CDRVES(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 CDRVES(3) — the Schur-form driver test, bestie edition 🎀

Part 1 of 2, and we're stopping right at W — no spoilers, no fake ending. The manual name is CDRVES(3), and this page comes from the Library Functions Manual.

✨ NAME ✨

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

That's the file path, and the manual name is CDRVES(3). It lives in the Library Functions Manual, and it's giving "I check the nonsymmetric eigenvalue (Schur form) problem driver CGEES" energy, fr fr.

🦋 SYNOPSIS 🦋

Functions/Subroutines:

subroutine CDRVES (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a,
    lda, h, ht, w, wt, vs, ldvs, result, work, nwork, rwork, iwork,
    bwork, info)
    CDRVES

🔥 Function/Subroutine Documentation 🔥

subroutine CDRVES (integer nsizes, integer, dimension( * ) nn, integer
    ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed,
    real thresh, integer nounit, complex, dimension( lda, * ) a, integer
    lda, complex, dimension( lda, * ) h, complex, dimension( lda, * ) ht,
    complex, dimension( * ) w, complex, dimension( * ) wt, complex,
    dimension( ldvs, * ) vs, integer ldvs, real, dimension( 13 ) result,
    complex, dimension( * ) work, integer nwork, real, dimension( * ) rwork,
    integer, dimension( * ) iwork, logical, dimension( * ) bwork, integer
    info)
    CDRVES

That's the whole signature, exactly as the page has it. No cap.

💖 Purpose 💖

CDRVES checks the nonsymmetric eigenvalue (Schur form) problem driver CGEES. Periodt.

When CDRVES is called, you specify a number of matrix sizes and a number of matrix types. For each size and each matrix type, one matrix will be generated and used to test the nonsymmetric eigenroutines. For each matrix, 13 tests will be performed:

  1. 0 if T is in Schur form, 1/ulp otherwise (no sorting of eigenvalues).
  2. | A - VS T VS' | / ( n |A| ulp )

Here VS is the matrix of Schur eigenvectors, and T is in Schur form (no sorting of eigenvalues).

  1. | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues).
  2. 0 if W are eigenvalues of T; 1/ulp otherwise (no sorting of eigenvalues).
  3. 0 if T(with VS) = T(without VS); 1/ulp otherwise (no sorting of eigenvalues).
  4. 0 if eigenvalues(with VS) = eigenvalues(without VS); 1/ulp otherwise (no sorting of eigenvalues).
  5. 0 if T is in Schur form, 1/ulp otherwise (with sorting of eigenvalues).
  6. | A - VS T VS' | / ( n |A| ulp )

Here VS is the matrix of Schur eigenvectors, and T is in Schur form (with sorting of eigenvalues).

  1. | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues).
  2. 0 if W are eigenvalues of T; 1/ulp otherwise (with sorting of eigenvalues).
  3. 0 if T(with VS) = T(without VS); 1/ulp otherwise (with sorting of eigenvalues).
  4. 0 if eigenvalues(with VS) = eigenvalues(without VS); 1/ulp otherwise (with sorting of eigenvalues).
  5. If sorting worked and SDIM is the number of eigenvalues which were SELECTed.

The sizes are specified by an array NN(1:NSIZES); the value of each element NN(j) specifies one size. 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:

  1. The zero matrix.
  2. The identity matrix.
  3. A (transposed) Jordan block, with 1's on the diagonal.
  4. A diagonal matrix with evenly spaced entries 1, ..., ULP and random complex angles.

(ULP = (first number larger than 1) - 1)

  1. A diagonal matrix with geometrically spaced entries 1, ..., ULP and random complex angles.
  2. A diagonal matrix with [blank] entries 1, ULP, ..., ULP and random complex angles.
  3. Same as (4), but multiplied by a constant near the overflow threshold.
  4. Same as (4), but multiplied by a constant near the underflow threshold.
  5. A matrix of the form U' T U, where U is unitary and T has evenly spaced entries 1, ..., ULP with random complex angles on the diagonal and random O(1) entries in the upper triangle.
  6. A matrix of the form U' T U, where U is unitary and T has geometrically spaced entries 1, ..., ULP with random complex angles on the diagonal and random O(1) entries in the upper triangle.
  7. A matrix of the form U' T U, where U is orthogonal and T has [blank] entries 1, ULP,..., ULP with random complex angles on the diagonal and random O(1) entries in the upper triangle.
  8. A matrix of the form U' T U, where U is unitary and T has complex eigenvalues randomly chosen from ULP < |z| < 1 and random O(1) entries in the upper triangle.
  9. A matrix of the form X' T X, where X has condition SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP with random complex angles on the diagonal and random O(1) entries in the upper triangle.
  10. A matrix of the form X' T X, where X has condition SQRT( ULP ) and T has geometrically spaced entries 1, ..., ULP with random complex angles on the diagonal and random O(1) entries in the upper triangle.
  11. A matrix of the form X' T X, where X has condition SQRT( ULP ) and T has [blank] entries 1, ULP,..., ULP with random complex angles on the diagonal and random O(1) entries in the upper triangle.
  12. A matrix of the form X' T X, where X has condition SQRT( ULP ) and T has complex eigenvalues randomly chosen from ULP < |z| < 1 and random O(1) entries in the upper triangle.
  13. Same as (16), but multiplied by a constant near the overflow threshold.
  14. Same as (16), but multiplied by a constant near the underflow threshold.
  15. Nonsymmetric matrix with random entries chosen from (-1,1). If N is at least 4, all entries in first two rows and last row, and first column and last two columns are zero.
  16. Same as (19), but multiplied by a constant near the overflow threshold.
  17. Same as (19), but multiplied by a constant near the underflow threshold.

🌈 Parameters 🌈

NSIZES

NSIZES is INTEGER. The number of sizes of matrices to use. If it is zero, CDRVES does nothing. It must be at least zero.

NN

NN is 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.

NTYPES

NTYPES is INTEGER. The number of elements in DOTYPE. If it is zero, CDRVES 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.

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 CDRVES to continue the same random number sequence.

THRESH

THRESH is REAL. A test will count as failed 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 INFO not equal to 0.)

A

A is COMPLEX 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.

LDA

LDA is INTEGER. The leading dimension of A, and H. LDA must be at least 1 and at least max( NN ).

H

H is COMPLEX array, dimension (LDA, max(NN)). Another copy of the test matrix A, modified by CGEES.

HT

HT is COMPLEX array, dimension (LDA, max(NN)). Yet another copy of the test matrix A, modified by CGEES.

W

(The source for part 1 ends right at W; the description continues in part 2.)

Continuing straight into the argument tea ☕ — no cap, every param stays exactly as it is, just with better vibes. 💅

  • W — W is COMPLEX array, dimension (max(NN)). The computed eigenvalues of A. 💖
  • WT — WT is COMPLEX array, dimension (max(NN)). Like W, this array contains the eigenvalues of A, but those computed when CGEES only computes a partial eigendecomposition, i.e. not Schur vectors. 🦋
  • VS — VS is COMPLEX array, dimension (LDVS, max(NN)). VS holds the computed Schur vectors. ✨
  • LDVS — LDVS is INTEGER. Leading dimension of VS. Must be at least max(1,max(NN)). 🎀
  • RESULT — RESULT is REAL array, dimension (13). The values computed by the 13 tests described above. The values are currently limited to 1/ulp, to avoid overflow. 🌸
  • WORK — WORK is COMPLEX array, dimension (NWORK). 🔥
  • NWORK — NWORK is INTEGER. The number of entries in WORK. This must be at least 5*NN(j)+2*NN(j)**2 for all j. 👑
  • RWORK — RWORK is REAL array, dimension (max(NN)). 🌈
  • IWORK — IWORK is INTEGER array, dimension (max(NN)). ⭐
  • BWORK — BWORK is LOGICAL array, dimension (max(NN)). 🍓
  • INFO — INFO is INTEGER. If 0, then everything ran OK. 🫶
    • -1: NSIZES < 0
    • -2: Some NN(j) < 0
    • -3: NTYPES < 0
    • -6: THRESH < 0
    • -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
    • -15: LDVS < 1 or LDVS < NMAX, where NMAX is max( NN(j) ).
    • -18: NWORK too small.

If CLATMR, CLATMS, CLATME or CGEES returns an error code, the absolute value of it is returned. 😭

🧚 Some Local Variables and Parameters 🧚

  • ZERO, ONE — Real 0 and 1.
  • MAXTYP — The number of types defined.
  • NMAX — Largest value in NN.
  • NERRS — The number of tests which have exceeded THRESH
  • COND, CONDS, 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.
  • RTULP, RTULPI — Square roots of the previous 4 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) )
  • KCONDS(j) — Select whether CONDS is to be 1 or 1/sqrt(ulp). (0 means irrelevant.)

👑 Author

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

Definition at line 375 of file cdrves.f. 🎀

👑 Author

Generated automatically by Doxygen for LAPACK from the source code. 💻

And that’s a wrap on CDRVES(3), bestie! 💅 Source: /home/abui...IG/cdrves.f(3); version: 3.12.0. The footer didn’t give a date, so I’m not inventing one — no cap. 🫶✨

📦 where this page comes from