SDRVSG(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 SDRVSG(3) — Library Functions Manual 💅

Okay bestie, this page is from the Library Functions Manual, and it's literally the vibe check for the real symmetric generalized eigenproblem drivers. The page is SDRVSG(3), and yes, the energy is very "trust me, I know what I'm doing with Fortran" ✨

✨ NAME ✨

The NAME here is this exact file path, no cap:

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

That's it. That's the name. The manual is the Library Functions Manual, and the page is SDRVSG(3) 🫶

🌸 SYNOPSIS 🌸

Under Functions/Subroutines, the synopsis is giving:

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

🦋 Function/Subroutine Documentation 🦋

Okay so here's the full signature with all the types and dimensions, because the synopsis loves a glow-up:

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

💖 Purpose: 💖

So the main-character mission is simple: SDRVSG checks the real symmetric generalized eigenproblem drivers. Periodt. 💅

Here's the driver lineup it's checking:

  • SSYGV computes all eigenvalues and, optionally, eigenvectors of a real symmetric-definite generalized eigenproblem.
  • SSYGVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric-definite generalized eigenproblem using a divide and conquer algorithm.
  • SSYGVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric-definite generalized eigenproblem.
  • SSPGV computes all eigenvalues and, optionally, eigenvectors of a real symmetric-definite generalized eigenproblem in packed storage.
  • SSPGVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric-definite generalized eigenproblem in packed storage using a divide and conquer algorithm.
  • SSPGVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric-definite generalized eigenproblem in packed storage.
  • SSBGV computes all eigenvalues and, optionally, eigenvectors of a real symmetric-definite banded generalized eigenproblem.
  • SSBGVD computes all eigenvalues and, optionally, eigenvectors of a real symmetric-definite banded generalized eigenproblem using a divide and conquer algorithm.
  • SSBGVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric-definite banded generalized eigenproblem.

When SDRVSG is called, a number of matrix sizes and a number of matrix types 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. SSYGV with ITYPE = 1 and UPLO ='U':

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

  1. as (1) but calling SSPGV
  2. as (1) but calling SSBGV
  3. as (1) but with UPLO = 'L'
  4. as (4) but calling SSPGV
  5. as (4) but calling SSBGV
  6. SSYGV with ITYPE = 2 and UPLO ='U':

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

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

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

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

SSYGVD, SSPGVD and SSBGVD performed the same 14 tests. 🔥

SSYGVX, SSPGVX and SSBGVX performed the above 14 tests with the parameter RANGE = 'A', 'N' and 'I', respectively.

The array NN(1:NSIZES) specifies the sizes; the value of each element NN(j) specifies one size. The logical array DOTYPE( 1:NTYPES ) specifies the types; 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
  • NSIZES — INTEGER 🌸 The number of sizes of matrices to use. If it’s zero, SDRVSG 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, SDRVSG 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 SDRVSG to continue the same random number sequence. Modified.
  • THRESH — REAL ⭐ A test counts as flagged if the error, 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 — REAL 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 — REAL 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 — REAL array, dimension (max(NN)) 🍓 The eigenvalues of A. On exit, the eigenvalues in D correspond with the matrix in A. Modified.
  • Z — REAL 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 — REAL array, dimension (LDA, max(NN)) 🌸 Workspace. Modified.
  • BB — REAL array, dimension (LDB, max(NN)) 🦋 Workspace. Modified.
  • AP — REAL array, dimension (max(NN)**2) ✨ Workspace. Modified.
  • BP — REAL array, dimension (max(NN)**2) 💅 Workspace. Modified.
  • WORK — REAL 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.
  • 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: LIWORK too small.
    • If SLATMR, SLATMS, SSYGV, SSPGV, SSBGV, SSYGVD, SSPGVD, SSBGVD, SSYGVX, SSPGVX or SSBGVX returns an error code, the absolute value of it is returned. Modified.

🧠 Some Local Variables and Parameters 🧠

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 j.
  • KMODE(j) — The MODE value to be passed to the matrix generator for type j.
  • 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 352 of file sdrvsg.f.

🪄 Author (Doxygen page credit) 🪄

Generated automatically by Doxygen for LAPACK from the source code.

And that’s the footer tea ☕: LAPACK Version 3.12.0, source path /home/abui...IG/sdrvsg.f(3). No date is printed in this footer, so I’m not gonna invent one — periodt. 💖

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