complex16_eig(3)

πŸ“¦
version 3.11.0 Β· 2 versions
, in debian bookworm

πŸ’– complex16_eig β€” the LAPACK testing tea, but make it iconic πŸ’–

okay bestie, this is complex16_eig(3) from the LAPACK manual, and it's literally the whole vibe of the complex16 eigenvalue testing group. grab a boba, we're going in πŸ§‹βœ¨

✨ NAME ✨

complex16_eig β€” complex16 🫢

🌸 SYNOPSIS 🌸

πŸŽ€ Functions

program zchkee
    ZCHKEE

πŸ¦‹ Detailed Description πŸ¦‹

okay so this is the group of complex16 LAPACK TESTING EIG routines. that's the whole assignment, no cap. πŸ’…

πŸ‘‘ Function Documentation πŸ‘‘

🌈 program zchkee

ZCHKEE

πŸ’œ Purpose:

ZCHKEE tests the COMPLEX*16 LAPACK subroutines for the matrix eigenvalue problem. the test paths in this version are, and bestie there are a LOT of them so buckle up:

  • NEP (Nonsymmetric Eigenvalue Problem): Test ZGEHRD, ZUNGHR, ZHSEQR, ZTREVC, ZHSEIN, and ZUNMHR
  • SEP (Hermitian Eigenvalue Problem): Test ZHETRD, ZUNGTR, ZSTEQR, ZSTERF, ZSTEIN, ZSTEDC, and drivers ZHEEV(X), ZHBEV(X), ZHPEV(X), ZHEEVD, ZHBEVD, ZHPEVD
  • SVD (Singular Value Decomposition): Test ZGEBRD, ZUNGBR, and ZBDSQR and the drivers ZGESVD, ZGESDD
  • ZEV (Nonsymmetric Eigenvalue/eigenvector Driver): Test ZGEEV
  • ZES (Nonsymmetric Schur form Driver): Test ZGEES
  • ZVX (Nonsymmetric Eigenvalue/eigenvector Expert Driver): Test ZGEEVX
  • ZSX (Nonsymmetric Schur form Expert Driver): Test ZGEESX
  • ZGG (Generalized Nonsymmetric Eigenvalue Problem): Test ZGGHD3, ZGGBAL, ZGGBAK, ZHGEQZ, and ZTGEVC
  • ZGS (Generalized Nonsymmetric Schur form Driver): Test ZGGES
  • ZGV (Generalized Nonsymmetric Eigenvalue/eigenvector Driver): Test ZGGEV
  • ZGX (Generalized Nonsymmetric Schur form Expert Driver): Test ZGGESX
  • ZXV (Generalized Nonsymmetric Eigenvalue/eigenvector Expert Driver): Test ZGGEVX
  • ZSG (Hermitian Generalized Eigenvalue Problem): Test ZHEGST, ZHEGV, ZHEGVD, ZHEGVX, ZHPGST, ZHPGV, ZHPGVD, ZHPGVX, ZHBGST, ZHBGV, ZHBGVD, and ZHBGVX
  • ZHB (Hermitian Band Eigenvalue Problem): Test ZHBTRD
  • ZBB (Band Singular Value Decomposition): Test ZGBBRD
  • ZEC (Eigencondition estimation): Test ZTRSYL, ZTREXC, ZTRSNA, and ZTRSEN
  • ZBL (Balancing a general matrix) Test ZGEBAL
  • ZBK (Back transformation on a balanced matrix) Test ZGEBAK
  • ZGL (Balancing a matrix pair) Test ZGGBAL
  • ZGK (Back transformation on a matrix pair) Test 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

each test path has a different set of inputs, but the data sets for the driver routines xEV, xES, xVX, and xSX can be concatenated in a single input file. 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 is found on the 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) β†’ Types β†’ Test routine
    • ZHS or NEP β†’ 21 β†’ ZCHKHS
    • ZST or SEP β†’ 21 β†’ ZCHKST (routines)
    • ZST or SEP β†’ 18 β†’ ZDRVST (drivers)
    • ZBD or SVD β†’ 16 β†’ ZCHKBD (routines)
    • ZBD or SVD β†’ 5 β†’ ZDRVBD (drivers)
    • ZEV β†’ 21 β†’ ZDRVEV
    • ZES β†’ 21 β†’ ZDRVES
    • ZVX β†’ 21 β†’ ZDRVVX
    • ZSX β†’ 21 β†’ ZDRVSX
    • ZGG β†’ 26 β†’ ZCHKGG (routines)
    • ZGS β†’ 26 β†’ ZDRGES
    • ZGX β†’ 5 β†’ ZDRGSX
    • ZGV β†’ 26 β†’ ZDRGEV
    • ZXV β†’ 2 β†’ ZDRGVX
    • ZSG β†’ 21 β†’ ZDRVSG
    • ZHB β†’ 15 β†’ ZCHKHB
    • ZBB β†’ 15 β†’ ZCHKBB
    • ZEC β†’ - β†’ ZCHKEC
    • ZBL β†’ - β†’ ZCHKBL
    • ZBK β†’ - β†’ ZCHKBK
    • ZGL β†’ - β†’ ZCHKGL
    • ZGK β†’ - β†’ ZCHKGK
    • GLM β†’ 8 β†’ ZCKGLM
    • GQR β†’ 8 β†’ ZCKGQR
    • GSV β†’ 8 β†’ ZCKGSV
    • CSD β†’ 3 β†’ ZCKCSD
    • LSE β†’ 8 β†’ ZCKLSE
-----------------------------------------------------------------------

πŸ’« 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 allow the user to 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.

-----------------------------------------------------------------------

πŸ’« 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.
-----------------------------------------------------------------------

πŸ’« 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 β€” a lil flag that says whether or not we're testing the driver routines. πŸ’…
  • line 13: TSTERR, LOGICAL β€” flag for whether or not to test the error exits for the LAPACK routines and the driver routines. Both. It's giving thorough.
  • line 14: NEWSD, INTEGER β€” a code telling us how to set the random number seed:
    • = 0 β€” set the seed to a default value before every single run
    • = 1 β€” initialize the seed to a default value only before the first run
    • = 2 β€” same energy as 1, but use the seed values on the next line

If line 14 was 2:

  • line 15: INTEGER array, dimension (4) β€” four integer values for the random number seed, bestie. Four. Not three. πŸ“
  • lines 15-EOF β€” the lines specifying matrix types, same as for NEP. The 3-character path names are 'SVD' or 'ZBD', for both the SVD routines and the SVD driver routines.

πŸ¦‹ ZEV and ZES data files πŸ¦‹

  • line 1: 'ZEV' or 'ZES' in columns 1 to 3.
  • line 2: NSIZES, INTEGER β€” how many sizes of matrices we're using. Should be at least 0 and at most 20. If NSIZES = 0, no testing happens at all (even though the remaining 3 lines are still read, so don't skip them, okay?).
  • line 3: NN, INTEGER array, dimension(NSIZES) β€” the dimensions of the matrices to be tested.
  • line 4: NB, NBMIN, NX, NS, NBCOL, INTEGERs β€” these integer parameters decide how blocking is done (peep ILAENV for the deets):
    • NB β€” block size
    • NBMIN β€” minimum block size
    • NX β€” minimum dimension for blocking
    • NS β€” number of shifts in xHSEQR
    • NBCOL β€” minimum column dimension for blocking
  • line 5: THRESH, REAL β€” 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. Yes, all of it. 😭
  • line 6: NEWSD, INTEGER β€” a code for how to set the random number seed:
    • = 0 β€” set the seed to a default value before each run
    • = 1 β€” initialize the seed to a default value only before the first run
    • = 2 β€” like 1, but use the seed values on the next line

If line 6 was 2:

  • line 7: INTEGER array, dimension (4) β€” four integer values for the random number seed. πŸŽ€
  • lines 8 and following β€” the lines specifying matrix types, same as for NEP. The 3-character path name is 'ZEV' to test CGEEV, or 'ZES' to test CGEES.

✨ The ZVX data ✨

The ZVX data has two parts, periodt. The first part is identical to ZEV, and the second part is made of test matrices with precomputed solutions.

  • line 1: 'ZVX' in columns 1-3.
  • line 2: NSIZES, INTEGER β€” 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 β€” 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. πŸ‘‘
  • remaining lines β€” 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:
    1. the real part of the eigenvalues
    2. the imaginary part of the eigenvalue
    3. the reciprocal condition number of the eigenvalues
    4. 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. No skipping, bestie. 🫢

🌈 The ZSX data 🌈

The ZSX data is like ZVX. 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 β€” 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 β€” 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 β€” 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 is 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. Again β€” at least one. It's non-negotiable. πŸ’€

🧚 ZGG input file 🧚

  • line 2: NN, INTEGER β€” number of values of N.
  • line 3: NVAL, INTEGER array, dimension (NN) β€” the values for the matrix dimension N.
  • line 4: NPARMS, INTEGER β€” number of values of the parameters NB, NBMIN, NBCOL, NS, and MAXB.
  • line 5: NBVAL, INTEGER array, dimension (NPARMS) β€” the values for the blocksize NB.
  • line 6: NBMIN, INTEGER array, dimension (NPARMS) β€” the values for NBMIN, the minimum row dimension for blocks.
  • line 7: NSVAL, INTEGER array, dimension (NPARMS) β€” the values for the number of shifts.
  • line 8: MXBVAL, INTEGER array, dimension (NPARMS) β€” the values for MAXB, used in determining minimum blocksize.
  • line 9: IACC22, INTEGER array, dimension (NPARMS) β€” select structured matrix multiply: 1 or 2.
  • line 10: NBCOL, INTEGER array, dimension (NPARMS) β€” the values for NBCOL, the minimum column dimension for blocks.
  • line 11: THRESH β€” 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 12: TSTCHK, LOGICAL β€” flag indicating whether or not to test the LAPACK routines.
  • line 13: TSTDRV, LOGICAL β€” flag indicating whether or not to test the driver routines.
  • line 14: TSTERR, LOGICAL β€” flag indicating whether or not to test the error exits for the LAPACK routines and driver routines.
  • line 15: NEWSD, INTEGER β€” a code indicating how to set the random number seed:
    • = 0 β€” set the seed to a default value before each run
    • = 1 β€” initialize the seed to a default value only before the first run
    • = 2 β€” like 1, but use the seed values on the next line

If line 15 was 2:

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

πŸ’œ ZGS and ZGV input files πŸ’œ

  • line 1: 'ZGS' or 'ZGV' in columns 1 to 3.
  • line 2: NN, INTEGER β€” number of values of N.
  • line 3: NVAL, INTEGER array, dimension(NN) β€” dimensions of matrices to be tested.
  • line 4: NB, NBMIN, NX, NS, NBCOL, INTEGERs β€” these integer parameters determine how blocking is done (see ILAENV for details):
    • NB β€” block size
    • NBMIN β€” minimum block size
    • NX β€” minimum dimension for blocking
    • NS β€” number of shifts in xHGEQR
    • NBCOL β€” minimum column dimension for blocking
  • line 5: THRESH, REAL β€” 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. πŸ™ˆ
  • line 6: TSTERR, LOGICAL β€” flag indicating whether or not to test the error exits.
  • line 7: NEWSD, INTEGER β€” a code indicating how to set the random number seed:
    • = 0 β€” set the seed to a default value before each run
    • = 1 β€” initialize the seed to a default value only before the first run
    • = 2 β€” like 1, but use the seed values on the next line

If line 17 was 2:

  • line 7: INTEGER array, dimension (4) β€” four integer values for the random number seed. ⭐

lines 7-EOF: Lines specifying matrix types, as for NEP. The 3-character path name is 'ZGS' for the generalized eigenvalue problem routines and driver routines.

🌸 ZGX input file 🌸

  • line 1: 'ZGX' sitting in columns 1 to 3, bestie. Non-negotiable.
  • line 2: N, INTEGER β€” it's literally just the value of N.
  • line 3: NB, NBMIN, NX, NS, NBCOL, all INTEGERs. These lil integers are the ones that decide how blocking gets done (peep ILAENV for the deets, iykyk):
    • NB β€” block size
    • NBMIN β€” minimum block size
    • NX β€” minimum dimension for blocking
    • NS β€” number of shifts in xHGEQR
    • NBCOL β€” minimum column dimension for blocking
  • line 4: THRESH, REAL β€” the test threshold that computed residuals get compared against. Generally it should be chillin' in the range from 10. to 20. πŸ’… Info gets printed for every test where the test ratio is greater than or equal to the threshold.
  • line 5: TSTERR, LOGICAL β€” a flag that says whether or not we're testing the error exits for the LAPACK routines and driver routines. Yay or nay energy.
  • line 6: NEWSD, INTEGER β€” a code telling us 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) β€” four integer values for the random number seed. Four of them. Iconic.

If line 2 was 0:

  • line 7-EOF: precomputed examples are tested. Slay, we're using the pre-made ones.
  • 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 line contains 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. And fr fr β€” even if no data is to be tested, there must be at least one line containing N=0. 🫢

πŸ¦‹ ZXV input files πŸ¦‹

  • line 1: 'ZXV' in columns 1 to 3.
  • line 2: N, INTEGER β€” the value of N.
  • line 3: NB, NBMIN, NX, NS, NBCOL, INTEGERs. These integer parameters determine how blocking is done (see ILAENV for details):
    • NB β€” block size
    • NBMIN β€” minimum block size
    • NX β€” minimum dimension for blocking
    • NS β€” number of shifts in xHGEQR
    • NBCOL β€” minimum column dimension for blocking
  • line 4: THRESH, REAL β€” the test threshold against which computed residuals are compared. Should generally be in the range from 10. to 20. Information will be printed about each test for which the test ratio is greater than or equal to the threshold.
  • line 5: TSTERR, LOGICAL β€” flag indicating whether or not to test the error exits for the LAPACK routines and driver routines.
  • line 6: NEWSD, INTEGER β€” 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) β€” 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. πŸŽ€

πŸ’œ ZHB input file πŸ’œ

  • line 2: NN, INTEGER β€” number of values of N.
  • line 3: NVAL, INTEGER array, dimension (NN) β€” the values for the matrix dimension N.
  • line 4: NK, INTEGER β€” number of values of K.
  • line 5: KVAL, INTEGER array, dimension (NK) β€” the values for the matrix dimension K.
  • line 6: THRESH β€” 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 β€” 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) β€” 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'.

πŸ“ ZBB input file πŸ“

  • line 2: NN, INTEGER β€” number of values of M and N.
  • line 3: MVAL, INTEGER array, dimension (NN) β€” the values for the matrix row dimension M.
  • line 4: NVAL, INTEGER array, dimension (NN) β€” the values for the matrix column dimension N.
  • line 4: NK, INTEGER β€” number of values of K.
  • line 5: KVAL, INTEGER array, dimension (NK) β€” the values for the matrix bandwidth K.
  • line 6: NPARMS, INTEGER β€” number of values of the parameter NRHS.
  • line 7: NSVAL, INTEGER array, dimension (NPARMS) β€” the values for the number of right hand sides NRHS.
  • line 8: THRESH β€” 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 β€” 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) β€” 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 β€” 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. 🚫 hands off, bestie, this one's not yours to touch.

🌈 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 'ZGК'... no wait, '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 β€” number of values of M, P, and N.
  • line 3: MVAL, INTEGER array, dimension(NN) β€” values of M (row dimension).
  • line 4: PVAL, INTEGER array, dimension(NN) β€” values of P (row dimension).
  • line 5: NVAL, INTEGER array, dimension(NN) β€” values of N (column dimension), and note that M <= N <= M+P. πŸ‘‘
  • line 6: THRESH, REAL β€” 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 β€” flag indicating whether or not to test the error exits for the LAPACK routines and driver routines.
  • line 8: NEWSD, INTEGER β€” 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) β€” 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.

πŸ’– GQR data file πŸ’–

  • line 1: 'GQR' in columns 1 to 3.
  • line 2: NN, INTEGER β€” number of values of M, P, and N.
  • line 3: MVAL, INTEGER array, dimension(NN) β€” bestie, these are the values of M πŸ’«
  • line 4: PVAL, INTEGER array, dimension(NN) β€” the values of P πŸŽ€
  • line 5: NVAL, INTEGER array, dimension(NN) β€” the values of N ✨
  • line 6: THRESH, REAL β€” the threshold value for the test ratios. Anything whose test ratio is greater than or equal to this? Yeah, we're printing info about it, no cap πŸ‘€
  • line 7: TSTERR, LOGICAL β€” a flag saying whether or not to test the error exits for the LAPACK routines and driver routines πŸšͺ
  • line 8: NEWSD, INTEGER β€” a code for 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) β€” four integer values for the random number seed, periodt πŸ’…
  • lines 9-EOF: Lines specifying matrix types, as for NEP. The 3-character path name is 'GQR' for the generalized QR and RQ routines. πŸ”₯

πŸ¦‹ GSV data file πŸ¦‹

  • line 1: 'GSV' in columns 1 to 3.
  • line 2: NN, INTEGER β€” the number of values of M, P, and N.
  • line 3: MVAL, INTEGER array, dimension(NN) β€” the values of M (row dimension).
  • line 4: PVAL, INTEGER array, dimension(NN) β€” the values of P (row dimension).
  • line 5: NVAL, INTEGER array, dimension(NN) β€” the values of N (column dimension).
  • line 6: THRESH, REAL β€” the threshold value for the test ratios. Info gets printed about every test whose test ratio is greater than or equal to the threshold.
  • line 7: TSTERR, LOGICAL β€” flag for whether or not to test the error exits for the LAPACK routines and driver routines.
  • line 8: NEWSD, INTEGER β€” code for 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) β€” 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. πŸ’–

🌸 CSD data file 🌸

  • line 1: 'CSD' in columns 1 to 3.
  • line 2: NM, INTEGER β€” the number of values of M, P, and N.
  • line 3: MVAL, INTEGER array, dimension(NM) β€” the values of M (row and column dimension of orthogonal matrix).
  • line 4: PVAL, INTEGER array, dimension(NM) β€” the values of P (row dimension of top-left block).
  • line 5: NVAL, INTEGER array, dimension(NM) β€” the values of N (column dimension of top-left block).
  • line 6: THRESH, REAL β€” the threshold value for the test ratios. Info gets printed about every test whose test ratio is greater than or equal to the threshold.
  • line 7: TSTERR, LOGICAL β€” flag for whether or not to test the error exits for the LAPACK routines and driver routines.
  • line 8: NEWSD, INTEGER β€” code for 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) β€” 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. ✨

πŸŽ€ LSE data file πŸŽ€

  • line 1: 'LSE' in columns 1 to 3.
  • line 2: NN, INTEGER β€” the number of values of M, P, and N.
  • line 3: MVAL, INTEGER array, dimension(NN) β€” the values of M.
  • line 4: PVAL, INTEGER array, dimension(NN) β€” the values of P.
  • line 5: NVAL, INTEGER array, dimension(NN) β€” the values of N, and heads up, note that P <= N <= P+M. 🫢
  • line 6: THRESH, REAL β€” the threshold value for the test ratios. Info gets printed about every test whose test ratio is greater than or equal to the threshold.
  • line 7: TSTERR, LOGICAL β€” flag for whether or not to test the error exits for the LAPACK routines and driver routines.
  • line 8: NEWSD, INTEGER β€” code for 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) β€” 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. πŸ‘‘

Okay so, the sizing tea β˜• β€” and this part matters, don't skip it:

NMAX is currently set to 132 and 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. πŸ’€ (yes, fourteen. they said what they said.)

πŸ‘‘ Author πŸ‘‘

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. πŸ€– (the robots wrote this one, and honestly? they ate.)

And that's a wrap, bestie 🫢 this whole thing is Version 3.11.0, dated Sun Nov 27 2022, and it lives at complex16_eig(3). Go forth and eigendecompose responsibly, mwah πŸ’…βœ¨

πŸ“¦ where this page comes from