ZDRVSG(3)

📦 version 3.12.0, in opensuse-leap 16.0

🦋 ZDRVSG(3) 🦋

okay bestie, we are literally in the Library Functions Manual right now, and this page is all about ZDRVSG — the complex Hermitian generalized eigenproblem driver checker. It's giving LAPACK main character energy, no cap. 💅✨

📛 NAME 📛

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

🌀 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 (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: 🎯

ZDRVSG checks the complex Hermitian generalized eigenproblem drivers. Like, that's the whole assignment. 👑

Here's the driver lineup, bestie — it's lowkey stacked:

  • 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 sizes (nsizes) and a number of matrix types (ntypes) 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. (1) — ZHEGV with ITYPE = 1 and UPLO ='U': | A Z - B Z D | / ( |A| |Z| n ulp )
  2. (2) — as (1) but calling ZHPGV
  3. (3) — as (1) but calling ZHBGV
  4. (4) — as (1) but with UPLO = 'L'
  5. (5) — as (4) but calling ZHPGV
  6. (6) — as (4) but calling ZHBGV
  7. (7) — ZHEGV with ITYPE = 2 and UPLO ='U': | A B Z - Z D | / ( |A| |Z| n ulp )
  8. (8) — as (7) but calling ZHPGV
  9. (9) — as (7) but with UPLO = 'L'
  10. (10) — as (9) but calling ZHPGV
  11. (11) — ZHEGV with ITYPE = 3 and UPLO ='U': | B A Z - Z D | / ( |A| |Z| n ulp )
  12. (12) — as (11) but calling ZHPGV
  13. (13) — as (11) but with UPLO = 'L'
  14. (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 sizes are specified by an array NN(1:NSIZES); the value of each element NN(j) specifies one size. The types are specified by a logical array DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type j 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. (1) — The zero matrix.
  2. (2) — The identity matrix.
  3. (3) — A diagonal matrix with evenly spaced entries 1, ..., ULP and random signs. (ULP = (first number larger than 1) - 1)
  4. (4) — A diagonal matrix with geometrically spaced entries 1, ..., ULP and random signs.
  5. (5) — A diagonal matrix with entries 1, ULP, ..., ULP and random signs.
  6. (6) — Same as (4), but multiplied by SQRT( overflow threshold )
  7. (7) — Same as (4), but multiplied by SQRT( underflow threshold )
  8. (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. (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. (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. (11) — Same as (8), but multiplied by SQRT( overflow threshold )
  12. (12) — Same as (8), but multiplied by SQRT( underflow threshold )
  13. (13) — Hermitian matrix with random entries chosen from (-1,1).
  14. (14) — Same as (13), but multiplied by SQRT( overflow threshold )
  15. (15) — Same as (13), but multiplied by SQRT( underflow threshold )
  16. (16) — Same as (8), but with KA = 1 and KB = 1
  17. (17) — Same as (8), but with KA = 2 and KB = 1
  18. (18) — Same as (8), but with KA = 2 and KB = 2
  19. (19) — Same as (8), but with KA = 3 and KB = 1
  20. (20) — Same as (8), but with KA = 3 and KB = 2
  21. (21) — Same as (8), but with KA = 3 and KB = 3

okay bestie, we're still in the argument docs — no heading repeat, just facts and fairy dust 🧚✨

  • NSIZES (INTEGER) — the number of sizes of matrices to use. If it is zero, ZDRVSG does nothing. It must be at least zero. Not modified.
  • 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. Not modified.
  • NTYPES (INTEGER) — the number of elements in DOTYPE. If it is zero, ZDRVSG 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. . Not modified.
  • 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. Not modified.
  • 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 ZDRVSG to continue the same random number sequence. Modified.
  • THRESH (DOUBLE PRECISION) — A test will count as if the , 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. Not modified.
  • NOUNIT (INTEGER) — the FORTRAN unit number for printing out error messages (e.g., if a routine returns IINFO not equal to 0.) Not modified.
  • A (COMPLEX*16 array, dimension (LDA , max(NN))) — used to hold the matrix whose eigenvalues are to be computed. On exit, A contains the last matrix actually used. Modified.
  • LDA (INTEGER) — the leading dimension of A. It must be at least 1 and at least max( NN ). Not modified.
  • B (COMPLEX*16 array, dimension (LDB , max(NN))) — used to hold 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. It 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. It must be at least 1 and at least max( NN ). 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) — the number of entries in WORK. This 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) — the number of entries in RWORK. This 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.
  • LIWORK (INTEGER) — the number of entries in IWORK. This 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 0, then everything ran OK. Then the error codes, bestie:
    • -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.

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 🧚

  • 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.

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 366 of file zdrvsg.f.

✨ Author ✨

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and that's the whole tea, bestie 💅 this iconic page is LAPACK Version 3.12.0, from /home/abui...IG/zdrvsg.f(3), and it was generated automatically by Doxygen for LAPACK from the source code — mwah 💋✨

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