DDRVST2STG(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/ddrvst2stg.f

okay so bestie, we're in drvst2stg.f(3) territory — that's the Library Functions Manual btw, and the whole page is literally about this one Fortran file and its favorite child, DDRVST2STG. buckle up 🎀

✨ SYNOPSIS ✨

Functions/Subroutines

  • subroutine DDRVST2STG — (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a, lda, d1, d2, d3, d4, eveigs, wa1, wa2, wa3, u, ldu, v, tau, z, work, lwork, iwork, liwork, result, info)
  • DDRVST2STG — yeah she's listed twice, that's just how the index do 💅

🦋 Function/Subroutine Documentation 🦋

subroutine DDRVST2STG

here's the full glow-up of the signature, every single argument, no skips:

subroutine DDRVST2STG (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( * ) d1, double
    precision, dimension( * ) d2, double precision, dimension( * ) d3,
    double precision, dimension( * ) d4, double precision, dimension( * )
    eveigs, double precision, dimension( * ) wa1, double precision,
    dimension( * ) wa2, double precision, dimension( * ) wa3, double
    precision, dimension( ldu, * ) u, integer ldu, double precision,
    dimension( ldu, * ) v, double precision, dimension( * ) tau, double
    precision, dimension( ldu, * ) z, double precision, dimension( * ) work,
    integer lwork, integer, dimension( * ) iwork, integer liwork, double
    precision, dimension( * ) result, integer info)

and the short version, for the girlies who just want the vibes:

subroutine DDRVST2STG (nsizes, nn, ntypes, dotype, iseed, thresh,
    nounit, a, lda, d1, d2, d3, d4, eveigs, wa1, wa2, wa3, u, ldu, v,
    tau, z, work, lwork, iwork, liwork, result, info)

🎯 Purpose

!> !> DDRVST2STG checks the symmetric eigenvalue problem drivers.

periodt. she is the vibe check for the symmetric eigenvalue drivers, and the cast of characters she's testing is iconic — every one of them, in order, no cap:

  • DSTEV — computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix.
  • DSTEVX — computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix.
  • DSTEVR — computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix, using the Relatively Robust Representation where it can.
  • DSYEV — computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix.
  • DSYEVX — computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix.
  • DSYEVR — computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, using the Relatively Robust Representation where it can.
  • DSPEV — computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix in packed storage.
  • DSPEVX — computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix in packed storage.
  • DSBEV — computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix.
  • DSBEVX — computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix.
  • DSYEVD — computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, using a divide and conquer algorithm.
  • DSPEVD — computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix in packed storage, using a divide and conquer algorithm.
  • DSBEVD — computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix, using a divide and conquer algorithm.

like... the whole friend group showed up 🌈

so the way this works 😌 — when DDRVST2STG is called, a number of matrix () and a number of matrix are specified. For each size () and each type of matrix, one matrix gets generated and used to test the appropriate drivers. and for each matrix, and each driver routine called, these three tests run:

  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. iykyk 🫶

the sizes are specified by an array NN(1:NSIZES) — 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 will be generated. and currently, the list of possible types is literally:

  1. The zero matrix.
  2. The identity matrix.
  3. A diagonal matrix with evenly spaced eigenvalues 1, ..., ULP and random signs. ( ULP = (first number larger than 1) - 1 )
  4. A diagonal matrix with geometrically spaced eigenvalues 1, ..., ULP and random signs.
  5. A diagonal matrix with eigenvalues 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 orthogonal 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 orthogonal 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 orthogonal 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 )

eighteen whole matrix types?? she's committed 💀 and we're not done — there's more page coming, so don't go anywhere bestie 🦋✨

  • NSIZES — INTEGER. The number of sizes of matrices to use. If it's zero, DDRVST2STG literally does nothing (it's giving unemployed, respectfully 💅). It must be at least zero. Not modified.
  • NN — INTEGER array, dimension (NSIZES). The array holding the sizes to use for the matrices. Zero values get skipped, so don't come for them. The values must be at least zero. Not modified.
  • NTYPES — INTEGER. The number of elements in DOTYPE. If it's zero, DDRVST2STG does nothing again (clocked out, no notes 🫶). It must be at least zero. If it's MAXTYP+1 and NSIZES is 1, then an extra type gets defined, MAXTYP+1, which is your "just use whatever matrix is already chilling in A" option. That one's 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 every size in NN a matrix of that size and of type j will be generated. If NTYPES is smaller than the max number of types defined (that's PARAMETER MAXTYP), then types NTYPES+1 through MAXTYP just won't be generated. And if NTYPES is larger than MAXTYP, then DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) get ignored, they're not beating the allegations. 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 they're not, they get reduced mod 4096, no cap. Also, ISEED(4) must be odd (bestie, fr fr, keep it odd). The RNG uses a linear congruential sequence limited to small integers, so it should produce machine independent random numbers 🌈. The values of ISEED change on exit and can be used in the next call to DDRVST2STG to keep the same random number sequence going. Modified.
  • THRESH — DOUBLE PRECISION. A test counts as (a fail) if the (error), computed as described above, exceeds THRESH. The original page is lowkey glitching here and the words are literally missing — that's canon, not me 💀. Anyway: 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. 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). Very "call me if anything goes wrong" energy. Not modified.
  • A — DOUBLE PRECISION array, dimension (LDA, max(NN)). Holds the matrix whose eigenvalues are to be computed. On exit, A contains the last matrix actually used — it keeps the receipts 👑. Modified.
  • LDA — INTEGER. The leading dimension of A. It must be at least 1 and at least max( NN ). Not modified.
  • D1 — DOUBLE PRECISION array, dimension (max(NN)). The eigenvalues of A, as computed by DSTEQR simultaneously with Z. On exit, the eigenvalues in D1 correspond with the matrix in A. Modified.
  • D2 — DOUBLE PRECISION array, dimension (max(NN)). The eigenvalues of A, as computed by DSTEQR if Z is not computed. On exit, the eigenvalues in D2 correspond with the matrix in A. Modified.
  • D3 — DOUBLE PRECISION array, dimension (max(NN)). The eigenvalues of A, as computed by DSTERF. On exit, the eigenvalues in D3 correspond with the matrix in A. Modified.
  • D4 — DOUBLE PRECISION array, dimension (and then the original just... doesn't say 😭 the dimension field is empty. Iconic of it.)
  • EVEIGS — DOUBLE PRECISION array, dimension (max(NN)). The eigenvalues as computed by DSTEV('N', ... ). And the author notes, and I quote: "(I reserve the right to change this to the output of whichever algorithm computes the most accurate eigenvalues)." We love a flexible queen 🎀.
  • WA1 — DOUBLE PRECISION array, dimension (again, the original leaves this blank 👀).
  • WA2 — DOUBLE PRECISION array, dimension (blank, same deal).
  • WA3 — DOUBLE PRECISION array, dimension (blank, same deal).
  • U — DOUBLE PRECISION array, dimension (LDU, max(NN)). The orthogonal matrix computed by DSYTRD + DORGTR. 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 — DOUBLE PRECISION array, dimension (LDU, max(NN)). The Housholder vectors computed by DSYTRD in reducing A to tridiagonal form (yes the original spells it like that, we stan a typo 💜). Modified.
  • TAU — DOUBLE PRECISION array, dimension (max(NN)). The Householder factors computed by DSYTRD in reducing A to tridiagonal form. Modified.
  • Z — DOUBLE PRECISION array, dimension (LDU, max(NN)). The orthogonal matrix of eigenvectors computed by DSTEQR, DPTEQR, and DSTEIN. Main character matrix energy. Modified.
  • WORK — DOUBLE PRECISION array, dimension (LWORK). Workspace. Modified.
  • LWORK — INTEGER. The number of entries in WORK. This must be at least
1 + 4 * Nmax + 2 * Nmax * lg Nmax + 4 * Nmax**2

where Nmax = max( NN(j), 2 ) and lg = log base 2. No shortcuts, bestie, do the math. Not modified.

  • IWORK — INTEGER array, dimension (6 + 6*Nmax + 5 * Nmax * lg Nmax) where Nmax = max( NN(j), 2 ) and lg = log base 2. Workspace. Modified.
  • RESULT — DOUBLE PRECISION array, dimension (105). The values computed by the tests described above. Right now the values are limited to 1/ulp, to avoid overflow — safety first 🦋. Modified.
  • INFO — INTEGER. If 0, then everything ran OK and we're thriving. Otherwise:
    • -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 DLATMR, DLATMS, DSYTRD, DORGTR, DSTEQR, DSTERF, or DORMTR returns an error code, the absolute value of it is returned. Modified.

🌸 Some Local Variables and Parameters 🌸

  • ZERO, ONE — Real 0 and 1. Simple. Elegant. Slay.
  • 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 DLAFTS).
  • 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 . (the original leaves the type number blank here too, love that for us 💀)
  • KMODE(j) — The MODE value to be passed to the matrix generator for type . (same blank situation)
  • KMAGN(j) — The order of magnitude ( O(1), O(overflow^(1/2) ), O(underflow^(1/2) )

💅 The tests performed are 💅

  • 1= | A - U S U' | / ( |A| n ulp ) — routine tested: DSTEV('V', ... )
  • 2= | I - U U' | / ( n ulp ) — routine tested: DSTEV('V', ... )
  • 3= |D(with Z) - D(w/o Z)| / (|D| ulp) — routine tested: DSTEV('N', ... )
  • 4= | A - U S U' | / ( |A| n ulp ) — routine tested: DSTEVX('V','A', ... )
  • 5= | I - U U' | / ( n ulp ) — routine tested: DSTEVX('V','A', ... )
  • 6= |D(with Z) - EVEIGS| / (|D| ulp) — routine tested: DSTEVX('N','A', ... )
  • 7= | A - U S U' | / ( |A| n ulp ) — routine tested: DSTEVR('V','A', ... )
  • 8= | I - U U' | / ( n ulp ) — routine tested: DSTEVR('V','A', ... )
  • 9= |D(with Z) - EVEIGS| / (|D| ulp) — routine tested: DSTEVR('N','A', ... )
  • 10= | A - U S U' | / ( |A| n ulp ) — routine tested: DSTEVX('V','I', ... )
  • 11= | I - U U' | / ( n ulp ) — routine tested: DSTEVX('V','I', ... )
  • 12= |D(with Z) - D(w/o Z)| / (|D| ulp) — routine tested: DSTEVX('N','I', ... )
  • 13= | A - U S U' | / ( |A| n ulp ) — routine tested: DSTEVX('V','V', ... )
  • 14= | I - U U' | / ( n ulp ) — routine tested: DSTEVX('V','V', ... )
  • 15= |D(with Z) - D(w/o Z)| / (|D| ulp) — routine tested: DSTEVX('N','V', ... )
  • 16= | A - U S U' | / ( |A| n ulp ) — routine tested: DSTEVD('V', ... )
  • 17= | I - U U' | / ( n ulp ) — routine tested: DSTEVD('V', ... )
  • 18= |D(with Z) - EVEIGS| / (|D| ulp) — routine tested: DSTEVD('N', ... )
  • 19= | A - U S U' | / ( |A| n ulp ) — routine tested: DSTEVR('V','I', ... )
  • 20= | I - U U' | / ( n ulp ) — routine tested: DSTEVR('V','I', ... )
  • 21= |D(with Z) - D(w/o Z)| / (|D| ulp) — routine tested: DSTEVR('N','I', ... )
  • 22= | A - U S U' | / ( |A| n ulp ) — routine tested: DSTEVR('V','V', ... )
  • 23= | I - U U' | / ( n ulp ) — routine tested: DSTEVR('V','V', ... )
  • 24= |D(with Z) - D(w/o Z)| / (|D| ulp) — routine tested: DSTEVR('N','V', ... )
  • 25= | A - U S U' | / ( |A| n ulp ) — routine tested: DSYEV('L','V', ... )
  • 26= | I - U U' | / ( n ulp ) — routine tested: DSYEV('L','V', ... )
  • 27= |D(with Z) - D(w/o Z)| / (|D| ulp) — routine tested: DSYEV_2STAGE('L','N', ... )

okay so the test list continues and it's giving "I have 69 tests and I'm not afraid to use them" energy. here's the rest, verbatim, no cap:

           !>    28= | A - U S U' | / ( |A| n ulp )        DSYEVX('L','V','A', ... )
           !>    29= | I - U U' | / ( n ulp )              DSYEVX('L','V','A', ... )
           !>    30= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSYEVX_2STAGE('L','N','A', ... )
           !>    31= | A - U S U' | / ( |A| n ulp )        DSYEVX('L','V','I', ... )
           !>    32= | I - U U' | / ( n ulp )              DSYEVX('L','V','I', ... )
           !>    33= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSYEVX_2STAGE('L','N','I', ... )
           !>    34= | A - U S U' | / ( |A| n ulp )        DSYEVX('L','V','V', ... )
           !>    35= | I - U U' | / ( n ulp )              DSYEVX('L','V','V', ... )
           !>    36= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSYEVX_2STAGE('L','N','V', ... )
           !>    37= | A - U S U' | / ( |A| n ulp )        DSPEV('L','V', ... )
           !>    38= | I - U U' | / ( n ulp )              DSPEV('L','V', ... )
           !>    39= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSPEV('L','N', ... )
           !>    40= | A - U S U' | / ( |A| n ulp )        DSPEVX('L','V','A', ... )
           !>    41= | I - U U' | / ( n ulp )              DSPEVX('L','V','A', ... )
           !>    42= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSPEVX('L','N','A', ... )
           !>    43= | A - U S U' | / ( |A| n ulp )        DSPEVX('L','V','I', ... )
           !>    44= | I - U U' | / ( n ulp )              DSPEVX('L','V','I', ... )
           !>    45= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSPEVX('L','N','I', ... )
           !>    46= | A - U S U' | / ( |A| n ulp )        DSPEVX('L','V','V', ... )
           !>    47= | I - U U' | / ( n ulp )              DSPEVX('L','V','V', ... )
           !>    48= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSPEVX('L','N','V', ... )
           !>    49= | A - U S U' | / ( |A| n ulp )        DSBEV('L','V', ... )
           !>    50= | I - U U' | / ( n ulp )              DSBEV('L','V', ... )
           !>    51= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSBEV_2STAGE('L','N', ... )
           !>    52= | A - U S U' | / ( |A| n ulp )        DSBEVX('L','V','A', ... )
           !>    53= | I - U U' | / ( n ulp )              DSBEVX('L','V','A', ... )
           !>    54= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSBEVX_2STAGE('L','N','A', ... )
           !>    55= | A - U S U' | / ( |A| n ulp )        DSBEVX('L','V','I', ... )
           !>    56= | I - U U' | / ( n ulp )              DSBEVX('L','V','I', ... )
           !>    57= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSBEVX_2STAGE('L','N','I', ... )
           !>    58= | A - U S U' | / ( |A| n ulp )        DSBEVX('L','V','V', ... )
           !>    59= | I - U U' | / ( n ulp )              DSBEVX('L','V','V', ... )
           !>    60= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSBEVX_2STAGE('L','N','V', ... )
           !>    61= | A - U S U' | / ( |A| n ulp )        DSYEVD('L','V', ... )
           !>    62= | I - U U' | / ( n ulp )              DSYEVD('L','V', ... )
           !>    63= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSYEVD_2STAGE('L','N', ... )
           !>    64= | A - U S U' | / ( |A| n ulp )        DSPEVD('L','V', ... )
           !>    65= | I - U U' | / ( n ulp )              DSPEVD('L','V', ... )
           !>    66= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSPEVD('L','N', ... )
           !>    67= | A - U S U' | / ( |A| n ulp )        DSBEVD('L','V', ... )
           !>    68= | I - U U' | / ( n ulp )              DSBEVD('L','V', ... )
           !>    69= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSBEVD_2STAGE('L','N', ... )
           !>    70= | A - U S U' | / ( |A| n ulp )        DSYEVR('L','V','A', ... )
           !>    71= | I - U U' | / ( n ulp )              DSYEVR('L','V','A', ... )
           !>    72= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSYEVR_2STAGE('L','N','A', ... )
           !>    73= | A - U S U' | / ( |A| n ulp )        DSYEVR('L','V','I', ... )
           !>    74= | I - U U' | / ( n ulp )              DSYEVR('L','V','I', ... )
           !>    75= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSYEVR_2STAGE('L','N','I', ... )
           !>    76= | A - U S U' | / ( |A| n ulp )        DSYEVR('L','V','V', ... )
           !>    77= | I - U U' | / ( n ulp )              DSYEVR('L','V','V', ... )
           !>    78= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSYEVR_2STAGE('L','N','V', ... )
           !>
           !>    Tests 25 through 78 are repeated (as tests 79 through 132)
           !>    with UPLO='U'
           !>
           !>    To be added in 1999
           !>
           !>    79= | A - U S U' | / ( |A| n ulp )        DSPEVR('L','V','A', ... )
           !>    80= | I - U U' | / ( n ulp )              DSPEVR('L','V','A', ... )
           !>    81= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSPEVR('L','N','A', ... )
           !>    82= | A - U S U' | / ( |A| n ulp )        DSPEVR('L','V','I', ... )
           !>    83= | I - U U' | / ( n ulp )              DSPEVR('L','V','I', ... )
           !>    84= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSPEVR('L','N','I', ... )
           !>    85= | A - U S U' | / ( |A| n ulp )        DSPEVR('L','V','V', ... )
           !>    86= | I - U U' | / ( n ulp )              DSPEVR('L','V','V', ... )
           !>    87= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSPEVR('L','N','V', ... )
           !>    88= | A - U S U' | / ( |A| n ulp )        DSBEVR('L','V','A', ... )
           !>    89= | I - U U' | / ( n ulp )              DSBEVR('L','V','A', ... )
           !>    90= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSBEVR('L','N','A', ... )
           !>    91= | A - U S U' | / ( |A| n ulp )        DSBEVR('L','V','I', ... )
           !>    92= | I - U U' | / ( n ulp )              DSBEVR('L','V','I', ... )
           !>    93= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSBEVR('L','N','I', ... )
           !>    94= | A - U S U' | / ( |A| n ulp )        DSBEVR('L','V','V', ... )
           !>    95= | I - U U' | / ( n ulp )              DSBEVR('L','V','V', ... )
           !>    96= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSBEVR('L','N','V', ... )
           !>

and yes, it literally says "To be added in 1999" — iconic vintage behavior, we love a retro to-do list. 💅

Author

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

Definition at line 449 of file ddrvst2stg.f.

Author

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