ZDRVST2STG(3)

📦
version 3.12.1 · 2 versions
, in arch rolling

🌸 NAME 🌸

Ok bestie, we're on the TESTING/EIG/zdrvst2stg.f(3) page from the Library Functions Manual, and the actual file being documented is TESTING/EIG/zdrvst2stg.f. 💖

🎀 SYNOPSIS 🎀

✨ Functions/Subroutines ✨

Here's the whole cast list, no cap:

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

💅 FUNCTION/SUBROUTINE DOCUMENTATION 💅

Say hi to the full signature, bestie — every type, every dimension, every lil parameter is right 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 🦋

So ZDRVST2STG checks the Hermitian eigenvalue problem drivers. That's the whole vibe. 🫶

Here's the driver lineup it's testing, and yes, every single one is included:

  • 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. 👑

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. For each matrix and each driver routine called, the following tests will be performed:

  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. 🧚

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:

  • (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 ) 💜

okay, argument roll call continued — every single one, no skips, no cap 💖

  • NSIZES INTEGER — the number of sizes of matrices to use. If it is 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 is 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, 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 ZDRVST2STG to continue the same random number sequence. Modified.
  • THRESH DOUBLE PRECISION — a test will count as blank-in-the-source if the also-blank-in-the-source, 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 — the source leaves the dimension blank here, bestie, so I'm not inventing a size 💅
  • WA2 DOUBLE PRECISION array, dimension — same blank-dimension situation as WA1 🫶
  • WA3 DOUBLE PRECISION array, dimension — yep, blank dimension again, no cap
  • 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 🧚

okay so the source also gives us this little backstage pass into the local variables and parameters — iconic, honestly:

  • 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: (the source says four here, then lists three — I'm just reporting the group chat 😭)

  • KTYPE(j) — the general type (1-10) for type (the source leaves the type blank here) .
  • KMODE(j) — the MODE value to be passed to the matrix generator for type (blank in the source again) .
  • 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 (the Doxygen encore) 👑

Generated automatically by Doxygen for LAPACK from the source code.

and that's the whole page, bestie 🫶 — LAPACK Version 3.12.0, source TESTING/EIG/zdrvst2stg.f(3). The footer doesn't give a date, so I'm not making one up 💅✨

📦 where this page comes from