TESTING/EIG/cchkbb.f(3)

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🎀 TESTING/EIG/cchkbb.f(3) — Library Functions Manual 🎀

okay bestie, this is the TESTING/EIG/cchkbb.f(3) page and it is so much. It’s giving “I test the reduction of a general complex rectangular band matrix to real bidiagonal form” and honestly? iconic. Let’s go 💅

🌸 NAME 🌸

TESTING/EIG/cchkbb.f

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine cchkbb — the whole squad of arguments, coming right up:

subroutine cchkbb (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, rwork, result, info)
           CCHKBB

💖 Function/Subroutine Documentation 💖

🧚 subroutine cchkbb 🧚

subroutine cchkbb (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, complex, dimension(
       lda, * ) a, integer lda, complex, dimension( ldab, * ) ab, integer ldab,
       real, dimension( * ) bd, real, dimension( * ) be, complex, dimension(
       ldq, * ) q, integer ldq, complex, dimension( ldp, * ) p, integer ldp,
       complex, dimension( ldc, * ) c, integer ldc, complex, dimension( ldc, *
       ) cc, complex, dimension( * ) work, integer lwork, real, dimension( * )
       rwork, real, dimension( * ) result, integer info)
       CCHKBB

CCHKBB — yes bestie, that’s the name, periodt 💅

🌟 Purpose 🌟

okay so CCHKBB tests the reduction of a general complex rectangular band matrix to real bidiagonal form. no cap, that’s the whole assignment.

CGBBRD factors a general band matrix A as Q B P*, where * means conjugate transpose, B is upper bidiagonal, and Q and P are unitary; CGBBRD 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:

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

The types are specified by a logical array DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type j 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, CCHKBB 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, CCHKBB 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, CCHKBB 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 CCHKBB to continue the same random number sequence.
THRESH — THRESH is REAL. A test will count as a fail if the error ratio, 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 REAL 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 REAL 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 REAL array, dimension (max(NN)). Used to hold the diagonal of the bidiagonal matrix computed by CGBBRD.
BE — BE is REAL array, dimension (max(NN)). Used to hold the off-diagonal of the bidiagonal matrix computed by CGBBRD.
Q — Q is COMPLEX array, dimension (LDQ, max(NN)). Used to hold the unitary matrix Q computed by CGBBRD.
LDQ — LDQ is INTEGER. The leading dimension of Q. It must be at least 1 and at least max( NN ).
P — P is COMPLEX array, dimension (LDP, max(NN)). Used to hold the unitary matrix P computed by CGBBRD.
LDP — LDP is INTEGER. The leading dimension of P. It must be at least 1 and at least max( NN ).
C — C is COMPLEX array, dimension (LDC, max(NN)). Used to hold the matrix C updated by CGBBRD.
LDC — LDC is INTEGER. The leading dimension of U. It must be at least 1 and at least max( NN ).
CC — CC is COMPLEX array, dimension (LDC, max(NN)). Used to hold a copy of the matrix C.
WORK — WORK is COMPLEX 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).
RWORK — RWORK is REAL array, dimension (max(NN)).
RESULT — 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 — (this part of the page stops here, bestie — part 2 has the rest of INFO 🌈)
INFO (INTEGER) — if it comes back as 0, literally everything ran OK, no notes, we love to see it 💖

🫶 Some Local Variables and Parameters (the supporting cast, and yes they all ate)

The original page literally spells out the section title as ---- ----- --------- --- ---------- under it, so here's that whole lineup explained, bestie:

ZERO, ONE — the real numbers 0 and 1. iconic basics, they never miss ✨
MAXTYP — how many types are defined, periodt.
NTEST — the number of tests performed — or like, the ones that can be performed so far — for the current matrix.
NTESTT — the total number of tests performed so far across the whole saga.
NMAX — the largest value in NN.
NMATS — the number of matrices generated so far.
NERRS — the number of tests that have exceeded THRESH so far 😭 (the oopsies counter)
COND, IMODE — values that get passed to the matrix generators.
ANORM — the norm of A, which also gets passed to the matrix generators.

Then the threshold girlies:

OVFL, UNFL — the overflow and underflow thresholds 💀
ULP, ULPINV — the finest relative precision and its inverse 🔥
RTOVFL, RTUNFL — the square roots of the previous 2 values 🧚

And the following four arrays decode JTYPE — lowkey the cheat sheet for what kind of matrix you're looking at:

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) ) )

ngl those last three lines are written with a little dangling "for type ." in the source and I'm keeping it exactly as it is, that's just how the original vibes, no cap 🫶

👑 Author

Not one, not two, not three, but four whole institutions living in the credits:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 357 of file cchkbb.f — that's the receipts, right there 💅

🌈 Author (the meta one)

Generated automatically by Doxygen for LAPACK from the source code. Yes bestie, a robot wrote the doc for a program that tests matrix generators, we're living in the future fr fr 🤖✨

That's the whole page, we made it to the end, so here's your cute little sign-off: this was LAPACK, Version 3.12.0, doing its thing in TESTING/EIG/cchkbb.f(3). Go forth and vibe check those matrices, queen 💜🦋🎀

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms