math

extract_coeff(expr, vec)

Extract the coefficient of vec from expr.

Dispatches to extract_from_scalar / extract_from_vector / extract_from_matrix based on expr.type.

Source code in geomech/core/math/extract.py

def extract_coeff(expr, vec):
    """Extract the coefficient of *vec* from *expr*.

    Dispatches to extract_from_scalar / extract_from_vector /
    extract_from_matrix based on expr.type.
    """
    match getattr(expr, "type", None):
        case ExprType.SCALAR:
            return extract_from_scalar(expr, vec)
        case ExprType.VECTOR:
            return extract_from_vector(expr, vec)
        case ExprType.MATRIX:
            return extract_from_matrix(expr, vec)
        case _:
            raise NotImplementedError(
                f"extract_coeff: unsupported type {getattr(expr, 'type', None)}"
            )

extract_from_matrix(expr, vec)

Extract the coefficient of vec from a matrix expression.

Partial — only limited cases supported.

Source code in geomech/core/math/extract.py

def extract_from_matrix(expr, vec):
    """Extract the coefficient of *vec* from a matrix expression.

    Partial — only limited cases supported.
    """
    match expr:
        case MAdd(nodes=nodes):
            extracted = [extract_from_matrix(n, vec) for n in nodes if _has_algebraic(n, vec)]
            if not extracted:
                return ZeroMatrix
            if len(extracted) == 1:
                return extracted[0]
            return MAdd(*extracted)

        case MMMul():
            l, r = expr.left, expr.right
            if _has_algebraic(l, vec) and _has_algebraic(r, vec):
                raise NotImplementedError("extract_from_matrix: both sides of MMMul contain vec")
            if _has_algebraic(l, vec):
                raise NotImplementedError("extract_from_matrix: MMMul.left contains vec")
            if _has_algebraic(r, vec):
                if r == vec:
                    return l
                raise NotImplementedError("extract_from_matrix: MMMul.right non-leaf contains vec")
            return ZeroMatrix

        case VVMul():
            raise NotImplementedError("extract_from_matrix: VVMul")

        case SMMul():
            raise NotImplementedError("extract_from_matrix: SMMul")

        case _:
            raise NotImplementedError(f"extract_from_matrix: unhandled {type(expr).__name__}")

extract_from_scalar(expr, vec)

Extract the coefficient of vec from a scalar expression.

Source code in geomech/core/math/extract.py

def extract_from_scalar(expr, vec):
    """Extract the coefficient of *vec* from a scalar expression."""
    match expr:
        # --- scalar addition: linearity ---
        case Add(nodes=nodes):
            extracted = [extract_from_scalar(n, vec) for n in nodes if _has_algebraic(n, vec)]
            if not extracted:
                return ZeroVector
            if len(extracted) == 1:
                return extracted[0]
            return VAdd(*extracted)

        # --- scalar multiplication ---
        case Mul():
            l, r = expr.left, expr.right
            if _has_algebraic(l, vec) and _has_algebraic(r, vec):
                raise NotImplementedError("extract_from_scalar: both sides of Mul contain vec")
            if _has_algebraic(l, vec):
                return SVMul(extract_from_scalar(l, vec), r)
            if _has_algebraic(r, vec):
                return SVMul(extract_from_scalar(r, vec), l)
            return ZeroVector

        # --- dot product: core extraction ---
        case Dot():
            l, r = expr.left, expr.right
            if _has_algebraic(l, vec) and _has_algebraic(r, vec):
                raise NotImplementedError("extract_from_scalar: both sides of Dot contain vec")
            if _has_algebraic(l, vec):
                if l == vec:
                    return r
                if l.type == ExprType.VECTOR:
                    return MVMul(Transpose(extract_from_vector(l, vec)), r)
                raise NotImplementedError(
                    f"extract_from_scalar: Dot.left contains vec but type={l.type}"
                )
            if _has_algebraic(r, vec):
                if r == vec:
                    return l
                if r.type == ExprType.VECTOR:
                    # Dot(l, M*vec) = l^T M vec = (M^T l)^T vec = Dot(vec, M^T l)
                    return MVMul(Transpose(extract_from_vector(r, vec)), l)
                raise NotImplementedError(
                    f"extract_from_scalar: Dot.right contains vec but type={r.type}"
                )
            return ZeroVector

        case VVMul():
            raise NotImplementedError("extract_from_scalar: VVMul")

        # --- leaf / unhandled ---
        case _:
            return ZeroVector

extract_from_vector(expr, vec)

Extract the coefficient of vec from a vector expression.

Source code in geomech/core/math/extract.py

def extract_from_vector(expr, vec):
    """Extract the coefficient of *vec* from a vector expression."""
    from geomech.core.base.expressions import IdentityMatrix

    # Base case: expr IS the target vector → coefficient is identity
    if str(expr) == str(vec):
        return IdentityMatrix

    match expr:
        # --- vector addition: linearity ---
        case VAdd(nodes=nodes):
            extracted = [extract_from_vector(n, vec) for n in nodes if _has_algebraic(n, vec)]
            if not extracted:
                return ZeroMatrix
            if len(extracted) == 1:
                return extracted[0]
            return MAdd(*extracted)

        # --- cross product ---
        case Cross():
            l, r = expr.left, expr.right
            if l == r:
                return ZeroMatrix
            # cross(a, vec) = Hat(a) * vec
            if r == vec:
                return Hat(l)
            # cross(vec, b) = -Hat(b) * vec
            if l == vec:
                return SMMul(Hat(r), -1)
            if _has_algebraic(l, vec) and _has_algebraic(r, vec):
                raise NotImplementedError("extract_from_vector: both sides of Cross contain vec")
            # cross(f(vec), b) = -Hat(b) * f(vec) = -Hat(b) * M * vec
            if _has_algebraic(l, vec):
                return MMMul(SMMul(Hat(r), -1), extract_from_vector(l, vec))
            # cross(a, g(vec)) = Hat(a) * g(vec) = Hat(a) * M * vec
            if _has_algebraic(r, vec):
                return MMMul(Hat(l), extract_from_vector(r, vec))
            return ZeroMatrix

        # --- matrix * vector ---
        case MVMul():
            mat, v = expr.left, expr.right
            if _has_algebraic(v, vec):
                if v == vec:
                    return mat
                # M * f(vec) = M * N * vec
                return MMMul(mat, extract_from_vector(v, vec))
            if _has_algebraic(mat, vec):
                return _extract_vec_mvmul_mat(mat, v, vec)
            return ZeroMatrix

        # --- scalar * vector ---
        case SVMul():
            v, s = expr.left, expr.right
            if _has_algebraic(v, vec) and _has_algebraic(s, vec):
                raise NotImplementedError("extract_from_vector: both sides of SVMul contain vec")
            if _has_algebraic(v, vec):
                # s * f(vec) = s * M * vec = (s*M) * vec
                return SMMul(extract_from_vector(v, vec), s)
            if _has_algebraic(s, vec):
                raise NotImplementedError("extract_from_vector: SVMul scalar contains vec")
            return ZeroMatrix

        # --- leaf / unhandled ---
        # Calculus ops (TimeDerivative, Variation, TimeIntegral) never reach
        # here — _has_algebraic() treats them as opaque, so parent nodes
        # (VAdd, Dot, Cross, etc.) skip terms containing them.
        case _:
            return ZeroMatrix

integrate_by_parts(expr, targets)

Expand, simplify, then apply collect + IBP for each target.

targets is a list of variation vector time-derivatives (e.g. dot_eta) that should be integrated by parts to remove the time derivative.

Source code in geomech/core/math/ibp.py

def integrate_by_parts(expr, targets):
    """Expand, simplify, then apply collect + IBP for each target.

    *targets* is a list of variation vector time-derivatives (e.g. dot_eta)
    that should be integrated by parts to remove the time derivative.
    """
    expr = expand(expr)
    expr = full_simplify(expr)
    for target in targets:
        expr = collect(expr, target)
        expr = _apply_ibp(expr, target)
        expr = full_simplify(expr)
    return expr