CDRVST(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 CDRVST(3) 💅

okay so this is cdrvst.f(3) from the Library Functions Manual, and it is lowkey iconic. The header line is a whole mood, but we're folding the manual name in right here like a responsible bestie. 🫶

✨ NAME ✨

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

that's the file path, character for character, no cap. 💖

🎀 SYNOPSIS 🎀

🫶 Functions/Subroutines 🫶

okay so here's the synopsis, bestie — it's a subroutine with a whole group chat of arguments:

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

and yes, the subroutine is literally CDRVST. periodt. 💅

🌸 Function/Subroutine Documentation 🌸

here's the full signature with every type and dimension, exactly as the source says — I am not touching a single character of this, bestie:

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

and it's CDRVST again, because consistency is cute. 🎀

💖 Purpose 💖

okay so the purpose is literally this: CDRVST checks the Hermitian eigenvalue problem drivers. no cap. 🦋

the drivers it checks are:

  • 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. and for each matrix and each driver routine called, these tests get performed, bestie:

(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. slay. 💅

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. (1) — The zero matrix. 💀
  2. (2) — The identity matrix. ✨
  3. (3) — A diagonal matrix with evenly spaced entries 1, ..., ULP and random signs. (ULP = (first number larger than 1) - 1) 🎀
  4. (4) — A diagonal matrix with geometrically spaced entries 1, ..., ULP and random signs. 🌸
  5. (5) — A diagonal matrix with entries 1, ULP, ..., ULP and random signs. 🦋
  6. (6) — Same as (4), but multiplied by SQRT( overflow threshold ). 🔥
  7. (7) — Same as (4), but multiplied by SQRT( underflow threshold ). 💜
  8. (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. (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. (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. (11) — Same as (8), but multiplied by SQRT( overflow threshold ). 🍓
  12. (12) — Same as (8), but multiplied by SQRT( underflow threshold ). 🧚
  13. (13) — Symmetric matrix with random entries chosen from (-1,1). 💖
  14. (14) — Same as (13), but multiplied by SQRT( overflow threshold ). ✨
  15. (15) — Same as (13), but multiplied by SQRT( underflow threshold ). 🎀
  16. (16) — A band matrix with half bandwidth randomly chosen between 0 and N-1, with evenly spaced eigenvalues 1, ..., ULP with random signs. 🌸
  17. (17) — Same as (16), but multiplied by SQRT( overflow threshold ). 🦋
  18. (18) — Same as (16), but multiplied by SQRT( underflow threshold ). 💜

okay bestie, picking up right where we left off with the arguments 💖 no cap, we're still in the parameter era and every single detail is staying.

  • NSIZES — INTEGER. The number of sizes of matrices to use. If it's zero, CDRVST does literally 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 get 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 (again, iconic minimalism). 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.. 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 in the original] if the [blank], 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. Not modified. 😭 (the original text is a little glitched here, but the cutoff vibe is clear)
  • 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 (the original just says “dimension” and then nothing — a mysterious icon, honestly). 🕵️‍♀️
  • WA2 — REAL array, dimension (same mystery vibe as WA1). 🕵️‍♀️
  • WA3 — REAL array, dimension (again, unspecified in the source — we love an enigma). 🕵️‍♀️
  • 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 computed by CHETRD in reducing A to tridiagonal form. Modified. (yes, “Housholder” is exactly how it's spelled in the source — periodt) 💅
  • 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. 🔢
  • IWORK — INTEGER array, dimension (6*max(NN)). Workspace. Modified. 🗂️
  • LIWORK — INTEGER. The number of entries in IWORK. 🔢
  • 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. Here's the error code lore:
    • -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 🧚

Some local variables and parameters (yes, the original calls them out like this, and we're keeping the whole crew):

  • 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:

  • KTYPE(j) — The general type (1-10) for type [blank in the original]. 🏷️
  • KMODE(j) — The MODE value to be passed to the matrix generator for type [blank in the original].
  • 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 at line 334 of file cdrvst.f.

🖥️ Author 🖥️

Generated automatically by Doxygen for LAPACK from the source code.

💅 that's the whole vibe check, bestie — this page came from LAPACK Version 3.12.0, source file /home/abui...IG/cdrvst.f(3). Stay iconic, and may your eigenvalues always be real and your workspace always be big enough. periodt. 💖✨

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