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Patches pour OS/2

    1:       SUBROUTINE DSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
    2:      $                  INFO )
    3: *
    4: *  -- LAPACK driver routine (version 3.2) --
    5: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    6: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    7: *     November 2006
    8: *
    9: *     .. Scalar Arguments ..
   10:       CHARACTER          JOBZ, UPLO
   11:       INTEGER            INFO, ITYPE, LDZ, N
   12: *     ..
   13: *     .. Array Arguments ..
   14:       DOUBLE PRECISION   AP( * ), BP( * ), W( * ), WORK( * ),
   15:      $                   Z( LDZ, * )
   16: *     ..
   17: *
   18: *  Purpose
   19: *  =======
   20: *
   21: *  DSPGV computes all the eigenvalues and, optionally, the eigenvectors
   22: *  of a real generalized symmetric-definite eigenproblem, of the form
   23: *  A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
   24: *  Here A and B are assumed to be symmetric, stored in packed format,
   25: *  and B is also positive definite.
   26: *
   27: *  Arguments
   28: *  =========
   29: *
   30: *  ITYPE   (input) INTEGER
   31: *          Specifies the problem type to be solved:
   32: *          = 1:  A*x = (lambda)*B*x
   33: *          = 2:  A*B*x = (lambda)*x
   34: *          = 3:  B*A*x = (lambda)*x
   35: *
   36: *  JOBZ    (input) CHARACTER*1
   37: *          = 'N':  Compute eigenvalues only;
   38: *          = 'V':  Compute eigenvalues and eigenvectors.
   39: *
   40: *  UPLO    (input) CHARACTER*1
   41: *          = 'U':  Upper triangles of A and B are stored;
   42: *          = 'L':  Lower triangles of A and B are stored.
   43: *
   44: *  N       (input) INTEGER
   45: *          The order of the matrices A and B.  N >= 0.
   46: *
   47: *  AP      (input/output) DOUBLE PRECISION array, dimension
   48: *                            (N*(N+1)/2)
   49: *          On entry, the upper or lower triangle of the symmetric matrix
   50: *          A, packed columnwise in a linear array.  The j-th column of A
   51: *          is stored in the array AP as follows:
   52: *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
   53: *          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
   54: *
   55: *          On exit, the contents of AP are destroyed.
   56: *
   57: *  BP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
   58: *          On entry, the upper or lower triangle of the symmetric matrix
   59: *          B, packed columnwise in a linear array.  The j-th column of B
   60: *          is stored in the array BP as follows:
   61: *          if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
   62: *          if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
   63: *
   64: *          On exit, the triangular factor U or L from the Cholesky
   65: *          factorization B = U**T*U or B = L*L**T, in the same storage
   66: *          format as B.
   67: *
   68: *  W       (output) DOUBLE PRECISION array, dimension (N)
   69: *          If INFO = 0, the eigenvalues in ascending order.
   70: *
   71: *  Z       (output) DOUBLE PRECISION array, dimension (LDZ, N)
   72: *          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
   73: *          eigenvectors.  The eigenvectors are normalized as follows:
   74: *          if ITYPE = 1 or 2, Z**T*B*Z = I;
   75: *          if ITYPE = 3, Z**T*inv(B)*Z = I.
   76: *          If JOBZ = 'N', then Z is not referenced.
   77: *
   78: *  LDZ     (input) INTEGER
   79: *          The leading dimension of the array Z.  LDZ >= 1, and if
   80: *          JOBZ = 'V', LDZ >= max(1,N).
   81: *
   82: *  WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)
   83: *
   84: *  INFO    (output) INTEGER
   85: *          = 0:  successful exit
   86: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   87: *          > 0:  DPPTRF or DSPEV returned an error code:
   88: *             <= N:  if INFO = i, DSPEV failed to converge;
   89: *                    i off-diagonal elements of an intermediate
   90: *                    tridiagonal form did not converge to zero.
   91: *             > N:   if INFO = n + i, for 1 <= i <= n, then the leading
   92: *                    minor of order i of B is not positive definite.
   93: *                    The factorization of B could not be completed and
   94: *                    no eigenvalues or eigenvectors were computed.
   95: *
   96: *  =====================================================================
   97: *
   98: *     .. Local Scalars ..
   99:       LOGICAL            UPPER, WANTZ
  100:       CHARACTER          TRANS
  101:       INTEGER            J, NEIG
  102: *     ..
  103: *     .. External Functions ..
  104:       LOGICAL            LSAME
  105:       EXTERNAL           LSAME
  106: *     ..
  107: *     .. External Subroutines ..
  108:       EXTERNAL           DPPTRF, DSPEV, DSPGST, DTPMV, DTPSV, XERBLA
  109: *     ..
  110: *     .. Executable Statements ..
  111: *
  112: *     Test the input parameters.
  113: *
  114:       WANTZ = LSAME( JOBZ, 'V' )
  115:       UPPER = LSAME( UPLO, 'U' )
  116: *
  117:       INFO = 0
  118:       IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
  119:          INFO = -1
  120:       ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
  121:          INFO = -2
  122:       ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
  123:          INFO = -3
  124:       ELSE IF( N.LT.0 ) THEN
  125:          INFO = -4
  126:       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
  127:          INFO = -9
  128:       END IF
  129:       IF( INFO.NE.0 ) THEN
  130:          CALL XERBLA( 'DSPGV ', -INFO )
  131:          RETURN
  132:       END IF
  133: *
  134: *     Quick return if possible
  135: *
  136:       IF( N.EQ.0 )
  137:      $   RETURN
  138: *
  139: *     Form a Cholesky factorization of B.
  140: *
  141:       CALL DPPTRF( UPLO, N, BP, INFO )
  142:       IF( INFO.NE.0 ) THEN
  143:          INFO = N + INFO
  144:          RETURN
  145:       END IF
  146: *
  147: *     Transform problem to standard eigenvalue problem and solve.
  148: *
  149:       CALL DSPGST( ITYPE, UPLO, N, AP, BP, INFO )
  150:       CALL DSPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO )
  151: *
  152:       IF( WANTZ ) THEN
  153: *
  154: *        Backtransform eigenvectors to the original problem.
  155: *
  156:          NEIG = N
  157:          IF( INFO.GT.0 )
  158:      $      NEIG = INFO - 1
  159:          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
  160: *
  161: *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
  162: *           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
  163: *
  164:             IF( UPPER ) THEN
  165:                TRANS = 'N'
  166:             ELSE
  167:                TRANS = 'T'
  168:             END IF
  169: *
  170:             DO 10 J = 1, NEIG
  171:                CALL DTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
  172:      $                     1 )
  173:    10       CONTINUE
  174: *
  175:          ELSE IF( ITYPE.EQ.3 ) THEN
  176: *
  177: *           For B*A*x=(lambda)*x;
  178: *           backtransform eigenvectors: x = L*y or U'*y
  179: *
  180:             IF( UPPER ) THEN
  181:                TRANS = 'T'
  182:             ELSE
  183:                TRANS = 'N'
  184:             END IF
  185: *
  186:             DO 20 J = 1, NEIG
  187:                CALL DTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
  188:      $                     1 )
  189:    20       CONTINUE
  190:          END IF
  191:       END IF
  192:       RETURN
  193: *
  194: *     End of DSPGV
  195: *
  196:       END