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Patches pour OS/2

    1:       SUBROUTINE ZPBEQU( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO )
    2: *
    3: *  -- LAPACK routine (version 3.2) --
    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    6: *     November 2006
    7: *
    8: *     .. Scalar Arguments ..
    9:       CHARACTER          UPLO
   10:       INTEGER            INFO, KD, LDAB, N
   11:       DOUBLE PRECISION   AMAX, SCOND
   12: *     ..
   13: *     .. Array Arguments ..
   14:       DOUBLE PRECISION   S( * )
   15:       COMPLEX*16         AB( LDAB, * )
   16: *     ..
   17: *
   18: *  Purpose
   19: *  =======
   20: *
   21: *  ZPBEQU computes row and column scalings intended to equilibrate a
   22: *  Hermitian positive definite band matrix A and reduce its condition
   23: *  number (with respect to the two-norm).  S contains the scale factors,
   24: *  S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
   25: *  elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
   26: *  choice of S puts the condition number of B within a factor N of the
   27: *  smallest possible condition number over all possible diagonal
   28: *  scalings.
   29: *
   30: *  Arguments
   31: *  =========
   32: *
   33: *  UPLO    (input) CHARACTER*1
   34: *          = 'U':  Upper triangular of A is stored;
   35: *          = 'L':  Lower triangular of A is stored.
   36: *
   37: *  N       (input) INTEGER
   38: *          The order of the matrix A.  N >= 0.
   39: *
   40: *  KD      (input) INTEGER
   41: *          The number of superdiagonals of the matrix A if UPLO = 'U',
   42: *          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
   43: *
   44: *  AB      (input) COMPLEX*16 array, dimension (LDAB,N)
   45: *          The upper or lower triangle of the Hermitian band matrix A,
   46: *          stored in the first KD+1 rows of the array.  The j-th column
   47: *          of A is stored in the j-th column of the array AB as follows:
   48: *          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
   49: *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
   50: *
   51: *  LDAB     (input) INTEGER
   52: *          The leading dimension of the array A.  LDAB >= KD+1.
   53: *
   54: *  S       (output) DOUBLE PRECISION array, dimension (N)
   55: *          If INFO = 0, S contains the scale factors for A.
   56: *
   57: *  SCOND   (output) DOUBLE PRECISION
   58: *          If INFO = 0, S contains the ratio of the smallest S(i) to
   59: *          the largest S(i).  If SCOND >= 0.1 and AMAX is neither too
   60: *          large nor too small, it is not worth scaling by S.
   61: *
   62: *  AMAX    (output) DOUBLE PRECISION
   63: *          Absolute value of largest matrix element.  If AMAX is very
   64: *          close to overflow or very close to underflow, the matrix
   65: *          should be scaled.
   66: *
   67: *  INFO    (output) INTEGER
   68: *          = 0:  successful exit
   69: *          < 0:  if INFO = -i, the i-th argument had an illegal value.
   70: *          > 0:  if INFO = i, the i-th diagonal element is nonpositive.
   71: *
   72: *  =====================================================================
   73: *
   74: *     .. Parameters ..
   75:       DOUBLE PRECISION   ZERO, ONE
   76:       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
   77: *     ..
   78: *     .. Local Scalars ..
   79:       LOGICAL            UPPER
   80:       INTEGER            I, J
   81:       DOUBLE PRECISION   SMIN
   82: *     ..
   83: *     .. External Functions ..
   84:       LOGICAL            LSAME
   85:       EXTERNAL           LSAME
   86: *     ..
   87: *     .. External Subroutines ..
   88:       EXTERNAL           XERBLA
   89: *     ..
   90: *     .. Intrinsic Functions ..
   91:       INTRINSIC          DBLE, MAX, MIN, SQRT
   92: *     ..
   93: *     .. Executable Statements ..
   94: *
   95: *     Test the input parameters.
   96: *
   97:       INFO = 0
   98:       UPPER = LSAME( UPLO, 'U' )
   99:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  100:          INFO = -1
  101:       ELSE IF( N.LT.0 ) THEN
  102:          INFO = -2
  103:       ELSE IF( KD.LT.0 ) THEN
  104:          INFO = -3
  105:       ELSE IF( LDAB.LT.KD+1 ) THEN
  106:          INFO = -5
  107:       END IF
  108:       IF( INFO.NE.0 ) THEN
  109:          CALL XERBLA( 'ZPBEQU', -INFO )
  110:          RETURN
  111:       END IF
  112: *
  113: *     Quick return if possible
  114: *
  115:       IF( N.EQ.0 ) THEN
  116:          SCOND = ONE
  117:          AMAX = ZERO
  118:          RETURN
  119:       END IF
  120: *
  121:       IF( UPPER ) THEN
  122:          J = KD + 1
  123:       ELSE
  124:          J = 1
  125:       END IF
  126: *
  127: *     Initialize SMIN and AMAX.
  128: *
  129:       S( 1 ) = DBLE( AB( J, 1 ) )
  130:       SMIN = S( 1 )
  131:       AMAX = S( 1 )
  132: *
  133: *     Find the minimum and maximum diagonal elements.
  134: *
  135:       DO 10 I = 2, N
  136:          S( I ) = DBLE( AB( J, I ) )
  137:          SMIN = MIN( SMIN, S( I ) )
  138:          AMAX = MAX( AMAX, S( I ) )
  139:    10 CONTINUE
  140: *
  141:       IF( SMIN.LE.ZERO ) THEN
  142: *
  143: *        Find the first non-positive diagonal element and return.
  144: *
  145:          DO 20 I = 1, N
  146:             IF( S( I ).LE.ZERO ) THEN
  147:                INFO = I
  148:                RETURN
  149:             END IF
  150:    20    CONTINUE
  151:       ELSE
  152: *
  153: *        Set the scale factors to the reciprocals
  154: *        of the diagonal elements.
  155: *
  156:          DO 30 I = 1, N
  157:             S( I ) = ONE / SQRT( S( I ) )
  158:    30    CONTINUE
  159: *
  160: *        Compute SCOND = min(S(I)) / max(S(I))
  161: *
  162:          SCOND = SQRT( SMIN ) / SQRT( AMAX )
  163:       END IF
  164:       RETURN
  165: *
  166: *     End of ZPBEQU
  167: *
  168:       END