ZDRVST2STG(3)

📦 version 3.12.0, in opensuse-leap 16.0

🦋 ZDRVST2STG(3) 🦋

okay so bestie, this page is from the Library Functions Manual, and the file it's documenting is /home/abui...drvst2stg.f(3) — say that three times fast, I dare you 💀. The full path it came from is sitting right down there in NAME, don't worry.

heads up: a couple of words in the original got straight-up swallowed by the typesetter (you'll spot the empty gaps, like "the are specified"). I kept every gap exactly where it was instead of guessing, because we do not make stuff up in this house 🙈

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/zdrvst2stg.f

like, that's the whole NAME section. it's a path. she's lowkey just a girl 💅

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine ZDRVST2STG (nsizes, nn, ntypes, dotype, iseed, thresh,
    nounit, a, lda, d1, d2, d3, wa1, wa2, wa3, u, ldu, v, tau, z, work,
    lwork, rwork, lrwork, iwork, liwork, result, info)

ZDRVST2STG

that's it. that's the vibe. a lot of arguments, no cap 🎀

👑 Function/Subroutine Documentation 👑

subroutine ZDRVST2STG

here she is in full, exactly character for character, because we respect the source around here 🫶

subroutine ZDRVST2STG (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, double precision, dimension( * ) d1, double precision,
    dimension( * ) d2, double precision, dimension( * ) d3, double
    precision, dimension( * ) wa1, double precision, dimension( * ) wa2,
    double precision, dimension( * ) wa3, complex*16, dimension( ldu, * ) u,
    integer ldu, complex*16, dimension( ldu, * ) v, complex*16, dimension( *
    ) tau, complex*16, dimension( ldu, * ) z, complex*16, dimension( * )
    work, integer lwork, double precision, dimension( * ) rwork, integer
    lrwork, integer, dimension( * ) iwork, integer liwork, double precision,
    dimension( * ) result, integer info)

ZDRVST2STG

💖 Purpose 💖

okay so the whole point of this icon: ZDRVST2STG checks the Hermitian eigenvalue problem drivers. plural. a whole lineup. a whole squad, if you will 🌈

here's the roster, and yes every single one of them is getting their moment:

  • ZHEEVD — computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, using a divide-and-conquer algorithm.
  • ZHEEVX — computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix.
  • ZHEEVR — computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, using the Relatively Robust Representation where it can.
  • ZHPEVD — computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage, using a divide-and-conquer algorithm.
  • ZHPEVX — computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage.
  • ZHBEVD — computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix, using a divide-and-conquer algorithm.
  • ZHBEVX — computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix.
  • ZHEEV — computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix.
  • ZHPEV — computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage.
  • ZHBEV — computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix.

like, the range?? the versatility?? we stan a thorough test suite 💅

so when ZDRVST2STG is called, a number of matrix () and a number of matrix are specified. for each size () and each type of matrix, one matrix will be generated and used to test the appropriate drivers. one matrix, many drivers, maximum drama ✨

and for each matrix and each driver routine called, these are the checks that go down:

  1. | A - Z D Z' | / ( |A| n ulp )
  2. | I - Z Z' | / ( n ulp )
  3. | D1 - D2 | / ( |D1| ulp )

where Z is the matrix of eigenvectors returned when the eigenvector option is given, and D1 and D2 are the eigenvalues returned with and without the eigenvector option. yes bestie, we're comparing them. that's the whole bit 🔥

🎀 the sizes and the types 🎀

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.

currently the list of possible types is, and buckle up because it's long:

  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. Symmetric 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. A band matrix with half bandwidth randomly chosen between 0 and N-1, with evenly spaced eigenvalues 1, ..., ULP with random signs.
  17. Same as (16), but multiplied by SQRT( overflow threshold ).
  18. Same as (16), but multiplied by SQRT( underflow threshold ).

eighteen whole matrix types, she really said "we're testing everything" 😭👑

and that's where this part wraps — there's more coming, don't go anywhere 💜

  • NSIZES — INTEGER. The number of sizes of matrices to use. If it’s zero, ZDRVST2STG 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’s zero, ZDRVST2STG 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 — and that one means “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 ZDRVST2STG to continue the same random number sequence. Modified.
  • THRESH — DOUBLE PRECISION. A test will count as [blank] if the [blank], 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.
  • D1 — DOUBLE PRECISION array, dimension (max(NN)). The eigenvalues of A, as computed by ZSTEQR simultaneously with Z. On exit, the eigenvalues in D1 correspond with the matrix in A. Modified.
  • D2 — DOUBLE PRECISION array, dimension (max(NN)). The eigenvalues of A, as computed by ZSTEQR if Z is not computed. On exit, the eigenvalues in D2 correspond with the matrix in A. Modified.
  • D3 — DOUBLE PRECISION array, dimension (max(NN)). The eigenvalues of A, as computed by DSTERF. On exit, the eigenvalues in D3 correspond with the matrix in A. Modified.
  • WA1 — DOUBLE PRECISION array, dimension.
  • WA2 — DOUBLE PRECISION array, dimension.
  • WA3 — DOUBLE PRECISION array, dimension.
  • U — COMPLEX*16 array, dimension (LDU, max(NN)). The unitary matrix computed by ZHETRD + ZUNGC3. Modified.
  • LDU — INTEGER. The leading dimension of U, Z, and V. It must be at least 1 and at least max( NN ). Not modified.
  • V — COMPLEX*16 array, dimension (LDU, max(NN)). The Housholder vectors computed by ZHETRD in reducing A to tridiagonal form. Modified.
  • TAU — COMPLEX*16 array, dimension (max(NN)). The Householder factors computed by ZHETRD in reducing A to tridiagonal form. Modified.
  • Z — COMPLEX*16 array, dimension (LDU, max(NN)). The unitary matrix of eigenvectors computed by ZHEEVD, ZHEEVX, ZHPEVD, CHPEVX, ZHBEVD, and CHBEVX. Modified.
  • WORK — COMPLEX*16 array of dimension ( LWORK ). Workspace. Modified.
  • LWORK — INTEGER. The number of entries in WORK. This must be at least 2*max( NN(j), 2 )**2. Not modified.
  • RWORK — DOUBLE PRECISION array, dimension (3*max(NN)). Workspace. Modified.
  • LRWORK — INTEGER. The number of entries in RWORK.
  • IWORK — INTEGER array, dimension (6*max(NN)). Workspace. Modified.
  • LIWORK — INTEGER. The number of entries in IWORK.
  • RESULT — DOUBLE PRECISION array, dimension (??). The values computed by the tests described above. The values are currently limited to 1/ulp, to avoid overflow. Modified.
  • INFO — INTEGER. If 0, then everything ran OK.
    • -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: LDU < 1 or LDU < NMAX.
    • -21: LWORK too small. If DLATMR, SLATMS, ZHETRD, DORGC3, ZSTEQR, DSTERF, or DORMC2 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 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 (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 334 of file zdrvst2stg.f.

Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

okay bestie, that’s the whole page — source/version sign-off: LAPACK Version 3.12.0, file /home/abui...drvst2stg.f(3). No date on this footer, just those vibes. mwah 💋

📦 where this page comes from