SDRVSG2STG checks the real symmetric generalized eigenproblem


      drivers.


              SSYGV computes all eigenvalues and, optionally,


              eigenvectors of a real symmetric-definite generalized


              eigenproblem.


              SSYGVD computes all eigenvalues and, optionally,


              eigenvectors of a real symmetric-definite generalized


              eigenproblem using a divide and conquer algorithm.


              SSYGVX computes selected eigenvalues and, optionally,


              eigenvectors of a real symmetric-definite generalized


              eigenproblem.


              SSPGV computes all eigenvalues and, optionally,


              eigenvectors of a real symmetric-definite generalized


              eigenproblem in packed storage.


              SSPGVD computes all eigenvalues and, optionally,


              eigenvectors of a real symmetric-definite generalized


              eigenproblem in packed storage using a divide and


              conquer algorithm.


              SSPGVX computes selected eigenvalues and, optionally,


              eigenvectors of a real symmetric-definite generalized


              eigenproblem in packed storage.


              SSBGV computes all eigenvalues and, optionally,


              eigenvectors of a real symmetric-definite banded


              generalized eigenproblem.


              SSBGVD computes all eigenvalues and, optionally,


              eigenvectors of a real symmetric-definite banded


              generalized eigenproblem using a divide and conquer


              algorithm.


              SSBGVX computes selected eigenvalues and, optionally,


              eigenvectors of a real symmetric-definite banded


              generalized eigenproblem.


      When SDRVSG2STG is called, a number of matrix 'sizes' ('n's') and a


      number of matrix 'types' are specified.  For each size ('n')


      and each type of matrix, one matrix A of the given type will be


      generated; a random well-conditioned matrix B is also generated


      and the pair (A,B) is used to test the drivers.


      For each pair (A,B), the following tests are performed:


      (1) SSYGV with ITYPE = 1 and UPLO ='U':


              | A Z - B Z D | / ( |A| |Z| n ulp )


              | D - D2 | / ( |D| ulp )   where D is computed by


                                         SSYGV and  D2 is computed by


                                         SSYGV_2STAGE. This test is


                                         only performed for SSYGV


      (2) as (1) but calling SSPGV


      (3) as (1) but calling SSBGV


      (4) as (1) but with UPLO = 'L'


      (5) as (4) but calling SSPGV


      (6) as (4) but calling SSBGV


      (7) SSYGV with ITYPE = 2 and UPLO ='U':


              | A B Z - Z D | / ( |A| |Z| n ulp )


      (8) as (7) but calling SSPGV


      (9) as (7) but with UPLO = 'L'


      (10) as (9) but calling SSPGV


      (11) SSYGV with ITYPE = 3 and UPLO ='U':


              | B A Z - Z D | / ( |A| |Z| n ulp )


      (12) as (11) but calling SSPGV


      (13) as (11) but with UPLO = 'L'


      (14) as (13) but calling SSPGV


      SSYGVD, SSPGVD and SSBGVD performed the same 14 tests.


      SSYGVX, SSPGVX and SSBGVX performed the above 14 tests with


      the parameter RANGE = 'A', 'N' and 'I', respectively.


      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.


      This type is used for the matrix A which has half-bandwidth KA.


      B is generated as a well-conditioned positive definite matrix


      with half-bandwidth KB (<= KA).


      Currently, the list of possible types for A is:


      (1)  The zero matrix.


      (2)  The identity matrix.


      (3)  A diagonal matrix with evenly spaced entries


           1, ..., ULP  and random signs.


           (ULP = (first number larger than 1) - 1 )


      (4)  A diagonal matrix with geometrically spaced entries


           1, ..., ULP  and random signs.


      (5)  A diagonal matrix with 'clustered' entries


           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 'clustered' 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) Same as (8), but with KA = 1 and KB = 1


      (17) Same as (8), but with KA = 2 and KB = 1


      (18) Same as (8), but with KA = 2 and KB = 2


      (19) Same as (8), but with KA = 3 and KB = 1


      (20) Same as (8), but with KA = 3 and KB = 2


      (21) Same as (8), but with KA = 3 and KB = 3

  NSIZES  INTEGER


          The number of sizes of matrices to use.  If it is zero,


          SDRVSG2STG 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, SDRVSG2STG


          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 SDRVSG2STG to continue the same random number


          sequence.


          Modified.


  THRESH  REAL


          A test will count as 'failed' if the 'error', 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. real)


          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 and AB.  It must be at


          least 1 and at least max( NN ).


          Not modified.


  B       REAL             array, dimension (LDB , max(NN))


          Used to hold the symmetric positive definite matrix for


          the generalized problem.


          On exit, B contains the last matrix actually


          used.


          Modified.


  LDB     INTEGER


          The leading dimension of B and BB.  It must be at


          least 1 and at least max( NN ).


          Not modified.


  D       REAL             array, dimension (max(NN))


          The eigenvalues of A. On exit, the eigenvalues in D


          correspond with the matrix in A.


          Modified.


  Z       REAL             array, dimension (LDZ, max(NN))


          The matrix of eigenvectors.


          Modified.


  LDZ     INTEGER


          The leading dimension of Z.  It must be at least 1 and


          at least max( NN ).


          Not modified.


  AB      REAL             array, dimension (LDA, max(NN))


          Workspace.


          Modified.


  BB      REAL             array, dimension (LDB, max(NN))


          Workspace.


          Modified.


  AP      REAL             array, dimension (max(NN)**2)


          Workspace.


          Modified.


  BP      REAL             array, dimension (max(NN)**2)


          Workspace.


          Modified.


  WORK    REAL array, dimension (NWORK)


          Workspace.


          Modified.


  NWORK   INTEGER


          The number of entries in WORK.  This must be at least


          1+5*N+2*N*lg(N)+3*N**2 where N = max( NN(j) ) and


          lg( N ) = smallest integer k such that 2**k >= N.


          Not modified.


  IWORK   INTEGER array, dimension (LIWORK)


          Workspace.


          Modified.


  LIWORK  INTEGER


          The number of entries in WORK.  This must be at least 6*N.


          Not modified.


  RESULT  REAL array, dimension (70)


          The values computed by the 70 tests described above.


          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: LDZ < 1 or LDZ < NMAX.


          -21: NWORK too small.


          -23: LIWORK too small.


          If  SLATMR, SLATMS, SSYGV, SSPGV, SSBGV, SSYGVD, SSPGVD,


              SSBGVD, SSYGVX, SSPGVX or SSBGVX 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 that have been run


                       on this matrix.


       NTESTT          The total number of tests for this call.


       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 'j'.


       KMODE(j)        The MODE value to be passed to the matrix


                       generator for type 'j'.


       KMAGN(j)        The order of magnitude ( O(1),


                       O(overflow^(1/2) ), O(underflow^(1/2) )

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.