TESTING/EIG/sdrves.f(3)

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version 3.12.1 · 3 versions
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💖 TESTING/EIG/sdrves.f 💖

okay bestie so this is sdrves.f, straight out of the Library Functions Manual (TESTING/EIG section) — and it is A LOT, so buckle up 🎀

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

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

SDRVES

🦋 Function/Subroutine Documentation 🦋

💅 the subroutine herself 💅

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

SDRVES

🎀 Purpose 🎀

k so here's the vibes: SDRVES checks the nonsymmetric eigenvalue (Schur form) problem driver SGEES. that's it, that's the job 💅

When SDRVES is called, a number of matrix () and a number of matrix 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 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 are specified by an array NN(1:NSIZES); the value of each element NN(j) specifies one size. The are specified by a logical array DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type 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, SDRVES 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, SDRVES 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 SDRVES to continue the same random number sequence.
  • THRESH — THRESH is REAL. A test will count as if the , 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 REAL 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 REAL array, dimension (LDA, max(NN)). Another copy of the test matrix A, modified by SGEES.
  • HT — HT is REAL array, dimension (LDA, max(NN)). Yet another copy of the test matrix A, modified by SGEES.
  • WR — WR is REAL array, dimension (max(NN)).
  • WI
  • WI — REAL array, dimension (max(NN)). The real and imaginary parts of the eigenvalues of A. On exit, WR + WI*i are the eigenvalues of the matrix in A.
  • WRT — REAL array, dimension (max(NN)). That's the whole spec, bestie — no extra description here.
  • WIT — REAL array, dimension (max(NN)). Like WR, WI, these arrays contain the eigenvalues of A, but those computed when SGEES only computes a partial eigendecomposition, i.e. not Schur vectors.
  • VS — REAL array, dimension (LDVS, max(NN)). VS holds the computed Schur vectors.
  • LDVS — INTEGER. Leading dimension of VS. Must be at least max(1,max(NN)).
  • RESULT — 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 — REAL 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.
  • IWORK — INTEGER array, dimension (max(NN)).
  • BWORK — LOGICAL array, dimension (max(NN)).
  • INFO — 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) ).
    • -17: LDVS < 1 or LDVS < NMAX, where NMAX is max( NN(j) ).
    • -20: NWORK too small.

If SLATMR, SLATMS, SLATME or SGEES 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) — 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 sdrves.f.

Author ✨

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And that's a wrap on this page, bestie 🫶 — footer source/version vibes: LAPACK Version 3.12.0, for TESTING/EIG/sdrves.f(3). 💖

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