TESTING/EIG/sdrvsg.f(3)

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version 3.12.1 · 3 versions
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💖 TESTING/EIG/sdrvsg.f 💖

Library Functions Manual — part 1, bestie. Every detail stays, the vibe just gets cuter.

NAME ✨

TESTING/EIG/sdrvsg.f — that's the page name, no cap.

SYNOPSIS 🎀

Functions/Subroutines

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 🦋

subroutine sdrvsg — the long signature, bestie 💅

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: 🌸

okay so SDRVSG is out here checking the real symmetric generalized eigenproblem drivers. It is not doing just one little eigendecomposition — it is running the whole squad through a vibe check:

  • 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 <italic>[blank in the source]</italic> () and a number of matrix <italic>[blank in the source]</italic> are specified. For each size <italic>[blank in the source]</italic> () 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 )
  • (2) as (1) but calling SSPGV
  • (3) as (1) but calling SSBGV
  • (4) as (1) but with UPLO = 'L'
  • (5) as (4) but calling SSPGV
  • (6) as (4) but calling SSBGV
  • (7) SSYGV with ITYPE = 2 and UPLO ='U': | A B Z - Z D | / ( |A| |Z| n ulp )
  • (8) as (7) but calling SSPGV
  • (9) as (7) but with UPLO = 'L'
  • (10) as (9) but calling SSPGV
  • (11) SSYGV with ITYPE = 3 and UPLO ='U': | B A Z - Z D | / ( |A| |Z| n ulp )
  • (12) as (11) but calling SSPGV
  • (13) as (11) but with UPLO = 'L'
  • (14) 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 <italic>[blank in the source]</italic> are specified by an array NN(1:NSIZES); the value of each element NN(j) specifies one size. The <italic>[blank in the source]</italic> are specified by a logical array DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type <italic>[blank in the source]</italic> 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 <italic>[blank in the source]</italic> 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 <italic>[blank in the source]</italic> 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 matrix sizes we’re testing. If it’s zero, SDRVSG literally does nothing. It must be at least zero. Not modified, bestie.
  • NN (INTEGER array, dimension (NSIZES)) — the actual sizes to use for the matrices. Zero values get skipped. Every value must be at least zero. Not modified.
  • NTYPES (INTEGER) — how many elements are 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 extra type, MAXTYP+1, is defined, which means “use whatever matrix is already 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 gets 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, then DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) get ignored. Not modified.
  • ISEED (INTEGER array, dimension (4)) — on entry, this is the seed for the random number generator. The array elements should be between 0 and 4095; if they aren’t, they get reduced mod 4096. Also, ISEED(4) must be odd. The random number generator uses a linear congruential sequence limited to small integers, so it should produce machine independent random numbers. The values of ISEED are changed on exit, and you can use them in the next call to SDRVSG to continue the same random number sequence. Modified.
  • THRESH (REAL) — a test will count as [the thing] if the [value], 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

  • 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 352 of file sdrvsg.f.

👑 Author

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Okay that’s the whole vibe 💖 — source/version: LAPACK Version 3.12.0; file: TESTING/EIG/sdrvsg.f(3); date: none shown in the footer. Mwah 💅

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