double_eig(3)

📦
version 3.11.0 · 2 versions
, in debian bookworm

double_eig(3) 💖

okay so bestie, welcome to double_eig — manual section 3, straight outta LAPACK ✨ this page is the whole squad of double-precision EIG testing routines and honestly it's giving ✨main character energy✨. she's long, she's thorough, and she's about to tell you literally everything. let's go 🦋

🌸 NAME 🌸

double_eig — double 💅

(that's it. that's the name. mysterious, iconic, no notes.)

✨ SYNOPSIS ✨

Functions

  • program dchkee
    • DCHKEE

💫 DETAILED DESCRIPTION 💫

This is the group of double LAPACK TESTING EIG routines. 🎀

📖 FUNCTION DOCUMENTATION 📖

🧚 program dchkee

DCHKEE

Purpose: 🫶

DCHKEE tests the DOUBLE PRECISION LAPACK subroutines for the matrix eigenvalue problem. the test paths in this version are, bestie, get comfy:

  • NEP (Nonsymmetric Eigenvalue Problem) — test DGEHRD, DORGHR, DHSEQR, DTREVC, DHSEIN, and DORMHR
  • SEP (Symmetric Eigenvalue Problem) — test DSYTRD, DORGTR, DSTEQR, DSTERF, DSTEIN, DSTEDC, and drivers DSYEV(X), DSBEV(X), DSPEV(X), DSTEV(X), DSYEVD, DSBEVD, DSPEVD, DSTEVD
  • SVD (Singular Value Decomposition) — test DGEBRD, DORGBR, DBDSQR, DBDSDC and the drivers DGESVD, DGESDD
  • DEV (Nonsymmetric Eigenvalue/eigenvector Driver) — test DGEEV
  • DES (Nonsymmetric Schur form Driver) — test DGEES
  • DVX (Nonsymmetric Eigenvalue/eigenvector Expert Driver) — test DGEEVX
  • DSX (Nonsymmetric Schur form Expert Driver) — test DGEESX
  • DGG (Generalized Nonsymmetric Eigenvalue Problem) — test DGGHD3, DGGBAL, DGGBAK, DHGEQZ, and DTGEVC
  • DGS (Generalized Nonsymmetric Schur form Driver) — test DGGES
  • DGV (Generalized Nonsymmetric Eigenvalue/eigenvector Driver) — test DGGEV
  • DGX (Generalized Nonsymmetric Schur form Expert Driver) — test DGGESX
  • DXV (Generalized Nonsymmetric Eigenvalue/eigenvector Expert Driver) — test DGGEVX
  • DSG (Symmetric Generalized Eigenvalue Problem) — test DSYGST, DSYGV, DSYGVD, DSYGVX, DSPGST, DSPGV, DSPGVD, DSPGVX, DSBGST, DSBGV, DSBGVD, and DSBGVX
  • DSB (Symmetric Band Eigenvalue Problem) — test DSBTRD
  • DBB (Band Singular Value Decomposition) — test DGBBRD
  • DEC (Eigencondition estimation) — test DLALN2, DLASY2, DLAEQU, DLAEXC, DTRSYL, DTREXC, DTRSNA, DTRSEN, and DLAQTR
  • DBL (Balancing a general matrix) — test DGEBAL
  • DBK (Back transformation on a balanced matrix) — test DGEBAK
  • DGL (Balancing a matrix pair) — test DGGBAL
  • DGK (Back transformation on a matrix pair) — test DGGBAK
  • GLM (Generalized Linear Regression Model) — tests DGGGLM
  • GQR (Generalized QR and RQ factorizations) — tests DGGQRF and DGGRQF
  • GSV (Generalized Singular Value Decomposition) — tests DGGSVD, DGGSVP, DTGSJA, DLAGS2, DLAPLL, and DLAPMT
  • CSD (CS decomposition) — tests DORCSD
  • LSE (Constrained Linear Least Squares) — tests DGGLSE

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 into a single input file 🧚. the first line of input should contain one of the 3-character path names in columns 1-3, and the number of remaining lines depends on what is found on that first line. iykyk.

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 — columns are path name(s), types, test routine:

  • DHS or NEP — 21 — DCHKHS
  • DST or SEP — 21 — DCHKST (routines)
  • DST or SEP — 18 — DDRVST (drivers)
  • DBD or SVD — 16 — DCHKBD (routines)
  • DBD or SVD — 5 — DDRVBD (drivers)
  • DEV — 21 — DDRVEV
  • DES — 21 — DDRVES
  • DVX — 21 — DDRVVX
  • DSX — 21 — DDRVSX
  • DGG — 26 — DCHKGG (routines)
  • DGS — 26 — DDRGES
  • DGX — 5 — DDRGSX
  • DGV — 26 — DDRGEV
  • DXV — 2 — DDRGVX
  • DSG — 21 — DDRVSG
  • DSB — 15 — DCHKSB
  • DBB — 15 — DCHKBB
  • DEC — - — DCHKEC
  • DBL — - — DCHKBL
  • DBK — - — DCHKBK
  • DGL — - — DCHKGL
  • DGK — - — DCHKGK
  • GLM — 8 — DCKGLM
  • GQR — 8 — DCKGQR
  • GSV — 8 — DCKGSV
  • CSD — 3 — DCKCSD
  • LSE — 8 — DCKLSE

okay bestie, now the input files. each path wants its own lil setup and here's exactly what each one expects 👑

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. info gets printed about each test whose test ratio is greater than or equal to the threshold. and if you want 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 has 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 gets read to grab 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 'SHS' for the nonsymmetric eigenvalue routines.

SEP or DSG 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. info gets printed about each test whose 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 3-character path names are 'SEP' or 'SST' for the symmetric eigenvalue routines and driver routines, and 'DSG' for the routines for the symmetric 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. info gets printed about each test whose test ratio is greater than or equal to the threshold.
ok bestie that's the vibe so far, and we're literally not even done 😭 keep scrolling, part 2 is right there and she has MORE. don't go anywhere 💖

✨ bestie we're back and we're still in the test-file-format trenches ✨

  • line 11: TSTCHK, LOGICAL — flag indicating whether or not to test the LAPACK routines. 💅
  • line 12: TSTDRV, LOGICAL — flag indicating whether or not to test the driver routines. 🚗
  • line 13: TSTERR, LOGICAL — flag indicating whether or not to test the error exits for the LAPACK routines and driver routines. 🚨
  • 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 — lines specifying matrix types, as for NEP. The 3-character path names are 'SVD' or 'SBD' for both the SVD routines and the SVD driver routines. 💖

✨ DEV and DES data files ✨

  • line 1: 'DEV' or 'DES' in columns 1 to 3. 🎀
  • 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 (although the remaining 3 lines are still read). 😭
  • line 3: NN, INTEGER array, dimension(NSIZES) — 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 xHSEQR
    • 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 7 was 2:

  • line 8: INTEGER array, dimension (4) — four integer values for the random number seed. 🎲
  • lines 9 and following — lines specifying matrix types, as for NEP. The 3-character path name is 'DEV' to test SGEEV, or 'DES' to test SGEES. 🔍

✨ DVX data ✨

The DVX data has two parts. The first part is identical to DEV, and the second part consists of test matrices with precomputed solutions. 💯

  • line 1: 'DVX' 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) — dimensions. 📐
  • line 4: NB, NBMIN, NX, NS, NBCOL, INTEGERs — blocking parameters. 🧱
  • line 5: THRESH, REAL — threshold. 🌡️
  • line 6: TSTERR, LOGICAL — test error exits flag. 🚨
  • line 7: NEWSD, INTEGER — seed code. 🌱

If line 7 was 2:

  • line 8: INTEGER array, dimension (4) — seed values. 🎲
  • lines 9 and following: The first line contains 'DVX' 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+2*N lines, where N is its dimension. The first line contains the dimension (a single integer). The next N lines contain the matrix, one row 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 eigenvalue, the imaginary part of the eigenvalue, the reciprocal condition number of the eigenvalues, and the reciprocal condition number of the 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. 🧮

✨ DSX data ✨

The DSX data is like DVX. The first part is identical to DEV, and the second part consists of test matrices with precomputed solutions. 💯

  • line 1: 'DSX' 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) — dimensions. 📐
  • line 4: NB, NBMIN, NX, NS, NBCOL, INTEGERs — blocking parameters. 🧱
  • line 5: THRESH, REAL — threshold. 🌡️
  • line 6: TSTERR, LOGICAL — test error exits flag. 🚨
  • line 7: NEWSD, INTEGER — seed code. 🌱

If line 7 was 2:

  • line 8: INTEGER array, dimension (4) — seed values. 🎲
  • lines 9 and following: The first line contains 'DSX' 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 lines, where N is its dimension. The first line contains the dimension N and the dimension M of an invariant subspace. 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). The next N lines contain the matrix. 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 and M=0. Even if no data is to be tested, there must be at least one line containing N=0 and M=0. 🧮

✨ DGG 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, NS, MAXB, and NBCOL. 🎛️
  • 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). 🤔
  • 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. 🖨️
  • 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 'DGG' for the generalized eigenvalue problem routines and driver routines. 🔍

✨ DGS and DGV input files ✨

  • line 1: 'DGS' or 'DGV' 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. 🎲

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

DXV input files 🦋

  • line 1: 'DXV' in columns 1 to 3. 💖
  • line 2: N, INTEGER — literally the value of N. ✨
  • line 3: NB, NBMIN, NX, NS, NBCOL, INTEGERs — these integer parameters decide 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 4: THRESH, REAL — the test threshold that computed residuals get compared against. Should generally be in the range from 10. to 20. Info gets printed about each 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 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 lines, where N is its dimension. The first line contains the dimension (a single integer). The next N lines contain the matrix A, one row per line. The next 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. 💀

DGX input files 🌈

  • line 1: 'DGX' in columns 1 to 3. ✨
  • line 2: N, INTEGER — value of N.
  • line 3: 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 4: THRESH, REAL — 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 — 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 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 lines contain the matrix A, one row per line. The next 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.

DSB 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 'DSB'.

DBB 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. (yes, another line 4, the original said it, not me 💀)
  • 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 'DBB'.

DEC 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.

DBL and DBK input files 👑

  • line 1: 'DBL' in columns 1-3 to test SGEBAL, or 'DBK' in columns 1-3 to test SGEBAK.
  • The remaining lines consist of specially constructed test cases.

DGL and DGK input files 🧚

  • line 1: 'DGL' in columns 1-3 to test DGGBAL, or 'DGK' in columns 1-3 to test DGGBAK.
  • 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 values of M. 💫
  • line 4: PVAL, INTEGER array, dimension(NN) — the values of P.
  • line 5: NVAL, INTEGER array, dimension(NN) — the values of N.
  • line 6: THRESH, REAL — 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 — a flag saying whether or not to test the error exits for the LAPACK routines and driver routines.
  • line 8: NEWSD, INTEGER — 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 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 'GQR' for the generalized QR and RQ routines.

🦋 GSV data file 🦋

  • line 1: 'GSV' 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 values of M (row dimension).
  • line 4: PVAL, INTEGER array, dimension(NN) — the values of P (row dimension).
  • line 5: NVAL, INTEGER array, dimension(NN) — the values of N (column dimension).
  • line 6: THRESH, REAL — 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 — a flag saying whether or not to test the error exits for the LAPACK routines and driver routines.
  • line 8: NEWSD, INTEGER — 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) — 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.
  • line 3: MVAL, INTEGER array, dimension(NM) — the values of M (row and column dimension of orthogonal matrix).
  • line 4: PVAL, INTEGER array, dimension(NM) — the values of P (row dimension of top-left block).
  • line 5: NVAL, INTEGER array, dimension(NM) — the values of N (column dimension of top-left block).
  • line 6: THRESH, REAL — 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 — a flag saying whether or not to test the error exits for the LAPACK routines and driver routines.
  • line 8: NEWSD, INTEGER — 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) — 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) — the values of M.
  • line 4: PVAL, INTEGER array, dimension(NN) — the values of P.
  • line 5: NVAL, INTEGER array, dimension(NN) — the values of N, note P <= N <= P+M. 👑
  • line 6: THRESH, REAL — 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 — a flag saying whether or not to test the error exits for the LAPACK routines and driver routines.
  • line 8: NEWSD, INTEGER — 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) — 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.

bestie, this next bit is literally the whole vibe of the sizing, do not 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+5)+1 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 DGG.

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

Generated automatically by Doxygen for LAPACK from the source code.

okay and that's a wrap on this whole page, no cap 💅 the version on this one is 3.11.0, dated Sun Nov 27 2022, and it's filed under double_eig(3). go forth and eig, queen 🎀✨

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