TESTING/EIG/zdrvsg.f(3)

📦
version 3.12.1 · 2 versions
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🌸 NAME 🌸

Okay bestie, this page is for TESTING/EIG/zdrvsg.f — it's giving LAPACK test-driver energy, and the main character is ZDRVSG, out here checking the complex Hermitian generalized eigenproblem drivers. Periodt. 💅

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

       subroutine zdrvsg (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a,
           lda, b, ldb, d, z, ldz, ab, bb, ap, bp, work, nwork, rwork, lrwork,
           iwork, liwork, result, info)
           ZDRVSG

💅 Function/Subroutine Documentation 💅

🦋 subroutine zdrvsg 🦋

   subroutine zdrvsg (integer nsizes, integer, dimension( * ) nn, integer
       ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed,
       double precision thresh, integer nounit, complex*16, dimension( lda, * )
       a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, double
       precision, dimension( * ) d, complex*16, dimension( ldz, * ) z, integer
       ldz, complex*16, dimension( lda, * ) ab, complex*16, dimension( ldb, * )
       bb, complex*16, dimension( * ) ap, complex*16, dimension( * ) bp,
       complex*16, dimension( * ) work, integer nwork, double precision,
       dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork,
       integer liwork, double precision, dimension( * ) result, integer info)
       ZDRVSG

🔥 Purpose 🔥

Okay so ZDRVSG is literally the vibe check for complex Hermitian generalized eigenproblem drivers. It checks these iconic routines:

  • ZHEGV — computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian-definite generalized eigenproblem.
  • ZHEGVD — computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian-definite generalized eigenproblem using a divide and conquer algorithm.
  • ZHEGVX — computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian-definite generalized eigenproblem.
  • ZHPGV — computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian-definite generalized eigenproblem in packed storage.
  • ZHPGVD — computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian-definite generalized eigenproblem in packed storage using a divide and conquer algorithm.
  • ZHPGVX — computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian-definite generalized eigenproblem in packed storage.
  • ZHBGV — computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian-definite banded generalized eigenproblem.
  • ZHBGVD — computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian-definite banded generalized eigenproblem using a divide and conquer algorithm.
  • ZHBGVX — computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian-definite banded generalized eigenproblem.

When ZDRVSG is called, a number of matrix () and a number of matrix are specified. For each size () and each type of matrix, one matrix A of the given type will be generated; a random well-conditioned matrix B is also generated and the pair (A,B) is used to test the drivers.

For each pair (A,B), the following tests are performed:

  1. ZHEGV with ITYPE = 1 and UPLO ='U': | A Z - B Z D | / ( |A| |Z| n ulp )
  2. as (1) but calling ZHPGV
  3. as (1) but calling ZHBGV
  4. as (1) but with UPLO = 'L'
  5. as (4) but calling ZHPGV
  6. as (4) but calling ZHBGV
  7. ZHEGV with ITYPE = 2 and UPLO ='U': | A B Z - Z D | / ( |A| |Z| n ulp )
  8. as (7) but calling ZHPGV
  9. as (7) but with UPLO = 'L'
  10. as (9) but calling ZHPGV
  11. ZHEGV with ITYPE = 3 and UPLO ='U': | B A Z - Z D | / ( |A| |Z| n ulp )
  12. as (11) but calling ZHPGV
  13. as (11) but with UPLO = 'L'
  14. as (13) but calling ZHPGV

ZHEGVD, ZHPGVD and ZHBGVD performed the same 14 tests.

ZHEGVX, ZHPGVX and ZHBGVX performed the above 14 tests with the parameter RANGE = 'A', 'N' and 'I', respectively.

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

The are specified by a logical array DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type will be generated. This type is used for the matrix A which has half-bandwidth KA. B is generated as a well-conditioned positive definite matrix with half-bandwidth KB (<= KA).

Currently, the list of possible types for A 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 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 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 )
  16. Same as (8), but with KA = 1 and KB = 1
  17. Same as (8), but with KA = 2 and KB = 1
  18. Same as (8), but with KA = 2 and KB = 2
  19. Same as (8), but with KA = 3 and KB = 1
  20. Same as (8), but with KA = 3 and KB = 2
  21. Same as (8), but with KA = 3 and KB = 3
  • NSIZES INTEGER — the number of matrix sizes you wanna mess with. If it's zero, ZDRVSG literally does nothing (it's giving "clocked out early" 💀). Must be at least zero. Not modified.
  • NN INTEGER array, dimension (NSIZES) — the actual list of sizes for the matrices. Zero values get skipped, and every value has to be at least zero. Not modified.
  • NTYPES INTEGER — how many entries live in DOTYPE. If it's zero, ZDRVSG does nothing, periodt. Must be at least zero. Special case bestie: if it's MAXTYP+1 and NSIZES is 1, then one extra type, MAXTYP+1, gets defined — and it just uses whatever matrix is already sitting in A. This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE.. Not modified.
  • DOTYPE LOGICAL array, dimension (NTYPES) — the vibe check for each type. If DOTYPE(j) is .TRUE., then for every size in NN a matrix of that size and of type j gets generated. If NTYPES is smaller than the max number of types defined (PARAMETER MAXTYP), then types NTYPES+1 through MAXTYP won't be generated. And if NTYPES is bigger than MAXTYP, then DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) get ignored (sorry to them). Not modified.
  • ISEED INTEGER array, dimension (4) — on entry this is the seed for the random number generator. The elements should be between 0 and 4095 — if they're not, they get reduced mod 4096 🎲. Also ISEED(4) must be odd. The generator uses a linear congruential sequence limited to small integers, so it should produce machine independent random numbers. The values of ISEED change on exit, and you can hand them to the next ZDRVSG call to keep the same random number sequence going. Modified.
  • THRESH DOUBLE PRECISION — a test counts as [that thing] if the [other thing], computed as described above, exceeds THRESH. 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. Must be at least zero. Not modified.
  • NOUNIT INTEGER — the FORTRAN unit number used for printing out error messages (like when a routine returns IINFO not equal to 0). Not modified.
  • A COMPLEX*16 array, dimension (LDA, max(NN)) — holds the matrix whose eigenvalues are getting computed. On exit, A contains the last matrix actually used. Modified.
  • LDA INTEGER — the leading dimension of A. Must be at least 1 and at least max( NN ). Not modified.
  • B COMPLEX*16 array, dimension (LDB, max(NN)) — holds the Hermitian positive definite matrix for the generalized problem. On exit, B contains the last matrix actually used. Modified.
  • LDB INTEGER — the leading dimension of B. Must be at least 1 and at least max( NN ). Not modified.
  • D DOUBLE PRECISION array, dimension (max(NN)) — the eigenvalues of A. On exit, the eigenvalues in D correspond with the matrix in A. Modified.
  • Z COMPLEX*16 array, dimension (LDZ, max(NN)) — the matrix of eigenvectors. Modified.
  • LDZ INTEGER — the leading dimension of ZZ. Must be at least 1 and at least max( NN ). (yeah, the docs say ZZ right there — I'm just relaying it faithfully, don't come for me 🙈) Not modified.
  • AB COMPLEX*16 array, dimension (LDA, max(NN)) — workspace. Modified.
  • BB COMPLEX*16 array, dimension (LDB, max(NN)) — workspace. Modified.
  • AP COMPLEX*16 array, dimension (max(NN)**2) — workspace. Modified.
  • BP COMPLEX*16 array, dimension (max(NN)**2) — workspace. Modified.
  • WORK COMPLEX*16 array, dimension (NWORK) — workspace. Modified.
  • NWORK INTEGER — how many entries are in WORK. Must be at least 2*N + N**2 where N = max( NN(j), 2 ). Not modified.
  • RWORK DOUBLE PRECISION array, dimension (LRWORK) — workspace. Modified.
  • LRWORK INTEGER — how many entries are in RWORK. Must be at least max( 7*N, 1 + 4*N + 2*N*lg(N) + 3*N**2 ) where N = max( NN(j) ) and lg( N ) = smallest integer k such that 2**k >= N. Not modified.
  • IWORK INTEGER array, dimension (LIWORK)) — workspace. Modified. (yes the extra ) is canon, I don't make the rules 💅)
  • LIWORK INTEGER — how many entries are in IWORK. Must be at least 2 + 5*max( NN(j) ). Not modified.
  • RESULT DOUBLE PRECISION array, dimension (70) — the values computed by the 70 tests described above. Modified.
  • INFO INTEGER — if it's 0, then everything ran OK, we love that for us ✨. Otherwise:
    • -1: NSIZES < 0
    • -2: Some NN(j) < 0
    • -3: NTYPES < 0
    • -5: THRESH < 0
    • -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
    • -16: LDZ < 1 or LDZ < NMAX.
    • -21: NWORK too small.
    • -23: LRWORK too small.
    • -25: LIWORK too small.

And if ZLATMR, CLATMS, ZHEGV, ZHPGV, ZHBGV, CHEGVD, CHPGVD, ZHPGVD, ZHEGVX, CHPGVX, ZHBGVX returns an error code, the absolute value of it is returned. Modified.

🧚 Some Local Variables and Parameters (the backstage crew)

ZERO, ONE — real 0 and 1.

MAXTYP — the number of types defined.

NTEST — the number of tests that have been run on this matrix.

NTESTT — the total number of tests for this call.

NMAX — largest value in NN.

NMATS — the number of matrices generated so far.

NERRS — the number of tests which have exceeded THRESH so far (computed by DLAFTS).

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.

And these four arrays decode JTYPE:

  • KTYPE(j) — the general type (1-10) for type [j].
  • KMODE(j) — the MODE value to be passed to the matrix generator for type [j].
  • 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 366 of file zdrvsg.f.

Generated automatically by Doxygen for LAPACK from the source code — so like, nobody hand-wrote that bit, the robots did it for us 🫶

And that's a wrap on TESTING/EIG/zdrvsg.f(3), bestie!! This whole thing came to you courtesy of LAPACK Version 3.12.0 💖✨🎀 go forth and test those generalized symmetric eigenproblems, iykyk 🌸🦋

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