Laboratoire de l'Informatique et du Parallélisme » Pobyso

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def smo_is_diagonal_complete_matrix(mat):

    """

    Check that all the element on the diagonal are not 0.

    """

    dimensions = mat.dimensions()

    # Must be a bidimensional matrix.

    if len(dimensions) != 2:

        return False

    # Must be square.

    if dimensions[0] != dimensions[1]:

        return False

    # A 1x1 matrix is diagonal complete if it's single element is not 0.

    if dimensions[0] == 1:

        if mat[0, 0] != 0:

            return True

        else:

            return False

    # End if

    for rowIndex in xrange(0, dimensions[0]):

        if mat[rowIndex, rowIndex] == 0:

            print mat.rows()[rowIndex], rowIndex

            return False

    return True

# End smo_is_diagonal_complete_matrix

def smo_is_lower_triangular_matrix(mat):

    """

    Check that the matrix is lower triangular.

    """

    dimensions = mat.dimensions()

    # Must be a bidimensional matrix.

    if len(dimensions) != 2:

        return False

    # Must be square.

    if dimensions[0] != dimensions[1]:

        return False

    # A 1x1 matrix is lower triangular.

    if dimensions[0] == 1:

        return True

    for rowIndex in xrange(0, dimensions[0]):

        for colIndex in xrange(rowIndex + 1, dimensions[1]):

            if mat[rowIndex, colIndex] != 0:

                print mat.rows()[rowIndex]

                return False

    return True

# End smo_is_lower_triangular_matrix

def smo_is_upper_triangular_matrix(mat):

    """

    Check that the matrix is upper triangular.

    """

    dimensions = mat.dimensions()

    # Must be a bidimensional matrix.

    if len(dimensions) != 2:

        return False

    # Must be square.

    if dimensions[0] != dimensions[1]:

        return False

    # A 1x1 matrix is lower triangular.

    if dimensions[0] == 1:

        return True

    for rowIndex in xrange(1, dimensions[0]):

        for colIndex in xrange(0, rowIndex):

            if mat[rowIndex, colIndex] != 0:

                print mat.rows()[rowIndex]

                return False

    return True

# End smo_is_upper_triangular_matrix

def smo_max_non_null_abs(mat):

    """

    Compute the maximum absolute value of the matrix elements.

    """

    maxNonNull = -Infinity

    mlist = mat._list()

    for i in mlist:

        if i != 0 and i.abs() > maxNonNull :

            maxNonNull = i.abs()

    return maxNonNull

# End smo_min_non_null_abs

#

def smo_min_non_null_abs(mat):

    """

    Compute the minimum absolute value of the matrix elements.

    """

    minNonNull = Infinity

    mlist = mat._list()

    for i in mlist:

        if i != 0 and i.abs() < minNonNull :

            minNonNull = i.abs()

    return minNonNull

# End smo_min_non_null_abs

def smo_transformation_row_matrix_strings(varPrefixString, matrix):

    """

    Create a string that will be evaluated to create one variable per

    matrix row.

    The first application is the computation of transformation matrices.

    """

    m = matrix.nrows()

    if m == 0 :

        return None

    varDeclarationString = "var('"

    varListArrayDeclaration ="["

    varListString = ""

    for k in xrange(1,m+1):

        if k != m:

            varListString += varPrefixString + str(k) + ","

        else:

            varListString += varPrefixString + str(k)

    varDeclarationString += varListString + "')"

    varListArrayDeclaration += "]"

    return(varDeclarationString, varListArrayDeclaration)

# End smo_transformation_row_matrix_strings.

def smo_triangular_matrix_determinant(matrix):

    if matrix == None:

        return None

    numRows = matrix.nrows()

    if numRows < 1:

        return 0

    determinant = 1

    for rowIndex in xrange(numRows):

        determinant *= matrix[rowIndex, rowIndex]

    return determinant

# End smo_triangular_matrix_determinant

#

def smo_zero_rows_index_list(matrix):

    """

    Compute the list of indices of the rows that have a 0 norm.

    """

    if 0 == matrix.nrows():

        return []

    zeroRowsList = []

    rowIndex = 0

    for row in matrix.rows():

        if row.norm(p=1) == 0 :

            zeroRowsList.append(rowIndex)

        rowIndex += 1

    return zeroRowsList

# End smo_zero_rows_index_list

print "\t...sageMatrixOperations loaded"