ZDRVSG2STG(3)

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version 3.12.1 · 2 versions
, in arch rolling

💅 TESTING/EIG/zdrvsg2stg.f 💅

okay so this is from the Library Functions Manual, and it's giving “test driver for the complex Hermitian generalized eigenproblem girlies.” Buckle up, bestie, because this one has a lot of literal details and we are keeping every single one. 💖

🎀 NAME 🎀

TESTING/EIG/zdrvsg2stg.f — that’s the whole name section, no cap. It’s literally just the file path, and honestly? Iconic minimalism. ✨

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

subroutine zdrvsg2stg (nsizes, nn, ntypes, dotype, iseed, thresh,
           nounit, a, lda, b, ldb, d, d2, z, ldz, ab, bb, ap, bp, work, nwork,
           rwork, lrwork, iwork, liwork, result, info)

ZDRVSG2STG

💖 Function/Subroutine Documentation 💖

subroutine zdrvsg2stg (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, double precision, dimension( * ) d2,
    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)

ZDRVSG2STG

🌸 Purpose 🌸

okay so ZDRVSG2STG checks the complex Hermitian generalized eigenproblem drivers. That’s the whole vibe. 🦋

Here’s the driver lineup, bestie — every single one:

  • 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 ZDRVSG2STG 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 )
| D - D2 | / ( |D| ulp )   where D is computed by
                           ZHEGV and  D2 is computed by
                           ZHEGV_2STAGE. This test is
                           only performed for DSYGV
  • (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 sizes of matrices to use. If it’s zero, ZDRVSG2STG does literally nothing. It must be at least zero. Not modified.
  • NN (INTEGER array, dimension (NSIZES)) — an array holding the sizes to use for the matrices. Zero values get skipped. The values must be at least zero. Not modified.
  • NTYPES (INTEGER) — the number of elements in DOTYPE. If it’s zero, ZDRVSG2STG does nothing. Must be at least zero. If it’s MAXTYP+1 and NSIZES is 1, then an extra type, MAXTYP+1, is defined — it uses whatever matrix is already 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 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. If NTYPES is larger than MAXTYP, then DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) get ignored. Not modified.
  • ISEED (INTEGER array, dimension (4)) — on entry, ISEED sets the random number generator seed. The array elements should be between 0 and 4095; if not, they get reduced mod 4096. Also, ISEED(4) must be odd. The RNG 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 can be used in the next call to ZDRVSG2STG to continue the same random sequence. Modified.
  • THRESH (DOUBLE PRECISION) — a test will count as (the original source literally has blanks here: A test will count as if the , computed as described above, exceeds THRESH. — no cap, that’s how it’s written 😭) if the computed thing exceeds THRESH. Note that the error is scaled to be O(1), so THRESH should be a reasonably small multiple of 1, like 10 or 100. In particular, it should not depend on precision (single vs. double) or matrix size. Must be at least zero. Not modified.
  • NOUNIT (INTEGER) — the FORTRAN unit number for printing error messages (like if a routine returns IINFO not equal to 0). Not modified.
  • A (COMPLEX*16 array, dimension (LDA , max(NN))) — holds 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. 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 ). 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. 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. 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. 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. 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

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 372 of file zdrvsg2stg.f.

Author

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That’s the whole vibe, bestie 💖 — this page is from LAPACK Version 3.12.0, source file TESTING/EIG/zdrvsg2stg.f(3). Stay slay ✨

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