pilaenvx.f

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      INTEGER FUNCTION pilaenvx( ICTXT, ISPEC, NAME, OPTS, N1, N2, N3,
     $                           N4 )
*
*     Contribution from the Department of Computing Science and HPC2N,
*     Umea University, Sweden
*
*  -- ScaLAPACK auxiliary routine (version 2.0.1) --
*     University of Tennessee, Knoxville, Oak Ridge National Laboratory,
*     Univ. of Colorado Denver and University of California, Berkeley.
*     January, 2012
*
      IMPLICIT NONE
*
*     .. Scalar Arguments ..
      CHARACTER*( * )    name, opts
      INTEGER            ictxt, ispec, n1, n2, n3, n4
*     ..
*
*  Purpose
*  =======
*
*  PILAENVX is called from the ScaLAPACK routines to choose problem-
*  dependent parameters for the local environment.  See ISPEC for a
*  description of the parameters.
*
*  This version provides a set of parameters which should give good,
*  but not optimal, performance on many of the currently available
*  computers.  Users are encouraged to modify this subroutine to set
*  the tuning parameters for their particular machine using the option
*  and problem size information in the arguments.
*
*  This routine will not function correctly if it is converted to all
*  lower case.  Converting it to all upper case is allowed.
*
*  Arguments
*  =========
*
*  ICTXT   (local input) INTEGER
*          On entry,  ICTXT  specifies the BLACS context handle, indica-
*          ting the global  context of the operation. The context itself
*          is global, but the value of ICTXT is local.
*
*  ISPEC   (global input) INTEGER
*          Specifies the parameter to be returned as the value of
*          PILAENVX.
*          = 1: the optimal blocksize; if this value is 1, an unblocked
*               algorithm will give the best performance (unlikely).
*          = 2: the minimum block size for which the block routine
*               should be used; if the usable block size is less than
*               this value, an unblocked routine should be used.
*          = 3: the crossover point (in a block routine, for N less
*               than this value, an unblocked routine should be used)
*          = 4: the number of shifts, used in the nonsymmetric
*               eigenvalue routines (DEPRECATED)
*          = 5: the minimum column dimension for blocking to be used;
*               rectangular blocks must have dimension at least k by m,
*               where k is given by PILAENVX(2,...) and m by PILAENVX(5,...)
*          = 6: the crossover point for the SVD (when reducing an m by n
*               matrix to bidiagonal form, if max(m,n)/min(m,n) exceeds
*               this value, a QR factorization is used first to reduce
*               the matrix to a triangular form.)
*          = 7: the number of processors
*          = 8: the crossover point for the multishift QR method
*               for nonsymmetric eigenvalue problems (DEPRECATED)
*          = 9: maximum size of the subproblems at the bottom of the
*               computation tree in the divide-and-conquer algorithm
*               (used by xGELSD and xGESDD)
*          =10: ieee NaN arithmetic can be trusted not to trap
*          =11: infinity arithmetic can be trusted not to trap
*          12 <= ISPEC <= 16:
*               PxHSEQR or one of its subroutines,
*               see PIPARMQ for detailed explanation
*          17 <= ISPEC <= 22:
*               Parameters for PBxTRORD/PxHSEQR (not all), as follows:
*               =17: maximum number of concurrent computational windows;
*               =18: number of eigenvalues/bulges in each window;
*               =19: computational window size;
*               =20: minimal percentage of flops required for
*                    performing matrix-matrix multiplications instead
*                    of pipelined orthogonal transformations;
*               =21: width of block column slabs for row-wise
*                    application of pipelined orthogonal
*                    transformations in their factorized form;
*               =22: the maximum number of eigenvalues moved together
*                    over a process border;
*               =23: the number of processors involved in AED;
*          =99: Maximum iteration chunksize in OpenMP parallelization
*
*  NAME    (global input) CHARACTER*(*)
*          The name of the calling subroutine, in either upper case or
*          lower case.
*
*  OPTS    (global input) CHARACTER*(*)
*          The character options to the subroutine NAME, concatenated
*          into a single character string.  For example, UPLO = 'U',
*          TRANS = 'T', and DIAG = 'N' for a triangular routine would
*          be specified as OPTS = 'UTN'.
*
*  N1      (global input) INTEGER
*  N2      (global input) INTEGER
*  N3      (global input) INTEGER
*  N4      (global input) INTEGER
*          Problem dimensions for the subroutine NAME; these may not all
*          be required.
*
* (PILAENVX) (global output) INTEGER
*          >= 0: the value of the parameter specified by ISPEC
*          < 0:  if PILAENVX = -k, the k-th argument had an illegal value.
*
*  Further Details
*  ===============
*
*  The following conventions have been used when calling ILAENV from the
*  LAPACK routines:
*  1)  OPTS is a concatenation of all of the character options to
*      subroutine NAME, in the same order that they appear in the
*      argument list for NAME, even if they are not used in determining
*      the value of the parameter specified by ISPEC.
*  2)  The problem dimensions N1, N2, N3, N4 are specified in the order
*      that they appear in the argument list for NAME.  N1 is used
*      first, N2 second, and so on, and unused problem dimensions are
*      passed a value of -1.
*  3)  The parameter value returned by ILAENV is checked for validity in
*      the calling subroutine.  For example, ILAENV is used to retrieve
*      the optimal blocksize for STRTRI as follows:
*
*      NB = ILAENV( 1, 'STRTRI', UPLO // DIAG, N, -1, -1, -1 )
*      IF( NB.LE.1 ) NB = MAX( 1, N )
*
*  The same conventions will hold for this ScaLAPACK-style variant.
*
*  =====================================================================
*
*     .. Local Scalars ..
      INTEGER            i, ic, iz, nb, nbmin, nx, nprow, npcol, myrow,
     $                   mycol
      LOGICAL            cname, sname
      CHARACTER          c1*1, c2*2, c4*2, c3*3, subnam*6
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          char, ichar, int, min, real
*     ..
*     .. External Functions ..
      INTEGER            ieeeck, piparmq, iceil
      EXTERNAL           ieeeck, piparmq, iceil
*     ..
*     .. Executable Statements ..
*
      IF( ispec.GT.23 ) GO TO 990
      GO TO ( 10, 10, 10, 80, 90, 100, 110, 120,
     $        130, 140, 150, 160, 160, 160, 160, 160,
     $        170, 180, 190, 200, 210, 220, 230, 160)ispec
*
*     Invalid value for ISPEC
*
      pilaenvx = -1
      RETURN
*
   10 CONTINUE
*
*     Convert NAME to upper case if the first character is lower case.
*
      pilaenvx = 1
      subnam = name
      ic = ichar( subnam( 1: 1 ) )
      iz = ichar( 'Z' )
      IF( iz.EQ.90 .OR. iz.EQ.122 ) THEN
*
*        ASCII character set
*
         IF( ic.GE.97 .AND. ic.LE.122 ) THEN
            subnam( 1: 1 ) = char( ic-32 )
            DO 20 i = 2, 6
               ic = ichar( subnam( i: i ) )
               IF( ic.GE.97 .AND. ic.LE.122 )
     $            subnam( i: i ) = char( ic-32 )
   20       CONTINUE
         END IF
*
      ELSE IF( iz.EQ.233 .OR. iz.EQ.169 ) THEN
*
*        EBCDIC character set
*
         IF( ( ic.GE.129 .AND. ic.LE.137 ) .OR.
     $       ( ic.GE.145 .AND. ic.LE.153 ) .OR.
     $       ( ic.GE.162 .AND. ic.LE.169 ) ) THEN
            subnam( 1: 1 ) = char( ic+64 )
            DO 30 i = 2, 6
               ic = ichar( subnam( i: i ) )
               IF( ( ic.GE.129 .AND. ic.LE.137 ) .OR.
     $             ( ic.GE.145 .AND. ic.LE.153 ) .OR.
     $             ( ic.GE.162 .AND. ic.LE.169 ) )subnam( i:
     $             i ) = char( ic+64 )
   30       CONTINUE
         END IF
*
      ELSE IF( iz.EQ.218 .OR. iz.EQ.250 ) THEN
*
*        Prime machines:  ASCII+128
*
         IF( ic.GE.225 .AND. ic.LE.250 ) THEN
            subnam( 1: 1 ) = char( ic-32 )
            DO 40 i = 2, 6
               ic = ichar( subnam( i: i ) )
               IF( ic.GE.225 .AND. ic.LE.250 )
     $            subnam( i: i ) = char( ic-32 )
   40       CONTINUE
         END IF
      END IF
*
      c1 = subnam( 1: 1 )
      sname = c1.EQ.'S' .OR. c1.EQ.'D'
      cname = c1.EQ.'C' .OR. c1.EQ.'Z'
      IF( .NOT.( cname .OR. sname ) )
     $   RETURN
      c2 = subnam( 2: 3 )
      c3 = subnam( 4: 6 )
      c4 = c3( 2: 3 )
*
      GO TO ( 50, 60, 70 )ispec
*
   50 CONTINUE
*
*     ISPEC = 1:  block size
*
*     In these examples, separate code is provided for setting NB for
*     real and complex.  We assume that NB will take the same value in
*     single or double precision.
*
      nb = 1
*
      IF( c2.EQ.'GE' ) THEN
         IF( c3.EQ.'TRF' ) THEN
            IF( sname ) THEN
               nb = 64
            ELSE
               nb = 64
            END IF
         ELSE IF( c3.EQ.'QRF' .OR. c3.EQ.'RQF' .OR. c3.EQ.'LQF' .OR.
     $            c3.EQ.'QLF' ) THEN
            IF( sname ) THEN
               nb = 32
            ELSE
               nb = 32
            END IF
         ELSE IF( c3.EQ.'HRD' ) THEN
            IF( sname ) THEN
               nb = 32
            ELSE
               nb = 32
            END IF
         ELSE IF( c3.EQ.'BRD' ) THEN
            IF( sname ) THEN
               nb = 32
            ELSE
               nb = 32
            END IF
         ELSE IF( c3.EQ.'TRI' ) THEN
            IF( sname ) THEN
               nb = 64
            ELSE
               nb = 64
            END IF
         END IF
      ELSE IF( c2.EQ.'PO' ) THEN
         IF( c3.EQ.'TRF' ) THEN
            IF( sname ) THEN
               nb = 64
            ELSE
               nb = 64
            END IF
         END IF
      ELSE IF( c2.EQ.'SY' ) THEN
         IF( c3.EQ.'TRF' ) THEN
            IF( sname ) THEN
               nb = 64
            ELSE
               nb = 64
            END IF
         ELSE IF( sname .AND. c3.EQ.'TRD' ) THEN
            nb = 32
         ELSE IF( sname .AND. c3.EQ.'GST' ) THEN
            nb = 64
         END IF
      ELSE IF( cname .AND. c2.EQ.'HE' ) THEN
         IF( c3.EQ.'TRF' ) THEN
            nb = 64
         ELSE IF( c3.EQ.'TRD' ) THEN
            nb = 32
         ELSE IF( c3.EQ.'GST' ) THEN
            nb = 64
         END IF
      ELSE IF( sname .AND. c2.EQ.'OR' ) THEN
         IF( c3( 1: 1 ).EQ.'G' ) THEN
            IF( c4.EQ.'QR' .OR. c4.EQ.'RQ' .OR. c4.EQ.'LQ' .OR. c4.EQ.
     $          'QL' .OR. c4.EQ.'HR' .OR. c4.EQ.'tr.OR..EQ.'  C4'br' )
     $           THEN
               NB = 32
            END IF
.EQ.         ELSE IF( C3( 1: 1 )'m' ) THEN
.EQ.            IF( C4'qr.OR..EQ.'  C4'rq.OR..EQ.'  C4'lq.OR..EQ.'  C4
     $          'ql.OR..EQ.'  C4'hr.OR..EQ.'  C4'tr.OR..EQ.'  C4'br' )
     $           THEN
               NB = 32
            END IF
         END IF
.AND..EQ.      ELSE IF( CNAME  C2'un' ) THEN
.EQ.         IF( C3( 1: 1 )'g' ) THEN
.EQ.            IF( C4'qr.OR..EQ.'  C4'rq.OR..EQ.'  C4'lq.OR..EQ.'  C4
     $          'ql.OR..EQ.'  C4'hr.OR..EQ.'  C4'tr.OR..EQ.'  C4'br' )
     $           THEN
               NB = 32
            END IF
.EQ.         ELSE IF( C3( 1: 1 )'m' ) THEN
.EQ.            IF( C4'qr.OR..EQ.'  C4'rq.OR..EQ.'  C4'lq.OR..EQ.'  C4
     $          'ql.OR..EQ.'  C4'hr.OR..EQ.'  C4'tr.OR..EQ.'  C4'br' )
     $           THEN
               NB = 32
            END IF
         END IF
.EQ.      ELSE IF( C2'gb' ) THEN
.EQ.         IF( C3'trf' ) THEN
            IF( SNAME ) THEN
.LE.               IF( N464 ) THEN
                  NB = 1
               ELSE
                  NB = 32
               END IF
            ELSE
.LE.               IF( N464 ) THEN
                  NB = 1
               ELSE
                  NB = 32
               END IF
            END IF
         END IF
.EQ.      ELSE IF( C2'pb' ) THEN
.EQ.         IF( C3'trf' ) THEN
            IF( SNAME ) THEN
.LE.               IF( N264 ) THEN
                  NB = 1
               ELSE
                  NB = 32
               END IF
            ELSE
.LE.               IF( N264 ) THEN
                  NB = 1
               ELSE
                  NB = 32
               END IF
            END IF
         END IF
.EQ.      ELSE IF( C2'tr' ) THEN
.EQ.         IF( C3'tri' ) THEN
            IF( SNAME ) THEN
               NB = 64
            ELSE
               NB = 64
            END IF
         END IF
.EQ.      ELSE IF( C2'la' ) THEN
.EQ.         IF( C3'uum' ) THEN
            IF( SNAME ) THEN
               NB = 64
            ELSE
               NB = 64
            END IF
         END IF
.AND..EQ.      ELSE IF( SNAME  C2'st' ) THEN
.EQ.         IF( C3'ebz' ) THEN
            NB = 1
         END IF
      END IF
      PILAENVX = NB
      RETURN
*
   60 CONTINUE
*
*     ISPEC = 2:  minimum block size
*
      NBMIN = 2
.EQ.      IF( C2'ge' ) THEN
.EQ.         IF( C3'qrf.OR..EQ.'  C3'rqf.OR..EQ.'  C3'lqf.OR..EQ.'  C3
     $       'qlf' ) THEN
            IF( SNAME ) THEN
               NBMIN = 2
            ELSE
               NBMIN = 2
            END IF
.EQ.         ELSE IF( C3'hrd' ) THEN
            IF( SNAME ) THEN
               NBMIN = 2
            ELSE
               NBMIN = 2
            END IF
.EQ.         ELSE IF( C3'brd' ) THEN
            IF( SNAME ) THEN
               NBMIN = 2
            ELSE
               NBMIN = 2
            END IF
.EQ.         ELSE IF( C3'tri' ) THEN
            IF( SNAME ) THEN
               NBMIN = 2
            ELSE
               NBMIN = 2
            END IF
         END IF
.EQ.      ELSE IF( C2'sy' ) THEN
.EQ.         IF( C3'trf' ) THEN
            IF( SNAME ) THEN
               NBMIN = 8
            ELSE
               NBMIN = 8
            END IF
.AND..EQ.         ELSE IF( SNAME  C3'trd' ) THEN
            NBMIN = 2
         END IF
.AND..EQ.      ELSE IF( CNAME  C2'he' ) THEN
.EQ.         IF( C3'trd' ) THEN
            NBMIN = 2
         END IF
.AND..EQ.      ELSE IF( SNAME  C2'or' ) THEN
.EQ.         IF( C3( 1: 1 )'g' ) THEN
.EQ.            IF( C4'qr.OR..EQ.'  C4'rq.OR..EQ.'  C4'lq.OR..EQ.'  C4
     $          'ql.OR..EQ.'  C4'hr.OR..EQ.'  C4'tr.OR..EQ.'  C4'br' )
     $           THEN
               NBMIN = 2
            END IF
.EQ.         ELSE IF( C3( 1: 1 )'m' ) THEN
.EQ.            IF( C4'qr.OR..EQ.'  C4'rq.OR..EQ.'  C4'lq.OR..EQ.'  C4
     $          'ql.OR..EQ.'  C4'hr.OR..EQ.'  C4'tr.OR..EQ.'  C4'br' )
     $           THEN
               NBMIN = 2
            END IF
         END IF
.AND..EQ.      ELSE IF( CNAME  C2'un' ) THEN
.EQ.         IF( C3( 1: 1 )'g' ) THEN
.EQ.            IF( C4'qr.OR..EQ.'  C4'rq.OR..EQ.'  C4'lq.OR..EQ.'  C4
     $          'ql.OR..EQ.'  C4'hr.OR..EQ.'  C4'tr.OR..EQ.'  C4'br' )
     $           THEN
               NBMIN = 2
            END IF
.EQ.         ELSE IF( C3( 1: 1 )'m' ) THEN
.EQ.            IF( C4'qr.OR..EQ.'  C4'rq' .OR. c4.EQ.'LQ' .OR. c4.EQ.
     $          'QL' .OR. c4.EQ.'HR' .OR. c4.EQ.'TR' .OR. c4.EQ.'BR' )
     $           THEN
               nbmin = 2
            END IF
         END IF
      END IF
      pilaenvx = nbmin
      RETURN
*
   70 CONTINUE
*
*     ISPEC = 3:  crossover point
*
      nx = 0
      IF( c2.EQ.'GE' ) THEN
         IF( c3.EQ.'QRF' .OR. c3.EQ.'RQF' .OR. c3.EQ.'LQF' .OR. c3.EQ.
     $       'QLF' ) THEN
            IF( sname ) THEN
               nx = 128
            ELSE
               nx = 128
            END IF
         ELSE IF( c3.EQ.'HRD' ) THEN
            IF( sname ) THEN
               nx = 128
            ELSE
               nx = 128
            END IF
         ELSE IF( c3.EQ.'BRD' ) THEN
            IF( sname ) THEN
               nx = 128
            ELSE
               nx = 128
            END IF
         END IF
      ELSE IF( c2.EQ.'SY' ) THEN
         IF( sname .AND. c3.EQ.'TRD' ) THEN
            nx = 32
         END IF
      ELSE IF( cname .AND. c2.EQ.'HE' ) THEN
         IF( c3.EQ.'TRD' ) THEN
            nx = 32
         END IF
      ELSE IF( sname .AND. c2.EQ.'OR' ) THEN
         IF( c3( 1: 1 ).EQ.'G' ) THEN
            IF( c4.EQ.'QR' .OR. c4.EQ.'RQ' .OR. c4.EQ.'LQ' .OR. c4.EQ.
     $          'QL' .OR. c4.EQ.'HR' .OR. c4.EQ.'TR' .OR. c4.EQ.'BR' )
     $           THEN
               nx = 128
            END IF
         END IF
      ELSE IF( cname .AND. c2.EQ.'UN' ) THEN
         IF( c3( 1: 1 ).EQ.'G' ) THEN
            IF( c4.EQ.'QR' .OR. c4.EQ.'RQ' .OR. c4.EQ.'LQ' .OR. c4.EQ.
     $          'QL' .OR. c4.EQ.'HR' .OR. c4.EQ.'TR' .OR. c4.EQ.'BR' )
     $           THEN
               nx = 128
            END IF
         END IF
      END IF
      pilaenvx = nx
      RETURN
*
   80 CONTINUE
*
*     ISPEC = 4:  number of shifts (used by xHSEQR)
*
      pilaenvx = 6
      RETURN
*
   90 CONTINUE
*
*     ISPEC = 5:  minimum column dimension (not used)
*
      pilaenvx = 2
      RETURN
*
  100 CONTINUE
*
*     ISPEC = 6:  crossover point for SVD (used by xGELSS and xGESVD)
*
      pilaenvx = int( real( min( n1, n2 ) )*1.6e0 )
      RETURN
*
  110 CONTINUE
*
*     ISPEC = 7:  number of processors (not used)
*
      pilaenvx = 1
      RETURN
*
  120 CONTINUE
*
*     ISPEC = 8:  crossover point for multishift (used by xHSEQR)
*
      pilaenvx = 50
      RETURN
*
  130 CONTINUE
*
*     ISPEC = 9:  maximum size of the subproblems at the bottom of the
*                 computation tree in the divide-and-conquer algorithm
*                 (used by xGELSD and xGESDD)
*
      pilaenvx = 25
      RETURN
*
  140 CONTINUE
*
*     ISPEC = 10: ieee NaN arithmetic can be trusted not to trap
*
*     PILAENVX = 0
      pilaenvx = 1
      IF( pilaenvx.EQ.1 ) THEN
         pilaenvx = ieeeck( 0, 0.0, 1.0 )
      END IF
      RETURN
*
  150 CONTINUE
*
*     ISPEC = 11: infinity arithmetic can be trusted not to trap
*
*     PILAENVX = 0
      pilaenvx = 1
      IF( pilaenvx.EQ.1 ) THEN
         pilaenvx = ieeeck( 1, 0.0, 1.0 )
      END IF
      RETURN
*
  160 CONTINUE
*
*     12 <= ISPEC <= 16 or ISPEC = 24: xHSEQR or one of its subroutines.
*
      pilaenvx = piparmq( ictxt, ispec, name, opts, n1, n2, n3, n4 )
      RETURN
*
  170 CONTINUE
*
*     ISPEC = 17: maximum number of independent computational windows
*
      CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
      pilaenvx = min( iceil(n1,n2), min( nprow, npcol) )
      RETURN
*
  180 CONTINUE
*
*     ISPEC = 18: number of eigenvalues in each window
*
      pilaenvx = min(n2/2,40)
      RETURN
*
  190 CONTINUE
*
*     ISPEC = 19: computational window size
*
      pilaenvx = min(n2,80)
      RETURN
*
  200 CONTINUE
*
*     ISPEC = 20: minimal percentage of flops required for
*     performing matrix-matrix multiplications instead of
*     pipelined orthogonal transformations
*
*
      pilaenvx = 50
      RETURN
*
  210 CONTINUE
*
*     ISPEC = 21: width of block column slabs for row-wise
*     application of pipelined orthogonal transformations in
*     their factorized form
*
*
      pilaenvx = min(n2,32)
      RETURN
*
  220 CONTINUE
*
*     ISPEC = 22: maximum number of eigenvalues to bring over
*                 the block border
*
*
      pilaenvx = min(n2/2,40)
      RETURN
  230 CONTINUE
*
*     ISPEC = 23: number of processors involved in AED
*
*
      pilaenvx = iceil(n1, iceil(384, n2)*n2)
      RETURN
  990 CONTINUE
*
*     ISPEC = 99: maximum chunksize of iterations in OpenMP
*                 parallelization
*
      pilaenvx = 32
      RETURN
*
*     End of PILAENVX
*
      END