TESTING/EIG/cdrvst.f(3)

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version 3.12.1 · 2 versions
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🎀 TESTING/EIG/cdrvst.f(3) 🎀

Okay bestie, this is the TESTING/EIG/cdrvst.f page from the Library Functions Manual, and it is highkey iconic because it's all about CDRVST checking the Hermitian eigenvalue problem drivers. No cap. ✨

🌸 NAME 🌸

TESTING/EIG/cdrvst.f

✨ SYNOPSIS ✨

Functions/Subroutines

  • subroutine cdrvst (...) — the whole signature is right here, so copy it exactly, bestie:
subroutine cdrvst (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a,
    lda, d1, d2, d3, wa1, wa2, wa3, u, ldu, v, tau, z, work, lwork,
    rwork, lrwork, iwork, liwork, result, info)
  • CDRVST — that's the name, and yes it's giving main character energy. 💅

📚 Function/Subroutine Documentation 📚

🧚 subroutine cdrvst 🧚

subroutine cdrvst (integer nsizes, integer, dimension( * ) nn, integer
    ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed,
    real thresh, integer nounit, complex, dimension( lda, * ) a, integer
    lda, real, dimension( * ) d1, real, dimension( * ) d2, real, dimension(
    * ) d3, real, dimension( * ) wa1, real, dimension( * ) wa2, real,
    dimension( * ) wa3, complex, dimension( ldu, * ) u, integer ldu,
    complex, dimension( ldu, * ) v, complex, dimension( * ) tau, complex,
    dimension( ldu, * ) z, complex, dimension( * ) work, integer lwork,
    real, dimension( * ) rwork, integer lrwork, integer, dimension( * )
    iwork, integer liwork, real, dimension( * ) result, integer info)

CDRVST

Purpose 💖

CDRVST checks the Hermitian eigenvalue problem drivers. Basically it's the vibe check for these routines:

  • CHEEVD computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, using a divide-and-conquer algorithm.
  • CHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix.
  • CHEEVR computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix using the Relatively Robust Representation where it can.
  • CHPEVD computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage, using a divide-and-conquer algorithm.
  • CHPEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage.
  • CHBEVD computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix, using a divide-and-conquer algorithm.
  • CHBEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix.
  • CHEEV computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix.
  • CHPEV computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage.
  • CHBEV computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix.

When CDRVST 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 appropriate drivers. For each matrix and each driver routine called, the following tests will be performed:

  1. | A - Z D Z' | / ( |A| n ulp )
  2. | I - Z Z' | / ( n ulp )
  3. | D1 - D2 | / ( |D1| ulp )

where Z is the matrix of eigenvectors returned when the eigenvector option is given and D1 and D2 are the eigenvalues returned with and without the eigenvector option.

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 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 (4), but multiplied by SQRT( overflow threshold ).
  7. Same as (4), but multiplied by SQRT( underflow threshold ).
  8. A matrix of the form U* D U, where U is unitary and D has evenly spaced entries 1, ..., ULP with random signs on the diagonal.
  9. A matrix of the form U* D U, where U is unitary and D has geometrically spaced entries 1, ..., ULP with random signs on the diagonal.
  10. A matrix of the form U* D U, where U is unitary 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. Symmetric 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 ).
  16. A band matrix with half bandwidth randomly chosen between 0 and N-1, with evenly spaced eigenvalues 1, ..., ULP with random signs.
  17. Same as (16), but multiplied by SQRT( overflow threshold ).
  18. Same as (16), but multiplied by SQRT( underflow threshold ).
  • NSIZES — INTEGER. The number of sizes of matrices to use. If it's zero, CDRVST does nothing. It must be at least zero. Not modified.
  • NN — INTEGER array, dimension (NSIZES). An array holding the sizes to use for the matrices. Zero values will be skipped. The values must be at least zero. Not modified.
  • NTYPES — INTEGER. The number of elements in DOTYPE. If it's zero, CDRVST does nothing. It must be at least zero. If it's MAXTYP+1 and NSIZES is 1, then an extra 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. . Not modified.
  • DOTYPE — 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. Not modified.
  • ISEED — 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 CDRVST to continue the same random number sequence. Modified.
  • THRESH — REAL. A test will count as [blank] if the [blank], computed as described above, exceeds THRESH. (Yes, the original has blanks there, bestie 😭 — I'm not making it up.) 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. Not modified.
  • NOUNIT — INTEGER. The FORTRAN unit number for printing out error messages (e.g., if a routine returns IINFO not equal to 0.) Not modified.
  • A — 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. Modified.
  • LDA — INTEGER. The leading dimension of A. It must be at least 1 and at least max( NN ). Not modified.
  • D1 — REAL array, dimension (max(NN)). The eigenvalues of A, as computed by CSTEQR simultaneously with Z. On exit, the eigenvalues in D1 correspond with the matrix in A. Modified.
  • D2 — REAL array, dimension (max(NN)). The eigenvalues of A, as computed by CSTEQR if Z is not computed. On exit, the eigenvalues in D2 correspond with the matrix in A. Modified.
  • D3 — REAL array, dimension (max(NN)). The eigenvalues of A, as computed by SSTERF. On exit, the eigenvalues in D3 correspond with the matrix in A. Modified.
  • WA1 — REAL array, dimension. (That's it. No dimension given. The original just leaves it hanging. 💀)
  • WA2 — REAL array, dimension. (Same vibe.)
  • WA3 — REAL array, dimension. (Same.)
  • U — COMPLEX array, dimension (LDU, max(NN)). The unitary matrix computed by CHETRD + CUNGC3. Modified.
  • LDU — INTEGER. The leading dimension of U, Z, and V. It must be at least 1 and at least max( NN ). Not modified.
  • V — COMPLEX array, dimension (LDU, max(NN)). The Housholder vectors (sic, one 'e' — original's spelling, not mine 💀) computed by CHETRD in reducing A to tridiagonal form. Modified.
  • TAU — COMPLEX array, dimension (max(NN)). The Householder factors computed by CHETRD in reducing A to tridiagonal form. Modified.
  • Z — COMPLEX array, dimension (LDU, max(NN)). The unitary matrix of eigenvectors computed by CHEEVD, CHEEVX, CHPEVD, CHPEVX, CHBEVD, and CHBEVX. Modified.
  • WORK — COMPLEX array of dimension ( LWORK ). Workspace. Modified.
  • LWORK — INTEGER. The number of entries in WORK. This must be at least 2*max( NN(j), 2 )**2. Not modified.
  • RWORK — REAL array, dimension (3*max(NN)). Workspace. Modified.
  • LRWORK — INTEGER. The number of entries in RWORK. (No modified note, because the original didn't give one. 🙈)
  • IWORK — INTEGER array, dimension (6*max(NN)). Workspace. Modified.
  • LIWORK — INTEGER. The number of entries in IWORK. (Again, no modified note in the original.)
  • RESULT — REAL array, dimension (??). The values computed by the tests described above. The values are currently limited to 1/ulp, to avoid overflow. Modified.
  • INFO — INTEGER. If 0, then everything ran OK. The error codes are:
    • -1: NSIZES < 0
    • -2: Some NN(j) < 0
    • -3: NTYPES < 0
    • -5: THRESH < 0
    • -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
    • -16: LDU < 1 or LDU < NMAX.
    • -21: LWORK too small. If SLATMR, SLATMS, CHETRD, SORGC3, CSTEQR, SSTERF, or SORMC2 returns an error code, the absolute value of it is returned. Modified.

✨ Some Local Variables and Parameters ✨

  • ZERO, ONE — Real 0 and 1.
  • MAXTYP — The number of types defined.
  • NTEST — The number of tests performed, or which can be performed so far, for the current matrix.
  • NTESTT — The total number of tests performed so far.
  • NMAX — Largest value in NN.
  • NMATS — The number of matrices generated so far.
  • NERRS — The number of tests which have exceeded THRESH so far (computed by SLAFTS).
  • COND, 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.
  • RTOVFL, RTUNFL — Square roots of the previous 2 values.
  • The following four arrays decode JTYPE: (and yes, it says four but lists three — iconic inconsistency 💀)
    • KTYPE(j) — The general type (1-10) for type . (The original has a blank after "type" — leaving it exactly as it landed.)
    • KMODE(j) — The MODE value to be passed to the matrix generator for type . (Another blank. Slay.)
    • KMAGN(j) — The order of magnitude ( O(1), O(overflow^(1/2) ), O(underflow^(1/2) ) )

🫶 Author 🫶

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

📜 Definition 📜

Definition at line 334 of file cdrvst.f.

Author (again) 💀

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okay that's the whole page, bestie 💖 source/version/date vibes: LAPACK, Version 3.12.0, TESTING/EIG/cdrvst.f(3), date in the footer — bye bestie! 🎀✨

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