TESTING/EIG/dchkbb.f(3)

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version 3.12.1 · 2 versions
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okay so this page is from TESTING/EIG/dchkbb.f(3) in the Library Functions Manual, and the file itself is TESTING/EIG/dchkbb.f. Buckle up, bestie 💅✨

💖 NAME 💖

TESTING/EIG/dchkbb.f

✨ SYNOPSIS ✨

Functions/Subroutines:

subroutine dchkbb (nsizes, mval, nval, nwdths, kk, ntypes, dotype, nrhs,
    iseed, thresh, nounit, a, lda, ab, ldab, bd, be, q, ldq, p, ldp, c,
    ldc, cc, work, lwork, result, info)
    DCHKBB

🧚 Function/Subroutine Documentation 🧚

Here's the subroutine in its full typed-out glory, no cap:

subroutine dchkbb (integer nsizes, integer, dimension( * ) mval, integer,
       dimension( * ) nval, integer nwdths, integer, dimension( * ) kk, integer
       ntypes, logical, dimension( * ) dotype, integer nrhs, integer,
       dimension( 4 ) iseed, double precision thresh, integer nounit, double
       precision, dimension( lda, * ) a, integer lda, double precision,
       dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )
       bd, double precision, dimension( * ) be, double precision, dimension(
       ldq, * ) q, integer ldq, double precision, dimension( ldp, * ) p,
       integer ldp, double precision, dimension( ldc, * ) c, integer ldc,
       double precision, dimension( ldc, * ) cc, double precision, dimension( *
       ) work, integer lwork, double precision, dimension( * ) result, integer
       info)
       DCHKBB

DCHKBB 👑

🌸 Purpose 🌸

DCHKBB tests the reduction of a general real rectangular band matrix to bidiagonal form. Periodt. 💖

DGBBRD factors a general band matrix A as Q B P*, where * means transpose, B is upper bidiagonal, and Q and P are orthogonal; DGBBRD can also overwrite a given matrix C with Q* C.

For each pair of matrix dimensions (M,N) and each selected matrix type, an M by N matrix A and an M by NRHS matrix C are generated. The problem dimensions are as follows:

  • A: M x N
  • Q: M x M
  • P: N x N
  • B: min(M,N) x min(M,N)
  • C: M x NRHS

For each generated matrix, 4 tests are performed:

  1. | A - Q B PT | / ( |A| max(M,N) ulp ), PT = P'
  2. | I - Q' Q | / ( M ulp )
  3. | I - PT PT' | / ( N ulp )
  4. | Y - Q' C | / ( |Y| max(M,NRHS) ulp ), where Y = Q' C.

These are specified by a logical array DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then that matrix type will be generated. Currently, the list of possible types is:

The possible matrix types are:

  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 (3), but multiplied by SQRT( overflow threshold )
  7. Same as (3), but multiplied by SQRT( underflow threshold )
  8. A matrix of the form U D V, where U and V are orthogonal and D has evenly spaced entries 1, ..., ULP with random signs on the diagonal.
  9. A matrix of the form U D V, where U and V are orthogonal and D has geometrically spaced entries 1, ..., ULP with random signs on the diagonal.
  10. A matrix of the form U D V, where U and V are 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. Rectangular 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 )

💜 Parameters 💜

  • NSIZES — NSIZES is INTEGER. The number of values of M and N contained in the vectors MVAL and NVAL. The matrix sizes are used in pairs (M,N). If NSIZES is zero, DCHKBB does nothing. NSIZES must be at least zero. 🫶
  • MVAL — MVAL is INTEGER array, dimension (NSIZES). The values of the matrix row dimension M.
  • NVAL — NVAL is INTEGER array, dimension (NSIZES). The values of the matrix column dimension N.
  • NWDTHS — NWDTHS is INTEGER. The number of bandwidths to use. If it is zero, DCHKBB does nothing. It must be at least zero.
  • KK — KK is INTEGER array, dimension (NWDTHS). An array containing the bandwidths to be used for the band matrices. The values must be at least zero.
  • NTYPES — NTYPES is INTEGER. The number of elements in DOTYPE. If it is zero, DCHKBB 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. .
  • DOTYPE — DOTYPE is 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.
  • NRHS — NRHS is INTEGER. The number of columns in the matrix C. If NRHS = 0, then the operations on the right-hand side will not be tested. NRHS must be at least 0.
  • ISEED — ISEED is 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 DCHKBB to continue the same random number sequence. 🎀
  • THRESH — THRESH is DOUBLE PRECISION. A test will count as a fail 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.
  • NOUNIT — NOUNIT is INTEGER. The FORTRAN unit number for printing out error messages (e.g., if a routine returns IINFO not equal to 0.)
  • A — A is DOUBLE PRECISION array, dimension (LDA, max(NN)). Used to hold the matrix A.
  • LDA — LDA is INTEGER. The leading dimension of A. It must be at least 1 and at least max( NN ).
  • AB — AB is DOUBLE PRECISION array, dimension (LDAB, max(NN)). Used to hold A in band storage format.
  • LDAB — LDAB is INTEGER. The leading dimension of AB. It must be at least 2 (not 1!) and at least max( KK )+1.
  • BD — BD is DOUBLE PRECISION array, dimension (max(NN)). Used to hold the diagonal of the bidiagonal matrix computed by DGBBRD.
  • BE — BE is DOUBLE PRECISION array, dimension (max(NN)). Used to hold the off-diagonal of the bidiagonal matrix computed by DGBBRD.
  • Q — Q is DOUBLE PRECISION array, dimension (LDQ, max(NN)). Used to hold the orthogonal matrix Q computed by DGBBRD.
  • LDQ — LDQ is INTEGER. The leading dimension of Q. It must be at least 1 and at least max( NN ).
  • P — P is DOUBLE PRECISION array, dimension (LDP, max(NN)). Used to hold the orthogonal matrix P computed by DGBBRD.
  • LDP — LDP is INTEGER. The leading dimension of P. It must be at least 1 and at least max( NN ).
  • C — C is DOUBLE PRECISION array, dimension (LDC, max(NN)). Used to hold the matrix C updated by DGBBRD.
  • LDC — LDC is INTEGER. The leading dimension of U — yes, U, bestie, that's literally what this page says 😭. It must be at least 1 and at least max( NN ).
  • CC — CC is DOUBLE PRECISION array, dimension (LDC, max(NN)). Used to hold a copy of the matrix C.
  • WORK — WORK is DOUBLE PRECISION array, dimension (LWORK).
  • LWORK — LWORK is INTEGER. The number of entries in WORK. This must be at least max( LDA+1, max(NN)+1 )*max(NN).
  • RESULT — RESULT is DOUBLE PRECISION array, dimension (4). The values computed by the tests described above. The values are currently limited to 1/ulp, to avoid overflow.
  • INFO

INFO is INTEGER — if it’s 0, then everything ran OK. That’s the whole vibe check, bestie: zero means success. ✨

🧸 Some Local Variables and Parameters:

---- ----- --------- --- ---------- — yes, that’s the original’s little decorative underline moment, not a value. 💅

  • ZERO, ONE — real 0 and 1.
  • MAXTYP — the number of types defined.
  • NTEST — the number of tests performed, or which can be performed so far, for the current matrix.
  • NTESTT — the total number of tests performed so far.
  • NMAX — largest value in NN.
  • NMATS — the number of matrices generated so far.
  • NERRS — the number of tests which have exceeded THRESH so far.
  • 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, the original says four and then lists these three — I’m not fixing it, I’m just delivering it exactly 💀)
    • 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 351 of file dchkbb.f.

🪄 Author

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Okay bestie, that’s the whole page: source TESTING/EIG/dchkbb.f(3), LAPACK Version 3.12.0 — and the date? Not in this footer, so we’re not inventing one. Periodt. 💖🫶

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