SDRVST(3)

📦 version 3.12.0, in opensuse-leap 16.0

🦋 SDRVST(3) — Library Functions Manual 🦋

💖 NAME 💖

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

Okay bestie, that’s the name/path situation — the original NAME section is literally just the file path, no extra lore. 💅

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine SDRVST (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)
           SDRVST

🌈 Function/Subroutine Documentation 🌈

💅 subroutine SDRVST 💅

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

🧚 Purpose 🧚

Okay so SDRVST is the vibe-checker for the symmetric eigenvalue problem drivers. Literally, it checks them. The drivers in question are:

  • SSTEV — computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix.
  • SSTEVX — computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix.
  • SSTEVR — computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix using the Relatively Robust Representation where it can.
  • SSYEV — computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix.
  • SSYEVX — computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix.
  • SSYEVR — computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix using the Relatively Robust Representation where it can.
  • SSPEV — computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix in packed storage.
  • SSPEVX — computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix in packed storage.
  • SSBEV — computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix.
  • SSBEVX — computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix.
  • SSYEVD — computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix using a divide and conquer algorithm.
  • SSPEVD — computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix in packed storage, using a divide and conquer algorithm.
  • SSBEVD — computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix, using a divide and conquer algorithm.

When SDRVST is called, a number of matrix sizes (() — yes, the original has empty parentheses there, bestie) 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 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 N 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 N 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 is zero, SDRVST does nothing. It must be at least zero. Not modified.
  • NN — 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. Not modified.
  • NTYPES — INTEGER. The number of elements in DOTYPE. If it is zero, SDRVST 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.. 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 SDRVST to continue the same random number sequence. Modified.
  • THRESH — REAL. A test will count as if the , computed as described above, exceeds THRESH. (yes, the page has blanks right there — we are not filling them in, 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. 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 — 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. 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 SSTEQR 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 SSTEQR 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.
  • D4 — REAL array, dimension. That is literally all the page says for this one — the dimension is left blank, no cap 💀.
  • EVEIGS — REAL array, dimension (max(NN)). The eigenvalues as computed by SSTEV('N', ... ) (I reserve the right to change this to the output of whichever algorithm computes the most accurate eigenvalues).
  • WA1 — REAL array, dimension. Also left blank on the page.
  • WA2 — REAL array, dimension. Also left blank on the page.
  • WA3 — REAL array, dimension. Also left blank on the page.
  • U — REAL array, dimension (LDU, max(NN)). The orthogonal matrix computed by SSYTRD + SORGTR. 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 — REAL array, dimension (LDU, max(NN)). The Housholder vectors computed by SSYTRD in reducing A to tridiagonal form. Modified.
  • TAU — REAL array, dimension (max(NN)). The Householder factors computed by SSYTRD in reducing A to tridiagonal form. Modified.
  • Z — REAL array, dimension (LDU, max(NN)). The orthogonal matrix of eigenvectors computed by SSTEQR, SPTEQR, and SSTEIN. Modified.
  • WORK — REAL 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. 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 — REAL array, dimension (105). 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.
    • -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, SSYTRD, SORGTR, SSTEQR, SSTERF, or SORMTR 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:

  • 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) )

(the page says four arrays and then lists three — iconic chaos, we just report it 💀)

🎀 The tests performed are: 🎀

Routine tested is the right-hand side, bestie 💅

  • 1= | A - U S U' | / ( |A| n ulp ) — SSTEV('V', ... )
  • 2= | I - U U' | / ( n ulp ) — SSTEV('V', ... )
  • 3= |D(with Z) - D(w/o Z)| / (|D| ulp) — SSTEV('N', ... )
  • 4= | A - U S U' | / ( |A| n ulp ) — SSTEVX('V','A', ... )
  • 5= | I - U U' | / ( n ulp ) — SSTEVX('V','A', ... )
  • 6= |D(with Z) - EVEIGS| / (|D| ulp) — SSTEVX('N','A', ... )
  • 7= | A - U S U' | / ( |A| n ulp ) — SSTEVR('V','A', ... )
  • 8= | I - U U' | / ( n ulp ) — SSTEVR('V','A', ... )
  • 9= |D(with Z) - EVEIGS| / (|D| ulp) — SSTEVR('N','A', ... )
  • 10= | A - U S U' | / ( |A| n ulp ) — SSTEVX('V','I', ... )
  • 11= | I - U U' | / ( n ulp ) — SSTEVX('V','I', ... )
  • 12= |D(with Z) - D(w/o Z)| / (|D| ulp) — SSTEVX('N','I', ... )
  • 13= | A - U S U' | / ( |A| n ulp ) — SSTEVX('V','V', ... )
  • 14= | I - U U' | / ( n ulp ) — SSTEVX('V','V', ... )
  • 15= |D(with Z) - D(w/o Z)| / (|D| ulp) — SSTEVX('N','V', ... )
  • 16= | A - U S U' | / ( |A| n ulp ) — SSTEVD('V', ... )
  • 17= | I - U U' | / ( n ulp ) — SSTEVD('V', ... )
  • 18= |D(with Z) - EVEIGS| / (|D| ulp) — SSTEVD('N', ... )
  • 19= | A - U S U' | / ( |A| n ulp ) — SSTEVR('V','I', ... )
  • 20= | I - U U' | / ( n ulp ) — SSTEVR('V','I', ... )
  • 21= |D(with Z) - D(w/o Z)| / (|D| ulp) — SSTEVR('N','I', ... )
  • 22= | A - U S U' | / ( |A| n ulp ) — SSTEVR('V','V', ... )
  • 23= | I - U U' | / ( n ulp ) — SSTEVR('V','V', ... )
  • 24= |D(with Z) - D(w/o Z)| / (|D| ulp) — SSTEVR('N','V', ... )
  • 25= | A - U S U' | / ( |A| n ulp ) — SSYEV('L','V', ... )
  • 26= | I - U U' | / ( n ulp ) — SSYEV('L','V', ... )
  • 27= |D(with Z) - D(w/o Z)| / (|D| ulp) — SSYEV('L','N', ... )
  • 28= | A - U S U' | / ( |A| n ulp ) — SSYEVX('L','V','A', ... )
  • 29= | I - U U' | / ( n ulp ) — SSYEVX('L','V','A', ... )
  • 30= |D(with Z) - D(w/o Z)| / (|D| ulp) — SSYEVX('L','N','A', ... )

Picking up right at test 31 — no recap, no repeated heading, just the exact test-list lines because these are literal code comments and I am not about to paraphrase math into vibes-only 💅

!>    31= | A - U S U' | / ( |A| n ulp )        SSYEVX('L','V','I', ... )
!>    32= | I - U U' | / ( n ulp )              SSYEVX('L','V','I', ... )
!>    33= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSYEVX('L','N','I', ... )
!>    34= | A - U S U' | / ( |A| n ulp )        SSYEVX('L','V','V', ... )
!>    35= | I - U U' | / ( n ulp )              SSYEVX('L','V','V', ... )
!>    36= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSYEVX('L','N','V', ... )
!>    37= | A - U S U' | / ( |A| n ulp )        SSPEV('L','V', ... )
!>    38= | I - U U' | / ( n ulp )              SSPEV('L','V', ... )
!>    39= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSPEV('L','N', ... )
!>    40= | A - U S U' | / ( |A| n ulp )        SSPEVX('L','V','A', ... )
!>    41= | I - U U' | / ( n ulp )              SSPEVX('L','V','A', ... )
!>    42= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSPEVX('L','N','A', ... )
!>    43= | A - U S U' | / ( |A| n ulp )        SSPEVX('L','V','I', ... )
!>    44= | I - U U' | / ( n ulp )              SSPEVX('L','V','I', ... )
!>    45= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSPEVX('L','N','I', ... )
!>    46= | A - U S U' | / ( |A| n ulp )        SSPEVX('L','V','V', ... )
!>    47= | I - U U' | / ( n ulp )              SSPEVX('L','V','V', ... )
!>    48= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSPEVX('L','N','V', ... )
!>    49= | A - U S U' | / ( |A| n ulp )        SSBEV('L','V', ... )
!>    50= | I - U U' | / ( n ulp )              SSBEV('L','V', ... )
!>    51= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSBEV('L','N', ... )
!>    52= | A - U S U' | / ( |A| n ulp )        SSBEVX('L','V','A', ... )
!>    53= | I - U U' | / ( n ulp )              SSBEVX('L','V','A', ... )
!>    54= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSBEVX('L','N','A', ... )
!>    55= | A - U S U' | / ( |A| n ulp )        SSBEVX('L','V','I', ... )
!>    56= | I - U U' | / ( n ulp )              SSBEVX('L','V','I', ... )
!>    57= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSBEVX('L','N','I', ... )
!>    58= | A - U S U' | / ( |A| n ulp )        SSBEVX('L','V','V', ... )
!>    59= | I - U U' | / ( n ulp )              SSBEVX('L','V','V', ... )
!>    60= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSBEVX('L','N','V', ... )
!>    61= | A - U S U' | / ( |A| n ulp )        SSYEVD('L','V', ... )
!>    62= | I - U U' | / ( n ulp )              SSYEVD('L','V', ... )
!>    63= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSYEVD('L','N', ... )
!>    64= | A - U S U' | / ( |A| n ulp )        SSPEVD('L','V', ... )
!>    65= | I - U U' | / ( n ulp )              SSPEVD('L','V', ... )
!>    66= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSPEVD('L','N', ... )
!>    67= | A - U S U' | / ( |A| n ulp )        SSBEVD('L','V', ... )
!>    68= | I - U U' | / ( n ulp )              SSBEVD('L','V', ... )
!>    69= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSBEVD('L','N', ... )
!>    70= | A - U S U' | / ( |A| n ulp )        SSYEVR('L','V','A', ... )
!>    71= | I - U U' | / ( n ulp )              SSYEVR('L','V','A', ... )
!>    72= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSYEVR('L','N','A', ... )
!>    73= | A - U S U' | / ( |A| n ulp )        SSYEVR('L','V','I', ... )
!>    74= | I - U U' | / ( n ulp )              SSYEVR('L','V','I', ... )
!>    75= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSYEVR('L','N','I', ... )
!>    76= | A - U S U' | / ( |A| n ulp )        SSYEVR('L','V','V', ... )
!>    77= | I - U U' | / ( n ulp )              SSYEVR('L','V','V', ... )
!>    78= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSYEVR('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 )        SSPEVR('L','V','A', ... )
!>    80= | I - U U' | / ( n ulp )              SSPEVR('L','V','A', ... )
!>    81= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSPEVR('L','N','A', ... )
!>    82= | A - U S U' | / ( |A| n ulp )        SSPEVR('L','V','I', ... )
!>    83= | I - U U' | / ( n ulp )              SSPEVR('L','V','I', ... )
!>    84= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSPEVR('L','N','I', ... )
!>    85= | A - U S U' | / ( |A| n ulp )        SSPEVR('L','V','V', ... )
!>    86= | I - U U' | / ( n ulp )              SSPEVR('L','V','V', ... )
!>    87= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSPEVR('L','N','V', ... )
!>    88= | A - U S U' | / ( |A| n ulp )        SSBEVR('L','V','A', ... )
!>    89= | I - U U' | / ( n ulp )              SSBEVR('L','V','A', ... )
!>    90= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSBEVR('L','N','A', ... )
!>    91= | A - U S U' | / ( |A| n ulp )        SSBEVR('L','V','I', ... )
!>    92= | I - U U' | / ( n ulp )              SSBEVR('L','V','I', ... )
!>    93= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSBEVR('L','N','I', ... )
!>    94= | A - U S U' | / ( |A| n ulp )        SSBEVR('L','V','V', ... )
!>    95= | I - U U' | / ( n ulp )              SSBEVR('L','V','V', ... )
!>    96= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSBEVR('L','N','V', ... )
!>

okay so the tea ☕: the source says tests 25 through 78 get repeated as tests 79 through 132 with UPLO='U', and it also has that iconic To be added in 1999 note sitting right before the SSPEVR / SSBEVR entries. Both are literally in there — I’m not merging or “fixing” the overlap, just preserving every detail 🫶

👑 Author 👑

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

Definition at line 449 of file sdrvst.f.

🎀 Author (the generated one) 🎀

Generated automatically by Doxygen for LAPACK from the source code.

That’s the whole page, bestie: LAPACK Version 3.12.0, source /home/abui...IG/sdrvst.f(3). The footer didn’t hand me a date, so I’m not inventing one — just version and path, periodt. 💅✨

📦 where this page comes from