TESTING/EIG/ddrves.f(3)

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version 3.12.1 · 3 versions
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🎀 NAME 🎀

Okay so this is the TESTING/EIG/ddrves.f(3) page from the Library Functions Manual — and yes, bestie, the whole NAME section is literally TESTING/EIG/ddrves.f. Iconic. 💖

✨ SYNOPSIS ✨

💅 Functions/Subroutines 💅

  • subroutine ddrves (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a, lda, h, ht, wr, wi, wrt, wit, vs, ldvs, result, work, nwork, iwork, bwork, info) — DDRVES

🌸 Function/Subroutine Documentation 🌸

Here's the full signature with all the types and dimensions, no cap:

subroutine ddrves (integer nsizes, integer, dimension( * ) nn, integer
ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed,
double precision thresh, integer nounit, double precision, dimension(
lda, * ) a, integer lda, double precision, dimension( lda, * ) h, double
precision, dimension( lda, * ) ht, double precision, dimension( * ) wr,
double precision, dimension( * ) wi, double precision, dimension( * )
wrt, double precision, dimension( * ) wit, double precision, dimension(
ldvs, * ) vs, integer ldvs, double precision, dimension( 13 ) result,
double precision, dimension( * ) work, integer nwork, integer,
dimension( * ) iwork, logical, dimension( * ) bwork, integer info)
DDRVES

DDRVES — that's the name again, periodt. 👑

🦋 Purpose 🦋

DDRVES checks the nonsymmetric eigenvalue (Schur form) problem driver DGEES.

When DDRVES is called, a number of matrix sizes (NSIZES) and a number of matrix types (NTYPES) are specified. For each size (NN(j)) 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 WR+sqrt(-1)*WI 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 WR+sqrt(-1)*WI 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 matrix sizes are specified by an array NN(1:NSIZES); the value of each element NN(j) specifies one size.

The matrix 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 signs. (ULP = (first number larger than 1) - 1 )
  • (5) A diagonal matrix with geometrically spaced entries 1, ..., ULP and random signs.
  • (6) A diagonal matrix with entries 1, ULP, ..., ULP and random signs.
  • (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 orthogonal and T has evenly spaced entries 1, ..., ULP with random signs on the diagonal and random O(1) entries in the upper triangle.
  • (10) A matrix of the form U' T U, where U is orthogonal and T has geometrically spaced entries 1, ..., ULP with random signs 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 signs on the diagonal and random O(1) entries in the upper triangle.
  • (12) A matrix of the form U' T U, where U is orthogonal and T has real or complex conjugate paired eigenvalues randomly chosen from ( ULP, 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 signs 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 signs 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 signs 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 real or complex conjugate paired eigenvalues randomly chosen from ( ULP, 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. The number of sizes of matrices to use. If it is zero, DDRVES 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, DDRVES 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 DDRVES to continue the same random number sequence.

THRESH

THRESH is DOUBLE PRECISION. A test will count as a failure if the error, computed as described above, exceeds THRESH.

Bestie, 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDA, max(NN)). Another copy of the test matrix A, modified by DGEES.

HT

HT — and this page part cuts off right here, bestie; part 2 picks it up. 🫶

  • HT — is a DOUBLE PRECISION array, dimension (LDA, max(NN)). It's yet another copy of the test matrix A, modified by DGEES. 💅
  • WR — is a DOUBLE PRECISION array, dimension (max(NN)).
  • WI — is a DOUBLE PRECISION array, dimension (max(NN)). Together, WR and WI hold the real and imaginary parts of the eigenvalues of A: on exit, WR + WI*i are the eigenvalues of the matrix in A. 💖
  • WRT — is a DOUBLE PRECISION array, dimension (max(NN)).
  • WIT — is a DOUBLE PRECISION array, dimension (max(NN)). Like WR, WI, these arrays contain the eigenvalues of A, but those computed when DGEES only computes a partial eigendecomposition, i.e. not Schur vectors. 🌀
  • VS — is a DOUBLE PRECISION array, dimension (LDVS, max(NN)). VS holds the computed Schur vectors. 👑
  • LDVS — is INTEGER. Leading dimension of VS. Must be at least max(1,max(NN)). ✨
  • RESULT — is a DOUBLE PRECISION array, dimension (13). The values computed by the 13 tests described above. The values are currently limited to 1/ulp, to avoid overflow. 🔥
  • WORK — is a DOUBLE PRECISION array, dimension (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. 🫶
  • IWORK — is INTEGER array, dimension (max(NN)).
  • BWORK — is LOGICAL array, dimension (max(NN)).
  • INFO — is INTEGER. If 0, then everything ran OK. 💚 The error codes are:
    • -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) ).
    • -17: LDVS < 1 or LDVS < NMAX, where NMAX is max( NN(j) ).
    • -20: NWORK too small.
    • If DLATMR, SLATMS, SLATME or DGEES 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) — selects (the source spells it Selectw) 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 385 of file ddrves.f.

🌈 AUTHOR (the Doxygen remix)

Generated automatically by Doxygen for LAPACK from the source code.

Bye bestie 💖 — this page is LAPACK Version 3.12.0, file TESTING/EIG/ddrves.f(3). Slay and stay curious. ✨
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