zhegvx.cpp

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/*
   -- MAGMA (version 1.2.0) --
      Univ. of Tennessee, Knoxville
      Univ. of California, Berkeley
      Univ. of Colorado, Denver
      May 2012
 
      @author Raffaele Solca

      @precisions normal z -> c
 
 */
#include "common_magma.h"

void Mymagma_ztrmm(char side, char uplo, char trans, char unit, magma_int_t n, magma_int_t m,
                   cuDoubleComplex alpha, cuDoubleComplex *db, magma_int_t lddb,
                   cuDoubleComplex *dz, magma_int_t lddz)
{
    magma_ztrmm(side, uplo, trans, unit, n, m, alpha, db, lddb, dz, lddz);
    magma_device_sync();
}

void Mymagma_ztrsm(char side, char uplo, char trans, char unit, magma_int_t n, magma_int_t m,
                   cuDoubleComplex alpha, cuDoubleComplex *db, magma_int_t lddb, 
                   cuDoubleComplex *dz, magma_int_t lddz)
{
    magma_ztrsm(side, uplo, trans, unit, n, m, alpha, db, lddb, dz, lddz);
    magma_device_sync();
}

extern "C" magma_int_t
magma_zhegvx(magma_int_t itype, char jobz, char range, char uplo, magma_int_t n,
             cuDoubleComplex *a, magma_int_t lda, cuDoubleComplex *b, magma_int_t ldb, 
             double vl, double vu, magma_int_t il, magma_int_t iu, double abstol,
             magma_int_t *m, double *w,  cuDoubleComplex *z, magma_int_t ldz, 
             cuDoubleComplex *work, magma_int_t lwork, double *rwork,
             magma_int_t *iwork, magma_int_t *ifail, magma_int_t *info)
{ 
/*  
   -- MAGMA (version 1.2.0) --
   Univ. of Tennessee, Knoxville
   Univ. of California, Berkeley
   Univ. of Colorado, Denver
   May 2012
   
   ITYPE   (input) INTEGER
           Specifies the problem type to be solved:
           = 1:  A*x = (lambda)*B*x
           = 2:  A*B*x = (lambda)*x
           = 3:  B*A*x = (lambda)*x
 
   JOBZ    (input) CHARACTER*1
           = 'N':  Compute eigenvalues only;
           = 'V':  Compute eigenvalues and eigenvectors.
 
   RANGE   (input) CHARACTER*1
           = 'A': all eigenvalues will be found.
           = 'V': all eigenvalues in the half-open interval (VL,VU]
                  will be found.
           = 'I': the IL-th through IU-th eigenvalues will be found.

   UPLO    (input) CHARACTER*1
           = 'U':  Upper triangles of A and B are stored;
           = 'L':  Lower triangles of A and B are stored.
 
   N       (input) INTEGER
           The order of the matrices A and B.  N >= 0.
 
   A       (input/output) COMPLEX*16 array, dimension (LDA, N)
           On entry, the Hermitian matrix A.  If UPLO = 'U', the
           leading N-by-N upper triangular part of A contains the
           upper triangular part of the matrix A.  If UPLO = 'L',
           the leading N-by-N lower triangular part of A contains
           the lower triangular part of the matrix A.
 
           On exit,  the lower triangle (if UPLO='L') or the upper
           triangle (if UPLO='U') of A, including the diagonal, is
           destroyed.
 
   LDA     (input) INTEGER
           The leading dimension of the array A.  LDA >= max(1,N).
 
   B       (input/output) COMPLEX*16 array, dimension (LDB, N)
           On entry, the Hermitian matrix B.  If UPLO = 'U', the
           leading N-by-N upper triangular part of B contains the
           upper triangular part of the matrix B.  If UPLO = 'L',
           the leading N-by-N lower triangular part of B contains
           the lower triangular part of the matrix B.
 
           On exit, if INFO <= N, the part of B containing the matrix is
           overwritten by the triangular factor U or L from the Cholesky
           factorization B = U**H*U or B = L*L**H.
 
   LDB     (input) INTEGER
           The leading dimension of the array B.  LDB >= max(1,N).
 
   VL      (input) DOUBLE PRECISION
   VU      (input) DOUBLE PRECISION
           If RANGE='V', the lower and upper bounds of the interval to
           be searched for eigenvalues. VL < VU.
           Not referenced if RANGE = 'A' or 'I'.
 
   IL      (input) INTEGER
   IU      (input) INTEGER
           If RANGE='I', the indices (in ascending order) of the
           smallest and largest eigenvalues to be returned.
           1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
           Not referenced if RANGE = 'A' or 'V'.
 
   ABSTOL  (input) DOUBLE PRECISION
           The absolute error tolerance for the eigenvalues.
           An approximate eigenvalue is accepted as converged
           when it is determined to lie in an interval [a,b]
           of width less than or equal to
 
                   ABSTOL + EPS *   max( |a|,|b| ) ,
 
           where EPS is the machine precision.  If ABSTOL is less than
           or equal to zero, then  EPS*|T|  will be used in its place,
           where |T| is the 1-norm of the tridiagonal matrix obtained
           by reducing A to tridiagonal form.
 
           Eigenvalues will be computed most accurately when ABSTOL is
           set to twice the underflow threshold 2*DLAMCH('S'), not zero.
           If this routine returns with INFO>0, indicating that some
           eigenvectors did not converge, try setting ABSTOL to
           2*DLAMCH('S').
 
   M       (output) INTEGER
           The total number of eigenvalues found.  0 <= M <= N.
           If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
 
   W       (output) DOUBLE PRECISION array, dimension (N)
           The first M elements contain the selected
           eigenvalues in ascending order.
 
   Z       (output) COMPLEX*16 array, dimension (LDZ, max(1,M))
           If JOBZ = 'N', then Z is not referenced.
           If JOBZ = 'V', then if INFO = 0, the first M columns of Z
           contain the orthonormal eigenvectors of the matrix A
           corresponding to the selected eigenvalues, with the i-th
           column of Z holding the eigenvector associated with W(i).
           The eigenvectors are normalized as follows:
           if ITYPE = 1 or 2, Z**T*B*Z = I;
           if ITYPE = 3, Z**T*inv(B)*Z = I.
 
           If an eigenvector fails to converge, then that column of Z
           contains the latest approximation to the eigenvector, and the
           index of the eigenvector is returned in IFAIL.
           Note: the user must ensure that at least max(1,M) columns are
           supplied in the array Z; if RANGE = 'V', the exact value of M
           is not known in advance and an upper bound must be used.
 
   LDZ     (input) INTEGER
           The leading dimension of the array Z.  LDZ >= 1, and if
           JOBZ = 'V', LDZ >= max(1,N).
 
   WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
           On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 
   LWORK   (input) INTEGER
           The length of the array WORK.  LWORK >= max(1,2*N).
           For optimal efficiency, LWORK >= (NB+1)*N,
           where NB is the blocksize for ZHETRD returned by ILAENV.
 
           If LWORK = -1, then a workspace query is assumed; the routine
           only calculates the optimal size of the WORK array, returns
           this value as the first entry of the WORK array, and no error
           message related to LWORK is issued by XERBLA.
 
   RWORK   (workspace) DOUBLE PRECISION array, dimension (7*N)
 
   IWORK   (workspace) INTEGER array, dimension (5*N)
 
   IFAIL   (output) INTEGER array, dimension (N)
           If JOBZ = 'V', then if INFO = 0, the first M elements of
           IFAIL are zero.  If INFO > 0, then IFAIL contains the
           indices of the eigenvectors that failed to converge.
           If JOBZ = 'N', then IFAIL is not referenced.
 
   INFO    (output) INTEGER
           = 0:  successful exit
           < 0:  if INFO = -i, the i-th argument had an illegal value
           > 0:  ZPOTRF or ZHEEVX returned an error code:
              <= N:  if INFO = i, ZHEEVX failed to converge;
                     i eigenvectors failed to converge.  Their indices
                     are stored in array IFAIL.
              > N:   if INFO = N + i, for 1 <= i <= N, then the leading
                     minor of order i of B is not positive definite.
                     The factorization of B could not be completed and
                     no eigenvalues or eigenvectors were computed.
 
   Further Details
   ===============
 
   Based on contributions by
      Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA 
=====================================================================  */
  
  char uplo_[2] = {uplo, 0};
  char jobz_[2] = {jobz, 0};
  char range_[2] = {range, 0};
  
  cuDoubleComplex c_one = MAGMA_Z_ONE;
  
  cuDoubleComplex *da;
  cuDoubleComplex *db;
  cuDoubleComplex *dz;  
  magma_int_t ldda = n;
  magma_int_t lddb = n;
  magma_int_t lddz = n;  
  
  static magma_int_t lower;
  static char trans[1];
  static magma_int_t wantz;
  static magma_int_t lquery;
  static magma_int_t alleig, valeig, indeig;
  
  static magma_int_t lwmin;
  
  static cudaStream_t stream;
  magma_queue_create( &stream );
  
  wantz = lapackf77_lsame(jobz_, MagmaVectorsStr);
  lower = lapackf77_lsame(uplo_, MagmaLowerStr);
  alleig = lapackf77_lsame(range_, "A");
  valeig = lapackf77_lsame(range_, "V");
  indeig = lapackf77_lsame(range_, "I");
  lquery = lwork == -1;
  
  *info = 0;
  if (itype < 1 || itype > 3) {
    *info = -1;
  } else if (! (alleig || valeig || indeig)) {
    *info = -2;
  } else if (! (wantz || lapackf77_lsame(jobz_, MagmaNoVectorsStr))) {
    *info = -3;
  } else if (! (lower || lapackf77_lsame(uplo_, MagmaUpperStr))) {
    *info = -4;
  } else if (n < 0) {
    *info = -5;
  } else if (lda < max(1,n)) {
    *info = -7;
  } else if (ldb < max(1,n)) {
    *info = -9;
  } else if (ldz < 1 || wantz && ldz < n) {
    *info = -18;
  } else {
    if (valeig) {
      if (n > 0 && vu <= vl) {
        *info = -11;
      }
    } else if (indeig) {
      if (il < 1 || il > max(1,n)) {
        *info = -12;
      } else if (iu < min(n,il) || iu > n) {
        *info = -13;
      }
    }
  }
  
  magma_int_t nb = magma_get_zhetrd_nb(n); 
  
  lwmin = n * (nb + 1);
  
  MAGMA_Z_SET2REAL(work[0],(double)lwmin);
  
  
  if (lwork < lwmin && ! lquery) {
    *info = -20;
  }
  
  if (*info != 0) {
      magma_xerbla( __func__, -(*info));
      return *info;
  } else if (lquery) {
      return *info;
  }
  
  /* Quick return if possible */
  if (n == 0) {
    return *info;
  }
  
  if (MAGMA_SUCCESS != magma_zmalloc( &da, n*ldda ) ||
      MAGMA_SUCCESS != magma_zmalloc( &db, n*lddb ) ||
      MAGMA_SUCCESS != magma_zmalloc( &dz, n*lddz )) {
    *info = MAGMA_ERR_DEVICE_ALLOC;
    return *info;
  }
  
  /*     Form a Cholesky factorization of B. */
  
  magma_zsetmatrix( n, n, b, ldb, db, lddb );
  
  magma_zsetmatrix_async( n, n,
                          a,  lda,
                          da, ldda, stream );  
  
  magma_zpotrf_gpu(uplo_[0], n, db, lddb, info);
  if (*info != 0) {
    *info = n + *info;
    return *info;
  }
  
  magma_queue_sync( stream );
  
  magma_zgetmatrix_async( n, n,
                          db, lddb,
                          b,  ldb, stream );
  
  /*     Transform problem to standard eigenvalue problem and solve. */
  
  magma_zhegst_gpu(itype, uplo, n, da, ldda, db, lddb, info);
  
  magma_zheevx_gpu(jobz, range, uplo, n, da, ldda, vl, vu, il, iu, abstol, m, w, dz, lddz, a, lda, z, ldz, work, lwork, rwork, iwork, ifail, info);
  
  if (wantz && *info == 0) {
    
    /*        Backtransform eigenvectors to the original problem. */
    
    if (itype == 1 || itype == 2) {
      
      /*           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;   
       backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
      
      if (lower) {
        *(unsigned char *)trans = MagmaConjTrans;
      } else {
        *(unsigned char *)trans = MagmaNoTrans;
      }
      
      Mymagma_ztrsm(MagmaLeft, uplo, *trans, MagmaNonUnit, n, *m, c_one, db, lddb, dz, lddz);
      
    } else if (itype == 3) {
      
      /*           For B*A*x=(lambda)*x;   
       backtransform eigenvectors: x = L*y or U'*y */
      
      if (lower) {
        *(unsigned char *)trans = MagmaNoTrans;
      } else {
        *(unsigned char *)trans = MagmaConjTrans;
      }
      
      Mymagma_ztrmm(MagmaLeft, uplo, *trans, MagmaNonUnit, n, *m, c_one, db, lddb, dz, lddz);
      
    }
    
    magma_zgetmatrix( n, *m, dz, lddz, z, ldz );
    
  }
  
  magma_queue_sync( stream );
  
  magma_queue_destroy( stream );
  
  magma_free( da );
  magma_free( db );
  magma_free( dz );
  
  return *info;
  
} /* zhegvx */