---
name: "ddrvst"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/ddrvst.f"
---

# ddrvst(3)

Part of [ddrvst.f(3)](/ddrvst.f/3.md).

## NAME

TESTING/EIG/ddrvst.f

## SYNOPSIS

### Functions/Subroutines

subroutine **ddrvst** (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)\
 **DDRVST**

## Function/Subroutine Documentation

### subroutine ddrvst (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)

**DDRVST**

**Purpose:**

```
!>
!>      DDRVST  checks the symmetric eigenvalue problem drivers.
!>
!>              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.
!>
!>      When DDRVST 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  are specified by an array NN(1:NSIZES); the value of
!>      each element NN(j) specifies one size.
!>      The  are specified by a logical array DOTYPE( 1:NTYPES );
!>      if DOTYPE(j) is .TRUE., then matrix type  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 is zero,
!>          DDRVST 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, DDRVST
!>          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 DDRVST to continue the same random number
!>          sequence.
!>          Modified.
!>
!>  THRESH  DOUBLE PRECISION
!>          A test will count as  if the , 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.
!>
!>  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       DOUBLE PRECISION 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      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
!>
!>  EVEIGS  DOUBLE PRECISION array, dimension (max(NN))
!>          The eigenvalues as computed by DSTEV('N', ... )
!>          (I reserve the right to change this to the output of
!>          whichever algorithm computes the most accurate eigenvalues).
!>
!>  WA1     DOUBLE PRECISION array, dimension
!>
!>  WA2     DOUBLE PRECISION array, dimension
!>
!>  WA3     DOUBLE PRECISION array, dimension
!>
!>  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.
!>          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.
!>          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.
!>          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.
!>          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  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.
!>       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 .
!>       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
!>    1= | A - U S U' | / ( |A| n ulp )         DSTEV('V', ... )
!>    2= | I - U U' | / ( n ulp )               DSTEV('V', ... )
!>    3= |D(with Z) - D(w/o Z)| / (|D| ulp)     DSTEV('N', ... )
!>    4= | A - U S U' | / ( |A| n ulp )         DSTEVX('V','A', ... )
!>    5= | I - U U' | / ( n ulp )               DSTEVX('V','A', ... )
!>    6= |D(with Z) - EVEIGS| / (|D| ulp)       DSTEVX('N','A', ... )
!>    7= | A - U S U' | / ( |A| n ulp )         DSTEVR('V','A', ... )
!>    8= | I - U U' | / ( n ulp )               DSTEVR('V','A', ... )
!>    9= |D(with Z) - EVEIGS| / (|D| ulp)       DSTEVR('N','A', ... )
!>    10= | A - U S U' | / ( |A| n ulp )        DSTEVX('V','I', ... )
!>    11= | I - U U' | / ( n ulp )              DSTEVX('V','I', ... )
!>    12= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSTEVX('N','I', ... )
!>    13= | A - U S U' | / ( |A| n ulp )        DSTEVX('V','V', ... )
!>    14= | I - U U' | / ( n ulp )              DSTEVX('V','V', ... )
!>    15= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSTEVX('N','V', ... )
!>    16= | A - U S U' | / ( |A| n ulp )        DSTEVD('V', ... )
!>    17= | I - U U' | / ( n ulp )              DSTEVD('V', ... )
!>    18= |D(with Z) - EVEIGS| / (|D| ulp)      DSTEVD('N', ... )
!>    19= | A - U S U' | / ( |A| n ulp )        DSTEVR('V','I', ... )
!>    20= | I - U U' | / ( n ulp )              DSTEVR('V','I', ... )
!>    21= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSTEVR('N','I', ... )
!>    22= | A - U S U' | / ( |A| n ulp )        DSTEVR('V','V', ... )
!>    23= | I - U U' | / ( n ulp )              DSTEVR('V','V', ... )
!>    24= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSTEVR('N','V', ... )
!>
!>    25= | A - U S U' | / ( |A| n ulp )        DSYEV('L','V', ... )
!>    26= | I - U U' | / ( n ulp )              DSYEV('L','V', ... )
!>    27= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSYEV('L','N', ... )
!>    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('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('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('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('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('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('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('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('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('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('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('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('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', ... )
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **449** of file **ddrvst.f**.

## Author

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