X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=test%2Frandomgen.py;h=9510c04767150b967283f62f72d7e7a88f112186;hb=79d8219c4ac2ce7972247f3e7690e776295fabba;hp=ef1b19e569825625e134eeef84be3445f2f87b3c;hpb=ac39a0b32d176fa78ecd5cf4ef21676e3bd56d6c;p=dunshire.git diff --git a/test/randomgen.py b/test/randomgen.py index ef1b19e..9510c04 100644 --- a/test/randomgen.py +++ b/test/randomgen.py @@ -23,12 +23,14 @@ properties within reason. def random_scalar(): """ - Generate a random scalar in ``[-RANDOM_MAX, RANDOM_MAX]``. + Generate a random scalar. Returns ------- float + A random real number between ``-RANDOM_MAX`` and ``RANDOM_MAX``, + inclusive. Examples -------- @@ -42,12 +44,14 @@ def random_scalar(): def random_nn_scalar(): """ - Generate a random nonnegative scalar in ``[0, RANDOM_MAX]``. + Generate a random nonnegative scalar. Returns ------- float + A random nonnegative real number between zero and ``RANDOM_MAX``, + inclusive. Examples -------- @@ -61,13 +65,13 @@ def random_nn_scalar(): def random_natural(): """ - Generate a random natural number between ``1 and RANDOM_MAX`` - inclusive. + Generate a random natural number. Returns ------- int + A random natural number between ``1`` and ``RANDOM_MAX`` inclusive. Examples -------- @@ -79,22 +83,26 @@ def random_natural(): return randint(1, RANDOM_MAX) -def random_matrix(dims): +def random_matrix(row_count, column_count=None): """ - Generate a random square matrix. + Generate a random matrix. Parameters ---------- - dims : int - The number of rows/columns you want in the returned matrix. + row_count : int + The number of rows you want in the returned matrix. + + column_count: int + The number of columns you want in the returned matrix (default: + the same as ``row_count``). Returns ------- matrix A new matrix whose entries are random floats chosen uniformly from - the interval [-RANDOM_MAX, RANDOM_MAX]. + the interval ``[-RANDOM_MAX, RANDOM_MAX]``. Examples -------- @@ -103,21 +111,31 @@ def random_matrix(dims): >>> A.size (3, 3) + >>> A = random_matrix(3,2) + >>> A.size + (3, 2) + """ - return matrix([[random_scalar() - for _ in range(dims)] - for _ in range(dims)]) + if column_count is None: + column_count = row_count + + entries = [random_scalar() for _ in range(row_count*column_count)] + return matrix(entries, (row_count, column_count)) -def random_nonnegative_matrix(dims): +def random_nonnegative_matrix(row_count, column_count=None): """ - Generate a random square matrix with nonnegative entries. + Generate a random matrix with nonnegative entries. Parameters ---------- - dims : int - The number of rows/columns you want in the returned matrix. + row_count : int + The number of rows you want in the returned matrix. + + column_count : int + The number of columns you want in the returned matrix (default: + the same as ``row_count``). Returns ------- @@ -134,10 +152,18 @@ def random_nonnegative_matrix(dims): >>> all([entry >= 0 for entry in A]) True + >>> A = random_nonnegative_matrix(3,2) + >>> A.size + (3, 2) + >>> all([entry >= 0 for entry in A]) + True + """ - return matrix([[random_nn_scalar() - for _ in range(dims)] - for _ in range(dims)]) + if column_count is None: + column_count = row_count + + entries = [random_nn_scalar() for _ in range(row_count*column_count)] + return matrix(entries, (row_count, column_count)) def random_diagonal_matrix(dims): @@ -200,9 +226,10 @@ def random_skew_symmetric_matrix(dims): >>> A.size (3, 3) + >>> from dunshire.options import ABS_TOL >>> from dunshire.matrices import norm >>> A = random_skew_symmetric_matrix(random_natural()) - >>> norm(A + A.trans()) < options.ABS_TOL + >>> norm(A + A.trans()) < ABS_TOL True """ @@ -240,7 +267,7 @@ def random_lyapunov_like_icecream(dims): matrix A new matrix, Lyapunov-like on the ice-cream cone in ``dims`` dimensions, whose free entries are random floats chosen uniformly - from the interval [-RANDOM_MAX, RANDOM_MAX]. + from the interval ``[-RANDOM_MAX, RANDOM_MAX]``. References ---------- @@ -255,9 +282,12 @@ def random_lyapunov_like_icecream(dims): >>> L = random_lyapunov_like_icecream(3) >>> L.size (3, 3) + + >>> from dunshire.options import ABS_TOL + >>> from dunshire.matrices import inner_product >>> x = matrix([1,1,0]) >>> s = matrix([1,-1,0]) - >>> abs(inner_product(L*x, s)) < options.ABS_TOL + >>> abs(inner_product(L*x, s)) < ABS_TOL True """ @@ -271,12 +301,25 @@ def random_lyapunov_like_icecream(dims): def random_orthant_game(): """ - Generate the ``L``, ``K``, ``e1``, and ``e2`` parameters for a - random game over the nonnegative orthant, and return the - corresponding :class:`SymmetricLinearGame`. + Generate a random game over the nonnegative orthant. + + We generate each of ``L``, ``K``, ``e1``, and ``e2`` randomly within + the constraints of the nonnegative orthant, and then construct a + game from them. The process is repeated until we generate a game with + a condition number under ``MAX_COND``. + + Returns + ------- + + SymmetricLinearGame + A random game over some nonnegative orthant. + + Examples + -------- + + >>> random_orthant_game() + - We keep going until we generate a game with a condition number under - 5000. """ ambient_dim = random_natural() + 1 K = NonnegativeOrthant(ambient_dim) @@ -293,9 +336,25 @@ def random_orthant_game(): def random_icecream_game(): """ - Generate the ``L``, ``K``, ``e1``, and ``e2`` parameters for a - random game over the ice-cream cone, and return the corresponding - :class:`SymmetricLinearGame`. + Generate a random game over the ice-cream cone. + + We generate each of ``L``, ``K``, ``e1``, and ``e2`` randomly within + the constraints of the ice-cream cone, and then construct a game + from them. The process is repeated until we generate a game with a + condition number under ``MAX_COND``. + + Returns + ------- + + SymmetricLinearGame + A random game over some ice-cream cone. + + Examples + -------- + + >>> random_icecream_game() + + """ # Use a minimum dimension of two to avoid divide-by-zero in # the fudge factor we make up later. @@ -326,6 +385,26 @@ def random_icecream_game(): def random_ll_orthant_game(): """ Return a random Lyapunov game over some nonnegative orthant. + + We first construct a :func:`random_orthant_game` and then modify it + to have a :func:`random_diagonal_matrix` as its operator. Such + things are Lyapunov-like on the nonnegative orthant. That process is + repeated until the condition number of the resulting game is within + ``MAX_COND``. + + Returns + ------- + + SymmetricLinearGame + A random game over some nonnegative orthant whose ``payoff`` method + is based on a Lyapunov-like ``L`` operator. + + Examples + -------- + + >>> random_ll_orthant_game() + + """ G = random_orthant_game() L = random_diagonal_matrix(G._K.dimension()) @@ -345,6 +424,25 @@ def random_ll_orthant_game(): def random_ll_icecream_game(): """ Return a random Lyapunov game over some ice-cream cone. + + We first construct a :func:`random_icecream_game` and then modify it + to have a :func:`random_lyapunov_like_icecream` operator. That + process is repeated until the condition number of the resulting game + is within ``MAX_COND``. + + Returns + ------- + + SymmetricLinearGame + A random game over some ice-cream cone whose ``payoff`` method + is based on a Lyapunov-like ``L`` operator. + + Examples + -------- + + >>> random_ll_icecream_game() + + """ G = random_icecream_game() L = random_lyapunov_like_icecream(G._K.dimension()) @@ -362,6 +460,30 @@ def random_ll_icecream_game(): def random_positive_orthant_game(): + """ + Return a random game over the nonnegative orthant with a positive + operator. + + We first construct a :func:`random_orthant_game` and then modify it + to have a :func:`random_nonnegative_matrix` as its operator. That + process is repeated until the condition number of the resulting game + is within ``MAX_COND``. + + Returns + ------- + + SymmetricLinearGame + A random game over some nonnegative orthant whose ``payoff`` method + is based on a positive ``L`` operator. + + Examples + -------- + + >>> random_positive_orthant_game() + + + """ + G = random_orthant_game() L = random_nonnegative_matrix(G._K.dimension()) @@ -378,6 +500,40 @@ def random_positive_orthant_game(): def random_nn_scaling(G): + """ + Scale the given game by a random nonnegative amount. + + We re-attempt the scaling with a new random number until the + resulting scaled game has an acceptable condition number. + + Parameters + ---------- + + G : SymmetricLinearGame + The game that you would like to scale. + + Returns + ------- + (float, SymmetricLinearGame) + A pair containing the both the scaling factor and the new scaled game. + + Examples + -------- + + >>> from dunshire.matrices import norm + >>> from dunshire.options import ABS_TOL + >>> G = random_orthant_game() + >>> (alpha, H) = random_nn_scaling(G) + >>> alpha >= 0 + True + >>> G._K == H._K + True + >>> norm(G._e1 - H._e1) < ABS_TOL + True + >>> norm(G._e2 - H._e2) < ABS_TOL + True + + """ alpha = random_nn_scalar() H = SymmetricLinearGame(alpha*G._L.trans(), G._K, G._e1, G._e2) @@ -388,7 +544,41 @@ def random_nn_scaling(G): return (alpha, H) + def random_translation(G): + """ + Translate the given game by a random amount. + + We re-attempt the translation with new random scalars until the + resulting translated game has an acceptable condition number. + + Parameters + ---------- + + G : SymmetricLinearGame + The game that you would like to translate. + + Returns + ------- + (float, SymmetricLinearGame) + A pair containing the both the translation distance and the new + scaled game. + + Examples + -------- + + >>> from dunshire.matrices import norm + >>> from dunshire.options import ABS_TOL + >>> G = random_orthant_game() + >>> (alpha, H) = random_translation(G) + >>> G._K == H._K + True + >>> norm(G._e1 - H._e1) < ABS_TOL + True + >>> norm(G._e2 - H._e2) < ABS_TOL + True + + """ alpha = random_scalar() tensor_prod = G._e1 * G._e2.trans() M = G._L + alpha*tensor_prod