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Mise à jour globale de Lapack 3.2.2.

    1:       SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
    2:      $                  LWORK, 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          UPLO
   11:       INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
   12: *     ..
   13: *     .. Array Arguments ..
   14:       INTEGER            IPIV( * )
   15:       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
   16: *     ..
   17: *
   18: *  Purpose
   19: *  =======
   20: *
   21: *  ZHESV computes the solution to a complex system of linear equations
   22: *     A * X = B,
   23: *  where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
   24: *  matrices.
   25: *
   26: *  The diagonal pivoting method is used to factor A as
   27: *     A = U * D * U**H,  if UPLO = 'U', or
   28: *     A = L * D * L**H,  if UPLO = 'L',
   29: *  where U (or L) is a product of permutation and unit upper (lower)
   30: *  triangular matrices, and D is Hermitian and block diagonal with
   31: *  1-by-1 and 2-by-2 diagonal blocks.  The factored form of A is then
   32: *  used to solve the system of equations A * X = B.
   33: *
   34: *  Arguments
   35: *  =========
   36: *
   37: *  UPLO    (input) CHARACTER*1
   38: *          = 'U':  Upper triangle of A is stored;
   39: *          = 'L':  Lower triangle of A is stored.
   40: *
   41: *  N       (input) INTEGER
   42: *          The number of linear equations, i.e., the order of the
   43: *          matrix A.  N >= 0.
   44: *
   45: *  NRHS    (input) INTEGER
   46: *          The number of right hand sides, i.e., the number of columns
   47: *          of the matrix B.  NRHS >= 0.
   48: *
   49: *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
   50: *          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
   51: *          N-by-N upper triangular part of A contains the upper
   52: *          triangular part of the matrix A, and the strictly lower
   53: *          triangular part of A is not referenced.  If UPLO = 'L', the
   54: *          leading N-by-N lower triangular part of A contains the lower
   55: *          triangular part of the matrix A, and the strictly upper
   56: *          triangular part of A is not referenced.
   57: *
   58: *          On exit, if INFO = 0, the block diagonal matrix D and the
   59: *          multipliers used to obtain the factor U or L from the
   60: *          factorization A = U*D*U**H or A = L*D*L**H as computed by
   61: *          ZHETRF.
   62: *
   63: *  LDA     (input) INTEGER
   64: *          The leading dimension of the array A.  LDA >= max(1,N).
   65: *
   66: *  IPIV    (output) INTEGER array, dimension (N)
   67: *          Details of the interchanges and the block structure of D, as
   68: *          determined by ZHETRF.  If IPIV(k) > 0, then rows and columns
   69: *          k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
   70: *          diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
   71: *          then rows and columns k-1 and -IPIV(k) were interchanged and
   72: *          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
   73: *          IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
   74: *          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
   75: *          diagonal block.
   76: *
   77: *  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
   78: *          On entry, the N-by-NRHS right hand side matrix B.
   79: *          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
   80: *
   81: *  LDB     (input) INTEGER
   82: *          The leading dimension of the array B.  LDB >= max(1,N).
   83: *
   84: *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
   85: *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
   86: *
   87: *  LWORK   (input) INTEGER
   88: *          The length of WORK.  LWORK >= 1, and for best performance
   89: *          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
   90: *          ZHETRF.
   91: *
   92: *          If LWORK = -1, then a workspace query is assumed; the routine
   93: *          only calculates the optimal size of the WORK array, returns
   94: *          this value as the first entry of the WORK array, and no error
   95: *          message related to LWORK is issued by XERBLA.
   96: *
   97: *  INFO    (output) INTEGER
   98: *          = 0: successful exit
   99: *          < 0: if INFO = -i, the i-th argument had an illegal value
  100: *          > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
  101: *               has been completed, but the block diagonal matrix D is
  102: *               exactly singular, so the solution could not be computed.
  103: *
  104: *  =====================================================================
  105: *
  106: *     .. Local Scalars ..
  107:       LOGICAL            LQUERY
  108:       INTEGER            LWKOPT, NB
  109: *     ..
  110: *     .. External Functions ..
  111:       LOGICAL            LSAME
  112:       INTEGER            ILAENV
  113:       EXTERNAL           LSAME, ILAENV
  114: *     ..
  115: *     .. External Subroutines ..
  116:       EXTERNAL           XERBLA, ZHETRF, ZHETRS
  117: *     ..
  118: *     .. Intrinsic Functions ..
  119:       INTRINSIC          MAX
  120: *     ..
  121: *     .. Executable Statements ..
  122: *
  123: *     Test the input parameters.
  124: *
  125:       INFO = 0
  126:       LQUERY = ( LWORK.EQ.-1 )
  127:       IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  128:          INFO = -1
  129:       ELSE IF( N.LT.0 ) THEN
  130:          INFO = -2
  131:       ELSE IF( NRHS.LT.0 ) THEN
  132:          INFO = -3
  133:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  134:          INFO = -5
  135:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
  136:          INFO = -8
  137:       ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
  138:          INFO = -10
  139:       END IF
  140: *
  141:       IF( INFO.EQ.0 ) THEN
  142:          IF( N.EQ.0 ) THEN
  143:             LWKOPT = 1
  144:          ELSE
  145:             NB = ILAENV( 1, 'ZHETRF', UPLO, N, -1, -1, -1 )
  146:             LWKOPT = N*NB
  147:          END IF
  148:          WORK( 1 ) = LWKOPT
  149:       END IF
  150: *
  151:       IF( INFO.NE.0 ) THEN
  152:          CALL XERBLA( 'ZHESV ', -INFO )
  153:          RETURN
  154:       ELSE IF( LQUERY ) THEN
  155:          RETURN
  156:       END IF
  157: *
  158: *     Compute the factorization A = U*D*U' or A = L*D*L'.
  159: *
  160:       CALL ZHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
  161:       IF( INFO.EQ.0 ) THEN
  162: *
  163: *        Solve the system A*X = B, overwriting B with X.
  164: *
  165:          CALL ZHETRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
  166: *
  167:       END IF
  168: *
  169:       WORK( 1 ) = LWKOPT
  170: *
  171:       RETURN
  172: *
  173: *     End of ZHESV
  174: *
  175:       END