TESTING/EIG/zdrves.f(3)

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version 3.12.1 · 2 versions
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✨ zdrves: Schur-form driver checks, but make it a vibe ✨

🌈 NAME 🌈

TESTING/EIG/zdrves.f — yes bestie, that's literally the manual name. This is the TESTING/EIG/zdrves.f(3) page from the Library Functions Manual, and we're testing ZGEES with 13 checks and 21 matrix types. No cap, it's giving thorough. 💅

🦋 SYNOPSIS 🦋

Functions/Subroutines

  • subroutine zdrves — the main character. Signature below, exactly as it lives in the source, bestie.
subroutine zdrves (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a,
           lda, h, ht, w, wt, vs, ldvs, result, work, nwork, rwork, iwork,
           bwork, info)
           ZDRVES

🎀 Function/Subroutine Documentation 🎀

subroutine zdrves (...)

Full typed signature, copied exactly because we do not play with function signatures:

subroutine zdrves (integer nsizes, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, double precision thresh, integer nounit, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( lda, * ) h, complex*16, dimension( lda, * ) ht, complex*16, dimension( * ) w, complex*16, dimension( * ) wt, complex*16, dimension( ldvs, * ) vs, integer ldvs, double precision, dimension( 13 ) result, complex*16, dimension( * ) work, integer nwork, double precision, dimension( * ) rwork, integer, dimension( * ) iwork, logical, dimension( * ) bwork, integer info)
ZDRVES

💖 Purpose 💖

Okay so ZDRVES checks the nonsymmetric eigenvalue (Schur form) problem driver ZGEES. That's the whole assignment. 🫶

When ZDRVES is called, a number of matrix sizes and a number of matrix types are specified. For each size and each type of matrix, 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.
  3. | I - VS VS' | / ( n ulp ) — no sorting of eigenvalues.
  4. 0 if W are eigenvalues of T, 1/ulp otherwise — no sorting of eigenvalues.
  5. 0 if T(with VS) = T(without VS), 1/ulp otherwise — no sorting of eigenvalues.
  6. 0 if eigenvalues(with VS) = eigenvalues(without VS), 1/ulp otherwise — no sorting of eigenvalues.
  7. 0 if T is in Schur form, 1/ulp otherwise — with sorting of eigenvalues.
  8. | 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.
  9. | I - VS VS' | / ( n ulp ) — with sorting of eigenvalues.
  10. 0 if W are eigenvalues of T, 1/ulp otherwise — with sorting of eigenvalues.
  11. 0 if T(with VS) = T(without VS), 1/ulp otherwise — with sorting of eigenvalues.
  12. 0 if eigenvalues(with VS) = eigenvalues(without VS), 1/ulp otherwise — with sorting of eigenvalues.
  13. 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)
  5. A diagonal matrix with geometrically spaced entries 1, ..., ULP and random complex angles.
  6. A diagonal matrix with entries 1, ULP, ..., ULP and random complex angles.
  7. Same as (4), but multiplied by a constant near the overflow threshold.
  8. Same as (4), but multiplied by a constant near the underflow threshold.
  9. 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.
  10. 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.
  11. A matrix of the form U' T U, where U is orthogonal and T has 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 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.
  13. 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.
  14. 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.
  15. A matrix of the form X' T X, where X has condition SQRT( ULP ) and T has entries 1, ULP,..., ULP with random complex angles on the diagonal and random O(1) entries in the upper triangle.
  16. 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.
  17. Same as (16), but multiplied by a constant near the overflow threshold.
  18. Same as (16), but multiplied by a constant near the underflow threshold.
  19. 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.
  20. Same as (19), but multiplied by a constant near the overflow threshold.
  21. Same as (19), but multiplied by a constant near the underflow threshold.

🌸 Parameters 🌸

NSIZES

NSIZES is INTEGER. It's the number of sizes of matrices to use. If it is zero, ZDRVES does nothing. It must be at least zero. Very "if you don't ask, you don't get" energy. 🎀

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, ZDRVES 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 ZDRVES to continue the same random number sequence. 🌀

THRESH

THRESH is DOUBLE PRECISION. A test will count as a fail if the computed error, 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). Ngl, helpful when something goes feral. 😭

A

A is COMPLEX*16 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*16 array, dimension (LDA, max(NN)). Another copy of the test matrix A, modified by ZGEES.

HT

HT is COMPLEX*16 array, dimension (LDA, max(NN)). Yet another copy of the test matrix A, modified by ZGEES.

W

Okay so picking up right where the arg list left off, no recap, we move:

  • W — COMPLEX*16 array, dimension (max(NN)). These are the computed eigenvalues of A. 💅
  • WT — COMPLEX*16 array, dimension (max(NN)). Like W, this one also holds the eigenvalues of A, but these are the ones computed when ZGEES only does a partial eigendecomposition, i.e. not Schur vectors. 🫶
  • VS — COMPLEX*16 array, dimension (LDVS, max(NN)). VS is where the computed Schur vectors live. 🌸
  • LDVS — INTEGER. Leading dimension of VS. Must be at least max(1,max(NN)). No cap.
  • RESULT — DOUBLE PRECISION array, dimension (13). The values computed by the 13 tests described above. Currently these values are limited to 1/ulp so they don't overflow. 😭
  • WORK — COMPLEX*16 array, dimension (NWORK). 🛠️
  • NWORK — INTEGER. The number of entries in WORK. This must be at least 5*NN(j)+2*NN(j)**2 for all j. Periodt.
  • RWORK — DOUBLE PRECISION array, dimension (max(NN)). ✨
  • IWORK — INTEGER array, dimension (max(NN)). ✨
  • BWORK — LOGICAL array, dimension (max(NN)). ✨
  • INFO — INTEGER. If 0, then everything ran OK. Other values are giving:
    • -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 ZLATMR, CLATMS, CLATME or ZGEES returns an error code, the absolute value of it is returned. 🔥

🔍 Some Local Variables and Parameters 🔍

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 zdrves.f.

🦋 Author 🦋

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And that's the footer vibe, bestie: source/version is LAPACK Version 3.12.0, page is TESTING/EIG/zdrves.f(3). That's literally the whole footer line, no extra date hiding there — still iconic. 💖✨

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