SCHKBB(3)

📦 version 3.12.0, in opensuse-leap 16.0

🎀 SCHKBB(3) — band-matrix bidiagonal reduction test vibes 🎀

🌸 NAME 🌸

SCHKBB is the main character here, and her source file is literally this path, bestie:

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

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

subroutine SCHKBB (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)
    SCHKBB

💖 Function/Subroutine Documentation 💖

🧚 subroutine SCHKBB

Here’s the full typed signature, no cap:

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

🦋 Purpose 🦋

Okay so SCHKBB tests the reduction of a general real rectangular band matrix to bidiagonal form. She’s literally the vibe-checker for that whole process.

SGBBRD factors a general band matrix A as Q B P*, where * means transpose, B is upper bidiagonal, and Q and P are orthogonal; SGBBRD 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.

The (the source leaves a blank right here, bestie) are specified by a logical array DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type (another source blank, iykyk) 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 (blank in the source) 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 (blank in the source) 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 — 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, SCHKBB does nothing. NSIZES must be at least zero.
  • MVAL — is INTEGER array, dimension (NSIZES). The values of the matrix row dimension M.
  • NVAL — is INTEGER array, dimension (NSIZES). The values of the matrix column dimension N.
  • NWDTHS — is INTEGER. The number of bandwidths to use. If it is zero, SCHKBB does nothing. It must be at least zero.
  • 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 — is INTEGER. The number of elements in DOTYPE. If it is zero, SCHKBB 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 — 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 — 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 — 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 SCHKBB to continue the same random number sequence.
  • THRESH — is REAL. A test will count as (blank in the source) if the (blank in the source), 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 — is INTEGER. The FORTRAN unit number for printing out error messages (e.g., if a routine returns IINFO not equal to 0.)
  • A — is REAL array, dimension (LDA, max(NN)). Used to hold the matrix A.
  • LDA — is INTEGER. The leading dimension of A. It must be at least 1 and at least max( NN ).
  • AB — is REAL array, dimension (LDAB, max(NN)). Used to hold A in band storage format.
  • LDAB — is INTEGER. The leading dimension of AB. It must be at least 2 (not 1!) and at least max( KK )+1.
  • BD — is REAL array, dimension (max(NN)). Used to hold the diagonal of the bidiagonal matrix computed by SGBBRD.
  • BE — is REAL array, dimension (max(NN)). Used to hold the off-diagonal of the bidiagonal matrix computed by SGBBRD.
  • Q — is REAL array, dimension (LDQ, max(NN)). Used to hold the orthogonal matrix Q computed by SGBBRD.
  • LDQ — is INTEGER. The leading dimension of Q. It must be at least 1 and at least max( NN ).
  • P — is REAL array, dimension (LDP, max(NN)). Used to hold the orthogonal matrix P computed by SGBBRD.
  • LDP — is INTEGER. The leading dimension of P. It must be at least 1 and at least max( NN ).
  • C — is REAL array, dimension (LDC, max(NN)). Used to hold the matrix C updated by SGBBRD.
  • LDC — is INTEGER. The leading dimension of U. It must be at least 1 and at least max( NN ).
  • CC — is REAL array, dimension (LDC, max(NN)). Used to hold a copy of the matrix C.
  • WORK — is REAL array, dimension (LWORK).
  • LWORK — is INTEGER. The number of entries in WORK. This must be at least max( LDA+1, max(NN)+1 )*max(NN).
  • RESULT — is REAL array, dimension (4). The values computed by the tests described above. The values are currently limited to 1/ulp, to avoid overflow.
  • INFO — the source cuts off right here in part 1, bestie, so no description yet.

…and then INFO is an INTEGER, bestie. If it's 0, then everything ran OK — zero is the slay result. ✨

🧚 Some Local Variables and Parameters

  • ZERO, ONE — the 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:

  • 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

Definition at line 351 of file schkbb.f.

🤖 Author (again)

Generated automatically by Doxygen for LAPACK from the source code.

That's a wrap, bestie — source/version: LAPACK Version 3.12.0, path: /home/abui...IG/schkbb.f(3). Date? Not in this footer chunk, but the vibes are eternal. 💖

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