAXB.
  • line 5: NBVAL, INTEGER array, dimension (NPARMS) — the values for the blocksize NB.
  • line 6: NBMIN, INTEGER array, dimension (NPARMS) — the values for the minimum blocksize NBMIN.
  • line 7: NXVAL, INTEGER array, dimension (NPARMS) — the values for the crossover point NX.
  • line 8: INMIN, INTEGER array, dimension (NPARMS) — LAHQR vs TTQRE crossover point, >= 11
  • line 9: INWIN, INTEGER array, dimension (NPARMS) — recommended deflation window size
  • line 10: INIBL, INTEGER array, dimension (NPARMS) — nibble crossover point
  • line 11: ISHFTS, INTEGER array, dimension (NPARMS) — number of simultaneous shifts)
  • line 12: IACC22, INTEGER array, dimension (NPARMS) — select structured matrix multiply: 0, 1 or 2)
  • line 13: THRESH — threshold value for the test ratios. Information will be printed about each test for which the test ratio is greater than or equal to the threshold. To have all of the test ratios printed, use THRESH = 0.0 .
  • line 14: NEWSD, INTEGER — a code indicating how to set the random number seed.
    • = 0: set the seed to a default value before each run
    • = 1: initialize the seed to a default value only before the first run
    • = 2: like 1, but use the seed values on the next line

If line 14 was 2:

  • line 15: INTEGER array, dimension (4) — four integer values for the random number seed.

lines 15-EOF: the remaining lines occur in sets of 1 or 2 and let the user specify the matrix types. Each line contains a 3-character path name in columns 1-3, and the number of matrix types must be the first nonblank item in columns 4-80. If the number of matrix types is at least 1 but is less than the maximum number of possible types, a second line will be read to get the numbers of the matrix types to be used. For example,

NEP 21

requests all of the matrix types for the nonsymmetric eigenvalue problem, while

NEP  4
9 10 11 12

requests only matrices of type 9, 10, 11, and 12. 💖

The valid 3-character path names are 'NEP' or 'ZHS' for the nonsymmetric eigenvalue routines.

🌸 SEP or ZSG input file 🌸

  • line 2: NN, INTEGER — number of values of N.
  • line 3: NVAL, INTEGER array, dimension (NN) — the values for the matrix dimension N.
  • line 4: NPARMS, INTEGER — number of values of the parameters NB, NBMIN, and NX.
  • line 5: NBVAL, INTEGER array, dimension (NPARMS) — the values for the blocksize NB.
  • line 6: NBMIN, INTEGER array, dimension (NPARMS) — the values for the minimum blocksize NBMIN.
  • line 7: NXVAL, INTEGER array, dimension (NPARMS) — the values for the crossover point NX.
  • line 8: THRESH — threshold value for the test ratios. Information will be printed about each test for which the test ratio is greater than or equal to the threshold.
  • line 9: TSTCHK, LOGICAL — flag indicating whether or not to test the LAPACK routines.
  • line 10: TSTDRV, LOGICAL — flag indicating whether or not to test the driver routines.
  • line 11: TSTERR, LOGICAL — flag indicating whether or not to test the error exits for the LAPACK routines and driver routines.
  • line 12: NEWSD, INTEGER — a code indicating how to set the random number seed.
    • = 0: set the seed to a default value before each run
    • = 1: initialize the seed to a default value only before the first run
    • = 2: like 1, but use the seed values on the next line

If line 12 was 2:

  • line 13: INTEGER array, dimension (4) — four integer values for the random number seed.

lines 13-EOF: lines specifying matrix types, as for NEP. The valid 3-character path names are 'SEP' or 'ZST' for the Hermitian eigenvalue routines and driver routines, and 'ZSG' for the routines for the Hermitian generalized eigenvalue problem. ✨

🎀 SVD input file 🎀

  • line 2: NN, INTEGER — number of values of M and N.
  • line 3: MVAL, INTEGER array, dimension (NN) — the values for the matrix row dimension M.
  • line 4: NVAL, INTEGER array, dimension (NN) — the values for the matrix column dimension N.
  • line 5: NPARMS, INTEGER — number of values of the parameter NB, NBMIN, NX, and NRHS.
  • line 6: NBVAL, INTEGER array, dimension (NPARMS) — the values for the blocksize NB.
  • line 7: NBMIN, INTEGER array, dimension (NPARMS) — the values for the minimum blocksize NBMIN.
  • line 8: NXVAL, INTEGER array, dimension (NPARMS) — the values for the crossover point NX.
  • line 9: NSVAL, INTEGER array, dimension (NPARMS) — the values for the number of right hand sides NRHS.
  • line 10: THRESH — threshold value for the test ratios. Information will be printed about each test for which the test ratio is greater than or equal to the threshold.
  • line 11: TSTCHK, LOGICAL — flag indicating whether or not to test the LAPACK routines.
  • line 12: TSTDRV, LOGICAL — flag that says whether or not we're testing the driver routines. bestie, it's a yes/no vibe check 💅
  • line 13: TSTERR, LOGICAL — flag for whether or not we test the error exits for the LAPACK routines and driver routines. like, do we poke it to make sure it screams correctly 😭
  • line 14: NEWSD, INTEGER — a code telling you how to set the random number seed. it's giving ✨control freak✨ but in a cute way:
    • = 0: Set the seed to a default value before each run
    • = 1: Initialize the seed to a default value only before the first run
    • = 2: Like 1, but use the seed values on the next line

If line 14 was 2:

  • line 15: INTEGER array, dimension (4) — four integer values for the random number seed. four. literally four. 🔢
  • lines 15-EOF — lines specifying matrix types, as for NEP. the 3-character path names are 'SVD' or 'ZBD', and they cover both the SVD routines and the SVD driver routines. no cap. 🌸

💖 ZEV and ZES data files 💖

  • line 1 — 'ZEV' or 'ZES' sitting in columns 1 to 3. that's the whole vibe. 👑
  • line 2: NSIZES, INTEGER — number of sizes of matrices to use. should be at least 0 and at most 20. if NSIZES = 0, no testing is done — but the remaining 3 lines are still read anyway (yes, they're still read, don't skip them 🙈).
  • line 3: NN, INTEGER array, dimension(NSIZES) — the dimensions of the matrices to be tested.
  • line 4: NB, NBMIN, NX, NS, NBCOL, INTEGERs — these integer parameters decide how blocking is done (peep ILAENV for the details):
    • NB: block size
    • NBMIN: minimum block size
    • NX: minimum dimension for blocking
    • NS: number of shifts in xHSEQR
    • NBCOL: minimum column dimension for blocking
  • line 5: THRESH, REAL — the test threshold that computed residuals get compared against. should generally be in the range from 10. to 20. if it's 0., all test case data will be printed. all of it. every crumb. 💀
  • line 6: NEWSD, INTEGER — a code indicating how to set the random number seed.
    • = 0: Set the seed to a default value before each run
    • = 1: Initialize the seed to a default value only before the first run
    • = 2: Like 1, but use the seed values on the next line

If line 6 was 2:

  • line 7: INTEGER array, dimension (4) — four integer values for the random number seed.
  • lines 8 and following — lines specifying matrix types, as for NEP. the 3-character path name is 'ZEV' to test CGEEV, or 'ZES' to test CGEES. pick your fighter 🥊

🌈 The ZVX data 🌈

okay so the ZVX data has two parts. the first part is identical to ZEV, and the second part consists of test matrices with precomputed solutions. very "here's the warmup AND the main event" of it all.

  • line 1 — 'ZVX' in columns 1-3.
  • line 2: NSIZES, INTEGER — if NSIZES = 0, no testing of randomly generated examples is done, but any precomputed examples are tested.
  • line 3: NN, INTEGER array, dimension(NSIZES)
  • line 4: NB, NBMIN, NX, NS, NBCOL, INTEGERs
  • line 5: THRESH, REAL
  • line 6: NEWSD, INTEGER

If line 6 was 2:

  • line 7: INTEGER array, dimension (4)
  • lines 8 and following — the first line contains 'ZVX' in columns 1-3 followed by the number of matrix types, possibly with a second line to specify certain matrix types. if the number of matrix types = 0, no testing of randomly generated examples is done, but any precomputed examples are tested. 🎀
  • remaining lines — each matrix is stored on 1+N+N**2 lines, where N is its dimension. the first line contains the dimension N and ISRT (two integers). ISRT indicates whether the last N lines are sorted by increasing real part of the eigenvalue (ISRT=0) or by increasing imaginary part (ISRT=1). the next N**2 lines contain the matrix rowwise, one entry per line. the last N lines correspond to each eigenvalue. each of these last N lines contains 4 real values: the real part of the eigenvalues, the imaginary part of the eigenvalue, the reciprocal condition number of the eigenvalues, and the reciprocal condition number of the vector eigenvector. the end of data is indicated by dimension N=0. even if no data is to be tested, there must be at least one line containing N=0. do not skip it, bestie, it WILL be mad 😤

🦋 The ZSX data 🦋

the ZSX data is like ZVX — same energy, different letter. the first part is identical to ZEV, and the second part consists of test matrices with precomputed solutions.

  • line 1 — 'ZSX' in columns 1-3.
  • line 2: NSIZES, INTEGER — if NSIZES = 0, no testing of randomly generated examples is done, but any precomputed examples are tested.
  • line 3: NN, INTEGER array, dimension(NSIZES)
  • line 4: NB, NBMIN, NX, NS, NBCOL, INTEGERs
  • line 5: THRESH, REAL
  • line 6: NEWSD, INTEGER

If line 6 was 2:

  • line 7: INTEGER array, dimension (4)
  • lines 8 and following — the first line contains 'ZSX' in columns 1-3 followed by the number of matrix types, possibly with a second line to specify certain matrix types. if the number of matrix types = 0, no testing of randomly generated examples is done, but any precomputed examples are tested.
  • remaining lines — each matrix is stored on 3+N**2 lines, where N is its dimension. the first line contains the dimension N, the dimension M of an invariant subspace, and ISRT. the second line contains M integers, identifying the eigenvalues in the invariant subspace (by their position in a list of eigenvalues ordered by increasing real part (if ISRT=0) or by increasing imaginary part (if ISRT=1)). the next N**2 lines contain the matrix rowwise. the last line contains the reciprocal condition number for the average of the selected eigenvalues, and the reciprocal condition number for the corresponding right invariant subspace. the end of data in indicated by a line containing N=0, M=0, and ISRT = 0. even if no data is to be tested, there must be at least one line containing N=0, M=0 and ISRT=0. 💀 (yes the original says "in indicated", we love a typo that's canon, moving on 💅)

🔥 ZGG input file 🔥

  • line 2: NN, INTEGER — number of values of N.
  • line 3: NVAL, INTEGER array, dimension (NN) — the values for the matrix dimension N.
  • line 4: NPARMS, INTEGER — number of values of the parameters NB, NBMIN, NBCOL, NS, and MAXB.
  • line 5: NBVAL, INTEGER array, dimension (NPARMS) — the values for the blocksize NB.
  • line 6: NBMIN, INTEGER array, dimension (NPARMS) — the values for NBMIN, the minimum row dimension for blocks.
  • line 7: NSVAL, INTEGER array, dimension (NPARMS) — the values for the number of shifts.
  • line 8: MXBVAL, INTEGER array, dimension (NPARMS) — the values for MAXB, used in determining minimum blocksize.
  • line 9: IACC22, INTEGER array, dimension (NPARMS) — select structured matrix multiply: 1 or 2. choose wisely bestie, it's a whole fork in the road 🛣️
  • line 10: NBCOL, INTEGER array, dimension (NPARMS) — the values for NBCOL, the minimum column dimension for blocks.
  • line 11: THRESH — threshold value for the test ratios. information will be printed about each test for which the test ratio is greater than or equal to the threshold. it's giving "only the dramatic ones get screen time" 🎬
  • line 12: TSTCHK, LOGICAL — flag indicating whether or not to test the LAPACK routines.
  • line 13: TSTDRV, LOGICAL — flag indicating whether or not to test the driver routines.
  • line 14: TSTERR, LOGICAL — flag indicating whether or not to test the error exits for the LAPACK routines and driver routines.
  • line 15: NEWSD, INTEGER — a code indicating how to set the random number seed.
    • = 0: Set the seed to a default value before each run
    • = 1: Initialize the seed to a default value only before the first run
    • = 2: Like 1, but use the seed values on the next line

If line 15 was 2:

  • line 16: INTEGER array, dimension (4) — four integer values for the random number seed.
  • lines 17-EOF — lines specifying matrix types, as for NEP. the 3-character path name is 'ZGG' for the generalized eigenvalue problem routines and driver routines. ✨

💜 ZGS and ZGV input files 💜

  • line 1 — 'ZGS' or 'ZGV' in columns 1 to 3.
  • line 2: NN, INTEGER — number of values of N.
  • line 3: NVAL, INTEGER array, dimension(NN) — dimensions of matrices to be tested.
  • line 4: NB, NBMIN, NX, NS, NBCOL, INTEGERs — these integer parameters determine how blocking is done (see ILAENV for details):
    • NB: block size
    • NBMIN: minimum block size
    • NX: minimum dimension for blocking
    • NS: number of shifts in xHGEQR
    • NBCOL: minimum column dimension for blocking
  • line 5: THRESH, REAL — the test threshold against which computed residuals are compared. should generally be in the range from 10. to 20. if it is 0., all test case data will be printed. 🌸
  • line 6: TSTERR, LOGICAL — flag indicating whether or not to test the error exits.
  • line 7: NEWSD, INTEGER — a code indicating how to set the random number seed.
    • = 0: Set the seed to a default value before each run
    • = 1: Initialize the seed to a default value only before the first run
    • = 2: Like 1, but use the seed values on the next line

If line 17 was 2:

  • line 7: INTEGER array, dimension (4) — four integer values for the random number seed.
ok so yes, it literally says line 17 up there and then line 7 right after — that's the original's own little chaos moment, we're keeping it exactly as written because facts are facts and we do not touch the numbers 🙈💅
  • lines 7-EOF: the lines that specify matrix types, same vibe as for NEP ✨ The 3-character path name is 'ZGS' — that one's for the generalized eigenvalue problem routines and driver routines 💅

🦋 ZGX input file 🦋

  • line 1: 'ZGX' in columns 1 to 3.
  • line 2: N, INTEGER — literally just the value of N bestie.
  • line 3: NB, NBMIN, NX, NS, NBCOL, INTEGERs — these integer parameters decide how the blocking gets done (peep ILAENV for the details 👀)
    • NB — block size
    • NBMIN — minimum block size
    • NX — minimum dimension for blocking
    • NS — number of shifts in xHGEQR
    • NBCOL — minimum column dimension for blocking
  • line 4: THRESH, REAL — the test threshold that computed residuals get compared against. Generally you wanna keep it in the range from 10. to 20. 💖 Info gets printed about every test where the test ratio is greater than or equal to the threshold.
  • line 5: TSTERR, LOGICAL — flag saying whether or not to test the error exits for the LAPACK routines and driver routines.
  • line 6: NEWSD, INTEGER — a code that says how to set the random number seed.
    • = 0: Set the seed to a default value before each run
    • = 1: Initialize the seed to a default value only before the first run
    • = 2: Like 1, but use the seed values on the next line

If line 6 was 2:

  • line 7: INTEGER array, dimension (4) — four integer values for the random number seed 🎲

If line 2 was 0:

  • line 7-EOF: Precomputed examples are tested.
  • remaining lines: each example is stored on 3+2*N*N lines, where N is its dimension. The first line holds the dimension (a single integer). The next line holds an integer k such that only the last k eigenvalues will be selected and appear in the leading diagonal blocks of $A$ and $B$. The next N*N lines contain the matrix A, one element per line. The next N*N lines contain the matrix B. The last line contains the reciprocal of the eigenvalue cluster condition number and the reciprocal of the deflating subspace (associated with the selected eigencluster) condition number. The end of data is indicated by dimension N=0. Even if no data is to be tested, there must be at least one line containing N=0 — no skipping, bestie, that line is mandatory 🙈

🌸 ZXV input files 🌸

  • line 1: 'ZXV' in columns 1 to 3.
  • line 2: N, INTEGER — the value of N.
  • line 3: NB, NBMIN, NX, NS, NBCOL, INTEGERs — these integer parameters determine how the blocking is done (see ILAENV for details)
    • NB — block size
    • NBMIN — minimum block size
    • NX — minimum dimension for blocking
    • NS — number of shifts in xHGEQR
    • NBCOL — minimum column dimension for blocking
  • line 4: THRESH, REAL — the test threshold that computed residuals get compared against. Should generally be in the range from 10. to 20. Info will be printed about each test for which the test ratio is greater than or equal to the threshold.
  • line 5: TSTERR, LOGICAL — flag indicating whether or not to test the error exits for the LAPACK routines and driver routines.
  • line 6: NEWSD, INTEGER — a code indicating how to set the random number seed.
    • = 0: Set the seed to a default value before each run
    • = 1: Initialize the seed to a default value only before the first run
    • = 2: Like 1, but use the seed values on the next line

If line 6 was 2:

  • line 7: INTEGER array, dimension (4) — four integer values for the random number seed 🎲

If line 2 was 0:

  • line 7-EOF: Precomputed examples are tested.
  • remaining lines: each example is stored on 3+2*N*N lines, where N is its dimension. The first line contains the dimension (a single integer). The next N*N lines contain the matrix A, one element per line. The next N*N lines contain the matrix B. The next line contains the reciprocals of the eigenvalue condition numbers. The last line contains the reciprocals of the eigenvector condition numbers. The end of data is indicated by dimension N=0. Even if no data is to be tested, there must be at least one line containing N=0 🫶

💜 ZHB input file 💜

  • line 2: NN, INTEGER — number of values of N.
  • line 3: NVAL, INTEGER array, dimension (NN) — the values for the matrix dimension N.
  • line 4: NK, INTEGER — number of values of K.
  • line 5: KVAL, INTEGER array, dimension (NK) — the values for the matrix dimension K.
  • line 6: THRESH — threshold value for the test ratios. Information will be printed about each test for which the test ratio is greater than or equal to the threshold.
  • line 7: NEWSD, INTEGER — a code indicating how to set the random number seed.
    • = 0: Set the seed to a default value before each run
    • = 1: Initialize the seed to a default value only before the first run
    • = 2: Like 1, but use the seed values on the next line

If line 7 was 2:

  • line 8: INTEGER array, dimension (4) — four integer values for the random number seed 🎲
  • lines 8-EOF: lines specifying matrix types, as for NEP. The 3-character path name is 'ZHB'.

🍓 ZBB input file 🍓

  • line 2: NN, INTEGER — number of values of M and N.
  • line 3: MVAL, INTEGER array, dimension (NN) — the values for the matrix row dimension M.
  • line 4: NVAL, INTEGER array, dimension (NN) — the values for the matrix column dimension N.
  • line 4: NK, INTEGER — number of values of K. (yep, the original really does say line 4 twice, iykyk 😭 not my typo, keeping it fr fr)
  • line 5: KVAL, INTEGER array, dimension (NK) — the values for the matrix bandwidth K.
  • line 6: NPARMS, INTEGER — number of values of the parameter NRHS
  • line 7: NSVAL, INTEGER array, dimension (NPARMS) — the values for the number of right hand sides NRHS.
  • line 8: THRESH — threshold value for the test ratios. Information will be printed about each test for which the test ratio is greater than or equal to the threshold.
  • line 9: NEWSD, INTEGER — a code indicating how to set the random number seed.
    • = 0: Set the seed to a default value before each run
    • = 1: Initialize the seed to a default value only before the first run
    • = 2: Like 1, but use the seed values on the next line

If line 9 was 2:

  • line 10: INTEGER array, dimension (4) — four integer values for the random number seed 🎲
  • lines 10-EOF: lines specifying matrix types, as for SVD. The 3-character path name is 'ZBB'.

✨ ZEC input file ✨

  • line 2: THRESH, REAL — threshold value for the test ratios. Information will be printed about each test for which the test ratio is greater than or equal to the threshold.
  • lines 3-EOF:

Input for testing the eigencondition routines consists of a set of specially constructed test cases and their solutions. The data format is not intended to be modified by the user — like, hands off bestie, it's not for you 🙅‍♀️

🌈 ZBL and ZBK input files 🌈

  • line 1: 'ZBL' in columns 1-3 to test CGEBAL, or 'ZBK' in columns 1-3 to test CGEBAK.

The remaining lines consist of specially constructed test cases.

🧚 ZGL and ZGK input files 🧚

  • line 1: 'ZGL' in columns 1-3 to test ZGGBAL, or 'ZGK' in columns 1-3 to test ZGGBAK.

The remaining lines consist of specially constructed test cases.

👑 GLM data file 👑

  • line 1: 'GLM' in columns 1 to 3.
  • line 2: NN, INTEGER — number of values of M, P, and N.
  • line 3: MVAL, INTEGER array, dimension(NN) — values of M (row dimension).
  • line 4: PVAL, INTEGER array, dimension(NN) — values of P (row dimension).
  • line 5: NVAL, INTEGER array, dimension(NN) — values of N (column dimension), note M <= N <= M+P.
  • line 6: THRESH, REAL — threshold value for the test ratios. Information will be printed about each test for which the test ratio is greater than or equal to the threshold.
  • line 7: TSTERR, LOGICAL — flag indicating whether or not to test the error exits for the LAPACK routines and driver routines.
  • line 8: NEWSD, INTEGER — a code indicating how to set the random number seed.
    • = 0: Set the seed to a default value before each run
    • = 1: Initialize the seed to a default value only before the first run
    • = 2: Like 1, but use the seed values on the next line

If line 8 was 2:

  • line 9: INTEGER array, dimension (4) — four integer values for the random number seed 🎲
  • lines 9-EOF: lines specifying matrix types, as for NEP. The 3-character path name is 'GLM' for the generalized linear regression model routines.

🎀 GQR data file 🎀

  • line 1: 'GQR' in columns 1 to 3.
  • line 2: NN, INTEGER — number of values of M, P, and N.
  • line 3: MVAL, INTEGER array, dimension(NN) — the M values, bestie 💅
  • line 4: PVAL, INTEGER array, dimension(NN) — the P values 🎀
  • line 5: NVAL, INTEGER array, dimension(NN) — the N values, iconic ✨
  • line 6: THRESH, REAL — the threshold for the test ratios. So like, for every test where the test ratio is greater than or equal to the threshold, the run is gonna print info about it. Obsessed with transparency 🫶
  • line 7: TSTERR, LOGICAL — a flag for whether or not to test the error exits for the LAPACK routines and driver routines 👑
  • line 8: NEWSD, INTEGER — a code that says how to set the random number seed:
    • = 0: set the seed to a default value before each run
    • = 1: initialize the seed to a default value only before the first run
    • = 2: like 1, but actually use the seed values on the next line 🌱

If line 8 was 2:

  • line 9: INTEGER array, dimension (4) — four integer values for the random number seed. Four. That's the whole vibe 🔢
  • lines 9-EOF: lines specifying matrix types, as for NEP. The 3-character path name is 'GQR' for the generalized QR and RQ routines 💖

🦋 GSV data file

  • line 1: 'GSV' in columns 1 to 3. Like, that's literally how it announces itself 💅
  • line 2: NN, INTEGER — number of values of M, P, and N.
  • line 3: MVAL, INTEGER array, dimension(NN) — values of M (the row dimension).
  • line 4: PVAL, INTEGER array, dimension(NN) — values of P (the row dimension).
  • line 5: NVAL, INTEGER array, dimension(NN) — values of N (the column dimension).
  • line 6: THRESH, REAL — threshold value for the test ratios. Information will be printed about each test for which the test ratio is greater than or equal to the threshold ✨
  • line 7: TSTERR, LOGICAL — flag indicating whether or not to test the error exits for the LAPACK routines and driver routines.
  • line 8: NEWSD, INTEGER — a code indicating how to set the random number seed.
    • = 0: set the seed to a default value before each run
    • = 1: initialize the seed to a default value only before the first run
    • = 2: like 1, but use the seed values on the next line

If line 8 was 2:

  • line 9: INTEGER array, dimension (4) — four integer values for the random number seed 🍓
  • lines 9-EOF: lines specifying matrix types, as for NEP. The 3-character path name is 'GSV' for the generalized SVD routines 🌸

🎀 CSD data file

  • line 1: 'CSD' in columns 1 to 3.
  • line 2: NM, INTEGER — number of values of M, P, and N. (Not NN, bestie — it's NM here, do not come for me, I'm just the messenger 😭)
  • line 3: MVAL, INTEGER array, dimension(NM) — values of M (row and column dimension of the orthogonal matrix).
  • line 4: PVAL, INTEGER array, dimension(NM) — values of P (row dimension of the top-left block).
  • line 5: NVAL, INTEGER array, dimension(NM) — values of N (column dimension of the top-left block).
  • line 6: THRESH, REAL — threshold value for the test ratios. Information will be printed about each test for which the test ratio is greater than or equal to the threshold 💜
  • line 7: TSTERR, LOGICAL — flag indicating whether or not to test the error exits for the LAPACK routines and driver routines.
  • line 8: NEWSD, INTEGER — a code indicating how to set the random number seed.
    • = 0: set the seed to a default value before each run
    • = 1: initialize the seed to a default value only before the first run
    • = 2: like 1, but use the seed values on the next line

If line 8 was 2:

  • line 9: INTEGER array, dimension (4) — four integer values for the random number seed 🌈
  • lines 9-EOF: lines specifying matrix types, as for NEP. The 3-character path name is 'CSD' for the CSD routine 🧚

💖 LSE data file

  • line 1: 'LSE' in columns 1 to 3.
  • line 2: NN, INTEGER — number of values of M, P, and N.
  • line 3: MVAL, INTEGER array, dimension(NN) — values of M.
  • line 4: PVAL, INTEGER array, dimension(NN) — values of P.
  • line 5: NVAL, INTEGER array, dimension(NN) — values of N, and note that P <= N <= P+M. Yes, that constraint is real, respect it 💅
  • line 6: THRESH, REAL — threshold value for the test ratios. Information will be printed about each test for which the test ratio is greater than or equal to the threshold ⭐
  • line 7: TSTERR, LOGICAL — flag indicating whether or not to test the error exits for the LAPACK routines and driver routines.
  • line 8: NEWSD, INTEGER — a code indicating how to set the random number seed.
    • = 0: set the seed to a default value before each run
    • = 1: initialize the seed to a default value only before the first run
    • = 2: like 1, but use the seed values on the next line

If line 8 was 2:

  • line 9: INTEGER array, dimension (4) — four integer values for the random number seed 🔥
  • lines 9-EOF: lines specifying matrix types, as for NEP. The 3-character path name is 'GSV' for the generalized SVD routines. (Yes, 'GSV' again here, that's not a typo, that's just the page being the page 🙈)

Okay so quick little heads-up on the numbers, because these matter fr fr 👇

NMAX is currently set to 132, and it must be at least 12 for some of the precomputed examples, and LWORK = NMAX*(5*NMAX+20) in the parameter statements below. For SVD, we assume NRHS may be as big as N. The parameter NEED is set to 14 to allow for 14 N-by-N matrices for ZGG. Those are the receipts, no cap 📝

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🌟 Definition

Definition at line 1033 of file zchkee.F.

💫 Author (the other one, yes really)

Generated automatically by Doxygen for LAPACK from the source code.

And that's a wrap on part 4, bestie 🫶 This whole page came to you courtesy of Version 3.12.0, stamped Tue Nov 28 2023 12:08:42, and it lives under TESTING/EIG/zchkee.F(3). Go forth and run your tests, you main character ✨💖🎀

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