CDRVSG(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 cdrvsg.f(3) — Library Functions Manual 💖

bestie, this is the CDRVSG page, the file is cdrvsg.f, and the header path is /home/abui...IG/cdrvsg.f(3). Library Functions Manual is the manual name, folded in right here so you don't have to parse the raw header line. 🫶

🌸 NAME 🌸

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

like, that's literally the NAME section. iconic. 💅

🌈 SYNOPSIS 🌈

✨ Functions/Subroutines ✨

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

🦋 Function/Subroutine Documentation 🦋

   subroutine CDRVSG (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, 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)
       CDRVSG

🎀 Purpose: 🎀

Okay so CDRVSG checks the complex Hermitian generalized eigenproblem drivers. It's giving test-suite main character energy, and here's the driver fam it's checking:

  • 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 CDRVSG 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. obsessed with this setup, ngl.

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 )
  • (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. slay.

CHEGVX, CHPGVX and CHBGVX 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. This is how many matrix sizes you're gonna throw at it. If it's zero, CDRVSG literally does nothing (respect, honestly). Gotta be at least zero. Not modified — she's just reading, not touching. 🫶
  • NN — INTEGER array, dimension (NSIZES). The actual sizes your matrices are gonna be. Zero values get skipped (they're not invited to the party). Every value has to be at least zero. Not modified.
  • NTYPES — INTEGER. How many elements live in DOTYPE. If it's zero, CDRVSG does nothing. Must be at least zero. ⚠️ Special little exception: if it's MAXTYP+1 and NSIZES is 1, then an extra type — MAXTYP+1 — gets defined, and that one means "just use whatever matrix is already chilling in A". This is only useful when 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 every size in NN you get a matrix of that size and of type j generated. If NTYPES is smaller than the max number of types defined (PARAMETER MAXTYP), then types NTYPES+1 through MAXTYP just don't get generated. If NTYPES is larger than MAXTYP, then DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) get ignored (they're extra, nobody asked). Not modified.
  • ISEED — INTEGER array, dimension (4). The random number generator's seed, bestie — the vibe check for randomness. 🎲 On entry, the elements should be between 0 and 4095; if they're not, they get reduced mod 4096. Also ISEED(4) must be odd (no cap, that's just the rule). The generator uses a linear congruential sequence limited to small integers, so it should produce machine independent random numbers. On exit the values of ISEED are changed, and you can pass them into the next CDRVSG call to continue the same random number sequence. Modified. ✨
  • THRESH — REAL. A test will count as (the source literally drops a word here, that's just how the page is 💀) if the (same, also blank) — computed as described above — exceeds THRESH. Key deets: the error is scaled to be O(1), so THRESH should be a reasonably small multiple of 1, like, e.g., 10 or 100. In particular it should not depend on the precision (single vs. double) or on the size of the matrix. Must be at least zero. Not modified.
  • NOUNIT — INTEGER. The FORTRAN unit number used for printing out error messages (e.g., if a routine returns IINFO not equal to 0). That's where the drama gets reported. Not modified. 📠
  • A — COMPLEX array, dimension (LDA, max(NN)). Holds the matrix whose eigenvalues are gonna 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)). 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 — REAL array, dimension (max(NN)). The eigenvalues of A. On exit, the eigenvalues sitting 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 (yes, the page says ZZ — iconic typo energy, we keep it fr fr). 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. How many entries fit 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. How many entries fit 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)) (double paren, we don't question it 🎀). Workspace. Modified.
  • LIWORK — INTEGER. How many entries fit in IWORK. 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. Seventy. Iconic number. 👑 Modified.
  • INFO — INTEGER. If it's 0, everything ran OK, slay. 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.

And 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 🧚

(That's literally the heading — "Some Local Variables and Parameters" — and the page draws little dashes under it:)

---- ----- --------- --- ----------
  • ZERO, ONE — real 0 and 1. Humble. Essential.
  • 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.

And the following four arrays decode JTYPE (iykyk 🫶):

  • KTYPE(j) — the general type (1-10) for type (blank in the source, we leave the gap).
  • KMODE(j) — the MODE value to be passed to the matrix generator for type (again, blank).
  • 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 366 of file cdrvsg.f.

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code. (Not a human, just a very diligent little robot 🧚✨)

That's the whole thing, bestie — you made it to the end. 🎀 This page is from LAPACK, Version 3.12.0, and its footer path is /home/abui...IG/cdrvsg.f(3). Go forth and test your symmetric generalized eigenvalue routines with confidence. Mwah. 💖🦋
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