TESTING/EIG/ddrvsg.f(3)

📦
version 3.12.1 · 3 versions
, in arch rolling

TESTING/EIG/ddrvsg.f — bestie, this is the Library Functions Manual page for the ddrvsg test routine, and it’s serving major “I test the drivers so you don’t have to” energy. ✨

🌸 NAME 🌸

TESTING/EIG/ddrvsg.f

✨ SYNOPSIS ✨

🫶 Functions/Subroutines

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

DDRVSG

🎀 Function/Subroutine Documentation 🎀

💅 subroutine ddrvsg

Here’s the full signature, exactly as written, no cap:

   subroutine ddrvsg (integer nsizes, integer, dimension( * ) nn, integer
       ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed,
       double precision thresh, integer nounit, double precision, dimension(
       lda, * ) a, integer lda, double precision, dimension( ldb, * ) b,
       integer ldb, double precision, dimension( * ) d, double precision,
       dimension( ldz, * ) z, integer ldz, double precision, dimension( lda, *
       ) ab, double precision, dimension( ldb, * ) bb, double precision,
       dimension( * ) ap, double precision, dimension( * ) bp, double
       precision, dimension( * ) work, integer nwork, integer, dimension( * )
       iwork, integer liwork, double precision, dimension( * ) result, integer
       info)

DDRVSG

💫 Purpose

Okay so DDRVSG checks the real symmetric generalized eigenproblem drivers. It is literally the vibe check for all these routines:

  • DSYGV computes all eigenvalues and, optionally, eigenvectors of a real symmetric-definite generalized eigenproblem.
  • DSYGVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric-definite generalized eigenproblem using a divide and conquer algorithm.
  • DSYGVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric-definite generalized eigenproblem.
  • DSPGV computes all eigenvalues and, optionally, eigenvectors of a real symmetric-definite generalized eigenproblem in packed storage.
  • DSPGVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric-definite generalized eigenproblem in packed storage using a divide and conquer algorithm.
  • DSPGVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric-definite generalized eigenproblem in packed storage.
  • DSBGV computes all eigenvalues and, optionally, eigenvectors of a real symmetric-definite banded generalized eigenproblem.
  • DSBGVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric-definite banded generalized eigenproblem using a divide and conquer algorithm.
  • DSBGVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric-definite banded generalized eigenproblem.

When DDRVSG 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. DSYGV with ITYPE = 1 and UPLO ='U':

| A Z - B Z D | / ( |A| |Z| n ulp )

  1. as (1) but calling DSPGV
  2. as (1) but calling DSBGV
  3. as (1) but with UPLO = 'L'
  4. as (4) but calling DSPGV
  5. as (4) but calling DSBGV
  6. DSYGV with ITYPE = 2 and UPLO ='U':

| A B Z - Z D | / ( |A| |Z| n ulp )

  1. as (7) but calling DSPGV
  2. as (7) but with UPLO = 'L'
  3. as (9) but calling DSPGV
  4. DSYGV with ITYPE = 3 and UPLO ='U':

| B A Z - Z D | / ( |A| |Z| n ulp )

  1. as (11) but calling DSPGV
  2. as (11) but with UPLO = 'L'
  3. as (13) but calling DSPGV

DSYGVD, DSPGVD and DSBGVD performed the same 14 tests.

DSYGVX, DSPGVX and DSBGVX 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 orthogonal 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 orthogonal 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 orthogonal 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. 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

Okay so here come the arguments, one by one, no skips, no cap 💅

  • NSIZES INTEGER — the number of sizes of matrices to use. If it's zero, DDRVSG does literally nothing (like, why even call it? 💀). 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, DDRVSG 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 DDRVSG to continue the same random number sequence. Modified.
  • THRESH DOUBLE PRECISION — a test will count as [blank in original] if the [another 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.
The original has a couple of blank spots in that THRESH description — no cap, we're keeping them exactly as-is. 🫶
  • 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 DOUBLE PRECISION 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 and AB. It must be at least 1 and at least max( NN ). Not modified.
  • B DOUBLE PRECISION array, dimension (LDB , max(NN)) — used to hold the symmetric positive definite matrix for the generalized problem. On exit, B contains the last matrix actually used. Modified.
  • LDB INTEGER — the leading dimension of B and BB. 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 DOUBLE PRECISION array, dimension (LDZ, max(NN)) — the matrix of eigenvectors. Modified.
  • LDZ INTEGER — the leading dimension of Z. It must be at least 1 and at least max( NN ). Not modified.
  • AB DOUBLE PRECISION array, dimension (LDA, max(NN)) — workspace. Modified.
  • BB DOUBLE PRECISION array, dimension (LDB, max(NN)) — workspace. Modified.
  • AP DOUBLE PRECISION array, dimension (max(NN)**2) — workspace. Modified.
  • BP DOUBLE PRECISION array, dimension (max(NN)**2) — workspace. Modified.
  • WORK DOUBLE PRECISION array, dimension (NWORK) — workspace. Modified.
  • NWORK INTEGER — the number of entries in WORK. This must be at least 1+5*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 WORK. This must be at least 6*N. Not modified.
Yes, it says WORK here even though it's LIWORK — we're not editing that, bestie, we just report it. 💀
  • 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: LIWORK too small.

If DLATMR, SLATMS, DSYGV, DSPGV, DSBGV, SSYGVD, SSPGVD, DSBGVD, DSYGVX, DSPGVX or SSBGVX returns an error code, the absolute value of it is returned.

Modified.

🔍 Some Local Variables and Parameters (the backstage crew)

  • 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 [blank in original].
  • KMODE(j) — the MODE value to be passed to the matrix generator for type [blank in original].
  • KMAGN(j) — the order of magnitude ( O(1), O(overflow^(1/2) ), O(underflow^(1/2) ) )
The original says "The following four arrays decode JTYPE:" but then only lists three. We're not fixing it, periodt. 💅

🌸 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 352 of file ddrvsg.f.

🤖 Author (the Doxygen one)

Generated automatically by Doxygen for LAPACK from the source code.

And that's the whole page, bestie 🫶 Shoutout to LAPACK Version 3.12.0, page TESTING/EIG/ddrvsg.f(3) — no date on this one, but the vibes are timeless ✨💖

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