CDRVSG2STG(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 CDRVSG2STG(3) — Library Functions Manual 💖

Bestie, welcome to the Library Functions Manual page for CDRVSG2STG(3). This is the source-file corner of the LAPACK testing universe, and we are going to keep every single detail. No skipping, no cap. 💅

🌸 NAME 🌸

CDRVSG2STG(3) — and the source file is exactly /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/cdrvsg2stg.f.

✨ SYNOPSIS ✨

💅 Functions/Subroutines 💅

subroutine CDRVSG2STG (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)
           CDRVSG2STG

🦋 Function/Subroutine Documentation 🦋

Full signature tea, served exactly:

subroutine CDRVSG2STG (integer nsizes, integer, dimension( * ) nn, integer
       ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed,
       real thresh, integer nounit, complex, dimension( lda, * ) a, integer
       lda, complex, dimension( ldb, * ) b, integer ldb, real, dimension( * )
       d, real, dimension( * ) d2, complex, dimension( ldz, * ) z, integer ldz,
       complex, dimension( lda, * ) ab, complex, dimension( ldb, * ) bb,
       complex, dimension( * ) ap, complex, dimension( * ) bp, complex,
       dimension( * ) work, integer nwork, real, dimension( * ) rwork, integer
       lrwork, integer, dimension( * ) iwork, integer liwork, real, dimension(
       * ) result, integer info)
       CDRVSG2STG

🌟 Purpose 🌟

Okay so here’s the vibe: CDRVSG2STG checks the complex Hermitian generalized eigenproblem drivers. It is giving very much “test manager for the eigenproblem girlies.” 💅

The drivers it checks are:

  • CHEGV — computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian-definite generalized eigenproblem.
  • CHEGVD — computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian-definite generalized eigenproblem using a divide and conquer algorithm.
  • CHEGVX — computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian-definite generalized eigenproblem.
  • CHPGV — computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian-definite generalized eigenproblem in packed storage.
  • CHPGVD — computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian-definite generalized eigenproblem in packed storage using a divide and conquer algorithm.
  • CHPGVX — computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian-definite generalized eigenproblem in packed storage.
  • CHBGV — computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian-definite banded generalized eigenproblem.
  • CHBGVD — computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian-definite banded generalized eigenproblem using a divide and conquer algorithm.
  • CHBGVX — computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian-definite banded generalized eigenproblem.

When CDRVSG2STG is called, a number of matrix sizes (NSIZES) and a number of matrix types (NTYPES) are specified. For each size (NN(j)) 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) CHEGV with ITYPE = 1 and UPLO ='U': | A Z - B Z D | / ( |A| |Z| n ulp ); | D - D2 | / ( |D| ulp ) — where D is computed by CHEGV and D2 is computed by CHEGV_2STAGE. This test is only performed for DSYGV.
  • (2) as (1) but calling CHPGV.
  • (3) as (1) but calling CHBGV.
  • (4) as (1) but with UPLO = 'L'.
  • (5) as (4) but calling CHPGV.
  • (6) as (4) but calling CHBGV.
  • (7) CHEGV with ITYPE = 2 and UPLO ='U': | A B Z - Z D | / ( |A| |Z| n ulp ).
  • (8) as (7) but calling CHPGV.
  • (9) as (7) but with UPLO = 'L'.
  • (10) as (9) but calling CHPGV.
  • (11) CHEGV with ITYPE = 3 and UPLO ='U': | B A Z - Z D | / ( |A| |Z| n ulp ).
  • (12) as (11) but calling CHPGV.
  • (13) as (11) but with UPLO = 'L'.
  • (14) as (13) but calling CHPGV.

CHEGVD, CHPGVD and CHBGVD performed the same 14 tests.

CHEGVX, CHPGVX and CHBGVX 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 that 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, CDRVSG2STG literally does nothing (fr fr, she’s on break 💅). 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 (lowkey ghosted 👻). The values must be at least zero. Not modified.
  • NTYPES INTEGER — the number of elements in DOTYPE. If it’s zero, CDRVSG2STG does nothing. It must be at least zero. If it’s 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 CDRVSG2STG to continue the same random number sequence. Modified.
  • THRESH REAL — a test will count as if the , computed as described above, exceeds THRESH (the original has a lil gap there, not me 🙈). 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 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 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 REAL array, dimension (max(NN)) — the eigenvalues of A. On exit, the eigenvalues in D correspond with the matrix in A. Modified.
  • Z COMPLEX 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 array, dimension (LDA, max(NN)) — workspace. Modified.
  • BB COMPLEX array, dimension (LDB, max(NN)) — workspace. Modified.
  • AP COMPLEX array, dimension (max(NN)**2) — workspace. Modified.
  • BP COMPLEX array, dimension (max(NN)**2) — workspace. Modified.
  • WORK COMPLEX 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 REAL 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 REAL array, dimension (70) — the values computed by the 70 tests described above. 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: LDZ < 1 or LDZ < NMAX.
    • -21: NWORK too small.
    • -23: LRWORK too small.
    • -25: LIWORK too small.

If CLATMR, CLATMS, CHEGV, CHPGV, CHBGV, CHEGVD, CHPGVD, CHPGVD, CHEGVX, CHPGVX, CHBGVX 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 SLAFTS).
  • 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 cdrvsg2stg.f.

🤖 Author (generated) 🤖

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