ZCHKHB2STG(3)

📦 version 3.12.0, in opensuse-leap 16.0

🌸 NAME 🌸

okay so bestie, this is ZCHKHB2STG(3) from the Library Functions Manual — yes, the whole thing has a path for a name and honestly? it's giving “LAPACK test routine with main character energy” fr fr 💅

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/zchkhb2stg.f

✨ SYNOPSIS ✨

💅 Functions/Subroutines

       subroutine ZCHKHB2STG (nsizes, nn, nwdths, kk, ntypes, dotype, iseed,
           thresh, nounit, a, lda, sd, se, d1, d2, d3, u, ldu, work, lwork,
           rwork, result, info)

ZCHKHB2STG — that's the icon, the moment, the whole vibe 🫶

🦋 Function/Subroutine Documentation 🦋

🌈 subroutine ZCHKHB2STG 🌈

   subroutine ZCHKHB2STG (integer nsizes, integer, dimension( * ) nn, integer
       nwdths, integer, dimension( * ) kk, integer ntypes, logical, dimension(
       * ) dotype, integer, dimension( 4 ) iseed, double precision thresh,
       integer nounit, complex*16, dimension( lda, * ) a, integer lda, double
       precision, dimension( * ) sd, double precision, dimension( * ) se,
       double precision, dimension( * ) d1, double precision, dimension( * )
       d2, double precision, dimension( * ) d3, complex*16, dimension( ldu, * )
       u, integer ldu, complex*16, dimension( * ) work, integer lwork, double
       precision, dimension( * ) rwork, double precision, dimension( * )
       result, integer info)

🌟 ZCHKHB2STG 🌟

🎯 Purpose 🎯

So ZCHKHB2STG tests the reduction of a Hermitian band matrix to tridiagonal from — yes bestie, the original page says from, not form, and we're keeping that little typo as a souvenir 😭 — and it's used with the Hermitian eigenvalue problem.

ZHBTRD factors a Hermitian band matrix A as U S U* , where * means conjugate transpose, S is symmetric tridiagonal, and U is unitary. ZHBTRD can use either just the lower or just the upper triangle of A; ZCHKHB2STG checks both cases.

ZHETRD_HB2ST factors a Hermitian band matrix A as U S U* , where * means conjugate transpose, S is symmetric tridiagonal, and U is unitary. ZHETRD_HB2ST can use either just the lower or just the upper triangle of A; ZCHKHB2STG checks both cases.

DSTEQR factors S as Z D1 Z'.

D1 is the matrix of eigenvalues computed when Z is not computed and from the S resulting of DSBTRD (used as reference for DSYTRD_SB2ST).

D2 is the matrix of eigenvalues computed when Z is not computed and from the S resulting of DSYTRD_SB2ST .

D3 is the matrix of eigenvalues computed when Z is not computed and from the S resulting of DSYTRD_SB2ST .

When ZCHKHB2STG is called, the original page says “a number of matrix (), a number of bandwidths (), and a number of matrix are specified” — lowkey the blanks are literally in the source, so we're not gonna invent names, bestie 🙈 For each size (()), each bandwidth (()) less than or equal to , and each type of matrix, one matrix will be generated and used to test the hermitian banded reduction routine. For each matrix, a number of tests will be performed:

  1. | A - V S V* | / ( |A| n ulp ) computed by ZHBTRD with UPLO='U'
  2. | I - UU* | / ( n ulp )
  3. | A - V S V* | / ( |A| n ulp ) computed by ZHBTRD with UPLO='L'
  4. | I - UU* | / ( n ulp )
  5. | D1 - D2 | / ( |D1| ulp ) where D1 is computed by DSBTRD with UPLO='U' and D2 is computed by ZHETRD_HB2ST with UPLO='U'
  6. | D1 - D3 | / ( |D1| ulp ) where D1 is computed by DSBTRD with UPLO='U' and D3 is computed by ZHETRD_HB2ST with UPLO='L'

The list is specified by an array NN(1:NSIZES); the value of each element NN(j) specifies one size.

The array DOTYPE( 1:NTYPES ) specifies which ones; if DOTYPE(j) is .TRUE., then matrix type [blank in the original] will be generated.

Currently, the list of possible types is:

  1. The zero matrix.
  2. The identity matrix.
  3. A diagonal matrix with evenly spaced entries 1, ..., ULP and random signs. (ULP = (first number larger than 1) - 1 )
  4. A diagonal matrix with geometrically spaced entries 1, ..., ULP and random signs.
  5. A diagonal matrix with [blank in the original] entries 1, ULP, ..., ULP and random signs.
  6. Same as (4), but multiplied by SQRT( overflow threshold )
  7. Same as (4), but multiplied by SQRT( underflow threshold )
  8. A matrix of the form U* D U, where U is unitary and D has evenly spaced entries 1, ..., ULP with random signs on the diagonal.
  9. A matrix of the form U* D U, where U is unitary and D has geometrically spaced entries 1, ..., ULP with random signs on the diagonal.
  10. A matrix of the form U* D U, where U is unitary and D has [blank in the original] entries 1, ULP,..., ULP with random signs on the diagonal.
  11. Same as (8), but multiplied by SQRT( overflow threshold )
  12. Same as (8), but multiplied by SQRT( underflow threshold )
  13. Hermitian matrix with random entries chosen from (-1,1).
  14. Same as (13), but multiplied by SQRT( overflow threshold )
  15. Same as (13), but multiplied by SQRT( underflow threshold )

🍓 Parameters 🍓

  • NSIZES — INTEGER. The number of sizes of matrices to use. If it is zero, ZCHKHB2STG does nothing. It must be at least zero.
  • NN — INTEGER array, dimension (NSIZES). An array containing the sizes to be used for the matrices. Zero values will be skipped. The values must be at least zero.
  • NWDTHS — INTEGER. The number of bandwidths to use. If it is zero, ZCHKHB2STG does nothing. It must be at least zero.
  • KK — INTEGER array, dimension (NWDTHS). An array containing the bandwidths to be used for the band matrices. The values must be at least zero.
  • NTYPES — INTEGER. The number of elements in DOTYPE. If it is zero, ZCHKHB2STG does nothing. It must be at least zero. If it is MAXTYP+1 and NSIZES is 1, then an additional type, MAXTYP+1 is defined, which is to use whatever matrix is in A. This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE. .
  • DOTYPE — LOGICAL array, dimension (NTYPES). If DOTYPE(j) is .TRUE., then for each size in NN a matrix of that size and of type j will be generated. If NTYPES is smaller than the maximum number of types defined (PARAMETER MAXTYP), then types NTYPES+1 through MAXTYP will not be generated. If NTYPES is larger than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) will be ignored.
  • ISEED — INTEGER array, dimension (4). On entry ISEED specifies the seed of the random number generator. The array elements should be between 0 and 4095; if not they will be reduced mod 4096. Also, ISEED(4) must be odd. The random number generator uses a linear congruential sequence limited to small integers, and so should produce machine independent random numbers. The values of ISEED are changed on exit, and can be used in the next call to ZCHKHB2STG to continue the same random number sequence.
  • THRESH — DOUBLE PRECISION. A test will count as [blank in the original] if the [blank in the original], computed as described above, exceeds THRESH. Note that the error is scaled to be O(1), so THRESH should be a reasonably small multiple of 1, e.g., 10 or 100. In particular, it should not depend on the precision (single vs. double) or the size of the matrix. It must be at least zero.
  • NOUNIT — INTEGER. The FORTRAN unit number for printing out error messages (e.g., if a routine returns IINFO not equal to 0.)
  • A — COMPLEX*16 array, dimension (LDA, max(NN)). Used to hold the matrix whose eigenvalues are to be computed.
  • LDA — INTEGER. The leading dimension of A. It must be at least 2 (not 1!) and at least max( KK )+1.
  • SD — DOUBLE PRECISION array, dimension (max(NN)). Used to hold the diagonal of the tridiagonal matrix computed by ZHBTRD.
  • SE — DOUBLE PRECISION array, dimension (max(NN)). Used to hold the off-diagonal of the tridiagonal matrix computed by ZHBTRD.
  • D1 — DOUBLE PRECISION array, dimension (max(NN)).
  • D2 — DOUBLE PRECISION array, dimension (max(NN)).
  • D3 — DOUBLE PRECISION array, dimension (max(NN)). (The original has a rogue *> hanging out just before this one — we see you, bestie 💀)
  • U — COMPLEX*16 array, dimension (LDU, max(NN)). Used to hold the unitary matrix computed by ZHBTRD.
  • LDU — INTEGER. The leading dimension of U. It must be at least 1 and at least max( NN ).
  • WORK — COMPLEX*16 array, dimension (LWORK).
  • LWORK — INTEGER. The number of entries in WORK. This must be at least max( LDA+1, max(NN)+1 )*max(NN).
  • RWORK — DOUBLE PRECISION array.
  • RESULT — DOUBLE PRECISION array, dimension (4). The values computed by the tests described above. The values are currently limited to 1/ulp, to avoid overflow.

🌸 INFO 🌸

INFO is INTEGER

If it's 0, then everything ran OK — the good timeline, bestie. No cap. 💅

Some Local Variables and Parameters: (the supporting cast, iykyk)

  • ZERO, ONE — Real 0 and 1.
  • MAXTYP — the number of types defined.
  • NTEST — the number of tests performed, or which can be performed so far, for the current matrix.
  • NTESTT — the total number of tests performed so far.
  • NMAX — largest value in NN.
  • NMATS — the number of matrices generated so far.
  • NERRS — the number of tests which have exceeded THRESH so far.
  • COND, IMODE — values to be passed to the matrix generators.
  • ANORM — norm of A; passed to matrix generators.
  • OVFL, UNFL — overflow and underflow thresholds.
  • ULP, ULPINV — finest relative precision and its inverse.
  • RTOVFL, RTUNFL — square roots of the previous 2 values.

The following four arrays decode JTYPE:

  • KTYPE(j) — The general type (1-10) for type .
  • KMODE(j) — The MODE value to be passed to the matrix generator for type .
  • KMAGN(j) — The order of magnitude ( O(1), O(overflow^(1/2) ), O(underflow^(1/2) )

Author 💖

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

Definition at line 334 of file zchkhb2stg.f.

Author 🤖

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Footer vibe check: LAPACK Version 3.12.0, source /home/abui...chkhb2stg.f(3). Date wasn't printed in this footer, so no invented dates — just iconic version energy. 🫶✨

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