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    1: *> \brief \b DSPGST
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download DSPGV + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspgv.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspgv.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspgv.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
   22: *                         INFO )
   23: * 
   24: *       .. Scalar Arguments ..
   25: *       CHARACTER          JOBZ, UPLO
   26: *       INTEGER            INFO, ITYPE, LDZ, N
   27: *       ..
   28: *       .. Array Arguments ..
   29: *       DOUBLE PRECISION   AP( * ), BP( * ), W( * ), WORK( * ),
   30: *      $                   Z( LDZ, * )
   31: *       ..
   32: *  
   33: *
   34: *> \par Purpose:
   35: *  =============
   36: *>
   37: *> \verbatim
   38: *>
   39: *> DSPGV computes all the eigenvalues and, optionally, the eigenvectors
   40: *> of a real generalized symmetric-definite eigenproblem, of the form
   41: *> A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
   42: *> Here A and B are assumed to be symmetric, stored in packed format,
   43: *> and B is also positive definite.
   44: *> \endverbatim
   45: *
   46: *  Arguments:
   47: *  ==========
   48: *
   49: *> \param[in] ITYPE
   50: *> \verbatim
   51: *>          ITYPE is INTEGER
   52: *>          Specifies the problem type to be solved:
   53: *>          = 1:  A*x = (lambda)*B*x
   54: *>          = 2:  A*B*x = (lambda)*x
   55: *>          = 3:  B*A*x = (lambda)*x
   56: *> \endverbatim
   57: *>
   58: *> \param[in] JOBZ
   59: *> \verbatim
   60: *>          JOBZ is CHARACTER*1
   61: *>          = 'N':  Compute eigenvalues only;
   62: *>          = 'V':  Compute eigenvalues and eigenvectors.
   63: *> \endverbatim
   64: *>
   65: *> \param[in] UPLO
   66: *> \verbatim
   67: *>          UPLO is CHARACTER*1
   68: *>          = 'U':  Upper triangles of A and B are stored;
   69: *>          = 'L':  Lower triangles of A and B are stored.
   70: *> \endverbatim
   71: *>
   72: *> \param[in] N
   73: *> \verbatim
   74: *>          N is INTEGER
   75: *>          The order of the matrices A and B.  N >= 0.
   76: *> \endverbatim
   77: *>
   78: *> \param[in,out] AP
   79: *> \verbatim
   80: *>          AP is DOUBLE PRECISION array, dimension
   81: *>                            (N*(N+1)/2)
   82: *>          On entry, the upper or lower triangle of the symmetric matrix
   83: *>          A, packed columnwise in a linear array.  The j-th column of A
   84: *>          is stored in the array AP as follows:
   85: *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
   86: *>          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
   87: *>
   88: *>          On exit, the contents of AP are destroyed.
   89: *> \endverbatim
   90: *>
   91: *> \param[in,out] BP
   92: *> \verbatim
   93: *>          BP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
   94: *>          On entry, the upper or lower triangle of the symmetric matrix
   95: *>          B, packed columnwise in a linear array.  The j-th column of B
   96: *>          is stored in the array BP as follows:
   97: *>          if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
   98: *>          if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
   99: *>
  100: *>          On exit, the triangular factor U or L from the Cholesky
  101: *>          factorization B = U**T*U or B = L*L**T, in the same storage
  102: *>          format as B.
  103: *> \endverbatim
  104: *>
  105: *> \param[out] W
  106: *> \verbatim
  107: *>          W is DOUBLE PRECISION array, dimension (N)
  108: *>          If INFO = 0, the eigenvalues in ascending order.
  109: *> \endverbatim
  110: *>
  111: *> \param[out] Z
  112: *> \verbatim
  113: *>          Z is DOUBLE PRECISION array, dimension (LDZ, N)
  114: *>          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
  115: *>          eigenvectors.  The eigenvectors are normalized as follows:
  116: *>          if ITYPE = 1 or 2, Z**T*B*Z = I;
  117: *>          if ITYPE = 3, Z**T*inv(B)*Z = I.
  118: *>          If JOBZ = 'N', then Z is not referenced.
  119: *> \endverbatim
  120: *>
  121: *> \param[in] LDZ
  122: *> \verbatim
  123: *>          LDZ is INTEGER
  124: *>          The leading dimension of the array Z.  LDZ >= 1, and if
  125: *>          JOBZ = 'V', LDZ >= max(1,N).
  126: *> \endverbatim
  127: *>
  128: *> \param[out] WORK
  129: *> \verbatim
  130: *>          WORK is DOUBLE PRECISION array, dimension (3*N)
  131: *> \endverbatim
  132: *>
  133: *> \param[out] INFO
  134: *> \verbatim
  135: *>          INFO is INTEGER
  136: *>          = 0:  successful exit
  137: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
  138: *>          > 0:  DPPTRF or DSPEV returned an error code:
  139: *>             <= N:  if INFO = i, DSPEV failed to converge;
  140: *>                    i off-diagonal elements of an intermediate
  141: *>                    tridiagonal form did not converge to zero.
  142: *>             > N:   if INFO = n + i, for 1 <= i <= n, then the leading
  143: *>                    minor of order i of B is not positive definite.
  144: *>                    The factorization of B could not be completed and
  145: *>                    no eigenvalues or eigenvectors were computed.
  146: *> \endverbatim
  147: *
  148: *  Authors:
  149: *  ========
  150: *
  151: *> \author Univ. of Tennessee 
  152: *> \author Univ. of California Berkeley 
  153: *> \author Univ. of Colorado Denver 
  154: *> \author NAG Ltd. 
  155: *
  156: *> \date November 2011
  157: *
  158: *> \ingroup doubleOTHEReigen
  159: *
  160: *  =====================================================================
  161:       SUBROUTINE DSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
  162:      $                  INFO )
  163: *
  164: *  -- LAPACK driver routine (version 3.4.0) --
  165: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  166: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  167: *     November 2011
  168: *
  169: *     .. Scalar Arguments ..
  170:       CHARACTER          JOBZ, UPLO
  171:       INTEGER            INFO, ITYPE, LDZ, N
  172: *     ..
  173: *     .. Array Arguments ..
  174:       DOUBLE PRECISION   AP( * ), BP( * ), W( * ), WORK( * ),
  175:      $                   Z( LDZ, * )
  176: *     ..
  177: *
  178: *  =====================================================================
  179: *
  180: *     .. Local Scalars ..
  181:       LOGICAL            UPPER, WANTZ
  182:       CHARACTER          TRANS
  183:       INTEGER            J, NEIG
  184: *     ..
  185: *     .. External Functions ..
  186:       LOGICAL            LSAME
  187:       EXTERNAL           LSAME
  188: *     ..
  189: *     .. External Subroutines ..
  190:       EXTERNAL           DPPTRF, DSPEV, DSPGST, DTPMV, DTPSV, XERBLA
  191: *     ..
  192: *     .. Executable Statements ..
  193: *
  194: *     Test the input parameters.
  195: *
  196:       WANTZ = LSAME( JOBZ, 'V' )
  197:       UPPER = LSAME( UPLO, 'U' )
  198: *
  199:       INFO = 0
  200:       IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
  201:          INFO = -1
  202:       ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
  203:          INFO = -2
  204:       ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
  205:          INFO = -3
  206:       ELSE IF( N.LT.0 ) THEN
  207:          INFO = -4
  208:       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
  209:          INFO = -9
  210:       END IF
  211:       IF( INFO.NE.0 ) THEN
  212:          CALL XERBLA( 'DSPGV ', -INFO )
  213:          RETURN
  214:       END IF
  215: *
  216: *     Quick return if possible
  217: *
  218:       IF( N.EQ.0 )
  219:      $   RETURN
  220: *
  221: *     Form a Cholesky factorization of B.
  222: *
  223:       CALL DPPTRF( UPLO, N, BP, INFO )
  224:       IF( INFO.NE.0 ) THEN
  225:          INFO = N + INFO
  226:          RETURN
  227:       END IF
  228: *
  229: *     Transform problem to standard eigenvalue problem and solve.
  230: *
  231:       CALL DSPGST( ITYPE, UPLO, N, AP, BP, INFO )
  232:       CALL DSPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO )
  233: *
  234:       IF( WANTZ ) THEN
  235: *
  236: *        Backtransform eigenvectors to the original problem.
  237: *
  238:          NEIG = N
  239:          IF( INFO.GT.0 )
  240:      $      NEIG = INFO - 1
  241:          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
  242: *
  243: *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
  244: *           backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
  245: *
  246:             IF( UPPER ) THEN
  247:                TRANS = 'N'
  248:             ELSE
  249:                TRANS = 'T'
  250:             END IF
  251: *
  252:             DO 10 J = 1, NEIG
  253:                CALL DTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
  254:      $                     1 )
  255:    10       CONTINUE
  256: *
  257:          ELSE IF( ITYPE.EQ.3 ) THEN
  258: *
  259: *           For B*A*x=(lambda)*x;
  260: *           backtransform eigenvectors: x = L*y or U**T*y
  261: *
  262:             IF( UPPER ) THEN
  263:                TRANS = 'T'
  264:             ELSE
  265:                TRANS = 'N'
  266:             END IF
  267: *
  268:             DO 20 J = 1, NEIG
  269:                CALL DTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
  270:      $                     1 )
  271:    20       CONTINUE
  272:          END IF
  273:       END IF
  274:       RETURN
  275: *
  276: *     End of DSPGV
  277: *
  278:       END