SDRVST2STG.F(3)

📦
version 3.12.1 · 3 versions
, in arch rolling

🎀 TESTING/EIG/sdrvst2stg.f(3) 🎀

From the Library Functions Manual, bestie — this is the page for TESTING/EIG/sdrvst2stg.f, and it's a whole mood. 💅

🌸 NAME 🌸

TESTING/EIG/sdrvst2stg.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

  • subroutine sdrvst2stg — the main character, with the full signature below. 🫶
subroutine sdrvst2stg (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)

SDRVST2STG — that's the name, periodt. ✨

💖 Function/Subroutine Documentation 💖

🫶 subroutine sdrvst2stg 🫶

subroutine sdrvst2stg (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)

SDRVST2STG

🎯 Purpose 🎯

Okay so SDRVST2STG checks the symmetric eigenvalue problem drivers. 💖 Like, it's the vibe-check friend for all these routines:

  • 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 SDRVST2STG 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 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 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 ).
  • NSIZES — INTEGER. The number of sizes of matrices to use. If it’s zero, SDRVST2STG does nothing. It must be at least zero. Status: not modified. 💅
  • NN — INTEGER array, dimension (NSIZES). Contains the sizes used for the matrices. Zero values get skipped. The values must be at least zero. Status: not modified. ✨
  • NTYPES — INTEGER. The number of elements in DOTYPE. If it’s zero, SDRVST2STG 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.. Status: 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. Status: not modified. 🦋
  • ISEED — INTEGER array, dimension (4). On entry, ISEED specifies the seed of the random number generator. 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 SDRVST2STG to continue the same random number sequence. Status: modified. 🎀
  • THRESH — REAL. A test will count as <something> if the <thing>, 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. Status: not modified. 🌸
  • NOUNIT — INTEGER. The FORTRAN unit number for printing out error messages (e.g., if a routine returns IINFO not equal to 0). Status: 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. Status: modified. 🔥
  • LDA — INTEGER. The leading dimension of A. It must be at least 1 and at least max( NN ). Status: 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. Status: 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. Status: 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. Status: modified. 🍓
  • D4 — REAL array, dimension. 😭
  • EVEIGS — REAL array, dimension (max(NN)). The eigenvalues as computed by SSTEV('N', ... ). And yes, there’s a note that the author reserves the right to change this to the output of whichever algorithm computes the most accurate eigenvalues. 🧚
  • WA1 — REAL array, dimension.
  • WA2 — REAL array, dimension.
  • WA3 — REAL array, dimension.
  • U — REAL array, dimension (LDU, max(NN)). The orthogonal matrix computed by SSYTRD + SORGTR. Status: modified. 👑
  • LDU — INTEGER. The leading dimension of U, Z, and V. It must be at least 1 and at least max( NN ). Status: not modified. 🦋
  • V — REAL array, dimension (LDU, max(NN)). The Householder vectors computed by SSYTRD in reducing A to tridiagonal form. Status: modified. ✨
  • TAU — REAL array, dimension (max(NN)). The Householder factors computed by SSYTRD in reducing A to tridiagonal form. Status: modified. 💅
  • Z — REAL array, dimension (LDU, max(NN)). The orthogonal matrix of eigenvectors computed by SSTEQR, SPTEQR, and SSTEIN. Status: modified. 🎀
  • WORK — REAL array, dimension (LWORK). Workspace. Status: 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. Status: 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. Status: 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. Status: 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. Status: 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 tests performed are… (Routine tested)

  • Test 1 — | A - U S U' | / ( |A| n ulp ) — routine tested: SSTEV('V', ... )
  • Test 2 — | I - U U' | / ( n ulp ) — routine tested: SSTEV('V', ... )
  • Test 3 — |D(with Z) - D(w/o Z)| / (|D| ulp) — routine tested: SSTEV('N', ... )
  • Test 4 — | A - U S U' | / ( |A| n ulp ) — routine tested: SSTEVX('V','A', ... )
  • Test 5 — | I - U U' | / ( n ulp ) — routine tested: SSTEVX('V','A', ... )
  • Test 6 — |D(with Z) - EVEIGS| / (|D| ulp) — routine tested: SSTEVX('N','A', ... )
  • Test 7 — | A - U S U' | / ( |A| n ulp ) — routine tested: SSTEVR('V','A', ... )
  • Test 8 — | I - U U' | / ( n ulp ) — routine tested: SSTEVR('V','A', ... )
  • Test 9 — |D(with Z) - EVEIGS| / (|D| ulp) — routine tested: SSTEVR('N','A', ... )
  • Test 10 — | A - U S U' | / ( |A| n ulp ) — routine tested: SSTEVX('V','I', ... )
  • Test 11 — | I - U U' | / ( n ulp ) — routine tested: SSTEVX('V','I', ... )
  • Test 12 — |D(with Z) - D(w/o Z)| / (|D| ulp) — routine tested: SSTEVX('N','I', ... )
  • Test 13 — | A - U S U' | / ( |A| n ulp ) — routine tested: SSTEVX('V','V', ... )
  • Test 14 — | I - U U' | / ( n ulp ) — routine tested: SSTEVX('V','V', ... )
  • Test 15 — |D(with Z) - D(w/o Z)| / (|D| ulp) — routine tested: SSTEVX('N','V', ... )
  • Test 16 — | A - U S U' | / ( |A| n ulp ) — routine tested: SSTEVD('V', ... )
  • Test 17 — | I - U U' | / ( n ulp ) — routine tested: SSTEVD('V', ... )
  • Test 18 — |D(with Z) - EVEIGS| / (|D| ulp) — routine tested: SSTEVD('N', ... )
  • Test 19 — | A - U S U' | / ( |A| n ulp ) — routine tested: SSTEVR('V','I', ... )
  • Test 20 — | I - U U' | / ( n ulp ) — routine tested: SSTEVR('V','I', ... )
  • Test 21 — |D(with Z) - D(w/o Z)| / (|D| ulp) — routine tested: SSTEVR('N','I', ... )
  • Test 22 — | A - U S U' | / ( |A| n ulp ) — routine tested: SSTEVR('V','V', ... )
  • Test 23 — | I - U U' | / ( n ulp ) — routine tested: SSTEVR('V','V', ... )
  • Test 24 — |D(with Z) - D(w/o Z)| / (|D| ulp) — routine tested: SSTEVR('N','V', ... )
  • Test 25 — | A - U S U' | / ( |A| n ulp ) — routine tested: SSYEV('L','V', ... )
  • Test 26 — | I - U U' | / ( n ulp ) — routine tested: SSYEV('L','V', ... )
  • Test 27 — |D(with Z) - D(w/o Z)| / (|D| ulp) — routine tested: SSYEV_2STAGE('L','N', ... )
  • Test 28 — | A - U S U' | / ( |A| n ulp ) — routine tested: SSYEVX('L','V','A', ... )

okay bestie, we’re deep in the test list now and it is long, but I promised no skipping, so here’s every single row exactly as the source gives it — line by line, no cap 💅

           !>    29= | I - U U' | / ( n ulp )              SSYEVX('L','V','A', ... )
           !>    30= |D(with Z) - D(w/o Z)| / (|D| ulp)    SSYEVX_2STAGE('L','N','A', ... )
           !>    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_2STAGE('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_2STAGE('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_2STAGE('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_2STAGE('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_2STAGE('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_2STAGE('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_2STAGE('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_2STAGE('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_2STAGE('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_2STAGE('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_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 )        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', ... )
           !>

👑 Author

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

Definition at line 449 of file sdrvst2stg.f.

👑 Author (the Doxygen one 🤖)

Generated automatically by Doxygen for LAPACK from the source code.

and that’s the whole page, bestie 🎀 — LAPACK Version 3.12.0, from TESTING/EIG/sdrvst2stg.f(3), mwah 💋

📦 where this page comes from