DDRVSG(3)

💅 NAME 💅

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

ok so that's literally the whole NAME section — it's just the file path, bestie. it's DDRVSG, it lives at that path, and the rest of this page is the ✨lore✨.

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

DDRVSG — the one and only subroutine this whole page is about.

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 🎀

ok so here's the FULL signature with every single type declaration, no cap, i'm not skipping a single one because that would be disrespectful to the compiler:

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 picture this: DDRVSG is basically the quality-control bestie for the real symmetric generalized eigenproblem drivers. it doesn't do the math for you — it checks the drivers that do the math. she's the vibe check. she's the group chat admin verifying everyone's homework. 🕵️‍♀️✨

here's the cast of drivers she's checking on, and what each one does, in her own words:

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.

like… the range. the versatility. the way they all just exist. 👑

so when DDRVSG gets 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.

like, one matrix A, one nice well-behaved B, and then the drivers get put through their paces together. it's giving collab era. 🫶

🔥 the tests 🔥

for each pair (A,B), the following tests are performed — and yes, i'm listing all of them, we don't do "etc." in this house:

(1) DSYGV with ITYPE = 1 and UPLO ='U':

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

(2) as (1) but calling DSPGV

(3) as (1) but calling DSBGV

(4) as (1) but with UPLO = 'L'

(5) as (4) but calling DSPGV

(6) as (4) but calling DSBGV

(7) DSYGV with ITYPE = 2 and UPLO ='U':

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

(8) as (7) but calling DSPGV

(9) as (7) but with UPLO = 'L'

(10) as (9) but calling DSPGV

(11) DSYGV with ITYPE = 3 and UPLO ='U':

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

(12) as (11) but calling DSPGV

(13) as (11) but with UPLO = 'L'

(14) as (13) but calling DSPGV

notice the pattern? ITYPE 1, 2, 3, and UPLO 'U' then 'L', and the packed and banded friends tagging along. it's a whole routine. literally a whole routine. 😭

DSYGVD, DSPGVD and DSBGVD performed the same 14 tests. same energy, different algorithm. 💫

DSYGVX, DSPGVX and DSBGVX performed the above 14 tests with the parameter RANGE = 'A', 'N' and 'I', respectively. so that's 14 tests × 3 range values for the X-suffixed girlies. she's thorough. she's that girl. 💅

🌈 the matrices 🌈

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).

ok so KA is the main character half-bandwidth and KB is the well-behaved sidekick, and KB is always <= KA because she's polite. 🎀

currently, the list of possible types for A is — brace yourself, there's 21 of them and i'm giving you all 21:

(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

quick vibe check on (6), (7), (11), (12), (14) and (15) — those are the ones multiplied by SQRT( overflow threshold ) and SQRT( underflow threshold ), so they're deliberately hanging out at the extreme edges of what floating point can handle. that's the whole point of them, bestie, don't be alarmed. 🌊

and that's the matrix menu — 21 flavours, evenly and geometrically spaced, orthogonal-sandwiched, banded, and threshold-pushed. a full buffet, no notes. 🍓🧚

NSIZES (INTEGER) — The number of sizes of matrices to use. If it is zero, DDRVSG 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 is 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 … if the …, computed as described above, exceeds THRESH. (Yep, the source literally has blanks there — I'm not out here inventing words, bestie.) 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 — 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.
RESULT — DOUBLE PRECISION 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 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 🧮

---- ----- --------- --- ----------

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 (yes, it says four — I'm just the messenger 🫶):

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 352 of file ddrvsg.f.

📝 Author 📝

Generated automatically by Doxygen for LAPACK from the source code.

Catch you later, bestie! 🌈 This page's footer is giving LAPACK, Version 3.12.0, and source path /home/abui...IG/ddrvsg.f(3). No date is shown in the footer — that's not me being shady, that's just what the footer says. 💅✨

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