math_tools.algebra.vectors_and_matrices Namespace Reference

Functions
def	colmax
def	colmin
def	plot_matrix
def	rep
def	as_matrix
def	value_to_str
def	values_to_str
def	vector_to_str
def	matrix_to_str
def	which
def	remove
def	matrix_column_multiply
def	normalize
def	linear_map
def	inner_product
def	as_vector
def	vectors_angle
def	linear_map_inv
def	diag_old
def	vector_element_multiply_old
def	cut_vector_old
def	extend_vector
def	equal
def	uvect
def	extract_rotation_matrix
def	cross_old
def	extended_matrix
def	right_pseudo_inverse
def	left_pseudo_inverse
def	right_dls_inverse
def	left_dls_inverse
def	weighted_pseudo_inverse
def	weighted_dls_inverse
def	clamp
def	positive
	Use this function to check if all elements of a given vector are positive. More...
def	feasible_stepsize
def	va_mean
def	va_shiftappend

Variables
int	err_code = 0

Function Documentation

def math_tools.algebra.vectors_and_matrices.as_matrix

(

v

)

gets vector v with n^2 elements and returns n*n matrix

Definition at line 98 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.as_vector

(

v

)

Returns a numpy array equal to v. Input argument v must be a normal array of numbers

Definition at line 242 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.clamp	(		v,
			max_norm
	)

if the magnitude(norm) of the given vector is smaller than max_norm, the given vctor is returned
otherwise a vector parallel to v with norm max_norm is returned

Definition at line 407 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.colmax

(

M

)

returns the maximums of each column in a vector

Definition at line 23 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.colmin

(

M

)

returns the minimums of each column in a vector

Definition at line 36 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.cross_old	(		u,
			v
	)

Return the cross product of two vectors u and v. u and v are (3 element) vectors

Definition at line 332 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.cut_vector_old

(

v4

)

returns a three element vector containing the first three elements of v4

Definition at line 294 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.diag_old

(

v

)

return an square diagonal matrix whose diagonal elements are elements of vector v

Definition at line 277 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.equal	(		v1,
			v2,
			epsilon = gen.epsilon
	)

Returns 1 if two vectors or matrices are equal otherwise returns 0

Definition at line 310 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.extend_vector

(

v3

)

get a three element vector and add one element to its end. Return a four element vector

Definition at line 300 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.extended_matrix	(		R,
			p
	)

Convert a (3 X 3) rotation matrix into a (4 X 4) transformation matrix. The added elements will be zero

Definition at line 338 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.extract_rotation_matrix

(

TRM

)

Returns the rotation matrix (3 X 3) extracted from transformation matrix TRM. TRM is a 4*4 matrix

Definition at line 326 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.feasible_stepsize	(		direction,
			x,
			x_min,
			x_max
	)

when the correction of vector x is restricted by limits
If you want to change vector x in a desired direction, and there are lower and upper bounds for x, 
how much are you allowed to change? 
This function returns a feasible stepsize for the given direction. 
The direction of change must be multiplied by a scalar value lower or equal to this feasible stepsize 
so that the applied changes are feasible.

Definition at line 428 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.inner_product	(		v1,
			v2
	)

returns the inner product of the two vectors v1 and v2

Definition at line 236 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.left_dls_inverse	(		M,
			k
	)

returns the left side damped least square inverse of matrix M. k is the damping factor:

[M^T*M + (k^2)*I]^(-1) * M^T

--> take a look at ! np.linalg.pinv(a, rcond=1.0000000000000001e-15) !

Definition at line 382 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.left_pseudo_inverse

(

J

)

Return the left pseudo-inverse of matrix J
(J^T*J)^(-1)*J^T

Definition at line 360 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.linear_map	(		q,
			f,
			g
	)

return the linear mapping of vector q by coefficients f and g
    
    u = (q - g) / f

This code should be implemented before:

    for i in range(0,len(f[i])):
        if abs(f[i]) < mgvlib.epsilon:
            print 'Error 01: Division by zero occured'
            print 'Something is wrong with the joint limits or the joint limit multipliers'
            print 'Make sure that the joint limits are well defined, and method "initialize" of the manipulator configuration has been implemented'
            assert False

Definition at line 217 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.linear_map_inv	(		u,
			f,
			g
	)

return the inverse linear mapping of vector u by coefficients f and g

    q = f * u + g 

Definition at line 268 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.matrix_column_multiply	(		A,
			v
	)

equivalent to np.dot( A, np.diag(v) ) 

multiplies each column of matrix A by the corresponding element in vector v. 
This is equivalent to A*diag(v) but requires less calculations

return np.dot( A, np.diag(v) ) 

Definition at line 189 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.matrix_to_str	(		matrix,
			format = "%.3f"
	)

parametrized usage of sprintf

Definition at line 141 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.normalize

(

v

)

Returns the unit vector parallel to the given vector.

Definition at line 207 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.plot_matrix	(		M,
			xlabel = None,
			ylabels = None,
			annotate = False,
			legend = True,
			annx = None,
			anny = None
	)

Definition at line 49 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.positive	(		v,
			non_zero = False
	)

Use this function to check if all elements of a given vector are positive.

Definition at line 419 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.remove	(		v,
			positions
	)

Removes the items from v whose positions are specified in given array "positions" and returns the filtered vector

Definition at line 179 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.rep	(		a,
			n
	)

returns a numpy vector of length n containing a (all elements of the vector will be a)

Definition at line 89 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.right_dls_inverse	(		M,
			k
	)

returns the right side damped least square inverse of matrix M. k is the damping factor:

M^T * [M*M^T + (k^2)*I]^(-1)

Definition at line 369 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.right_pseudo_inverse

(

J

)

Return the right pseudo-inverse of matrix J
J^T*(J*J^T)^(-1)
--> take a look at ! np.linalg.pinv(a) !

Definition at line 350 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.uvect	(		TRM,
			m
	)

uvect is a shorted phrase of "unit vector"

Returns a vector (3 X 1) containing the first three elements of the m-th column of transformation matrix TRM. 
(TRM is the 4*4 transformation matrix or a 3X3 rotation matrix) 
If m is in [0,1,2] the m-th unit vector is returned. If m is 3, then the function returns the position vector

Definition at line 316 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.va_mean

(

vectarray

)

Definition at line 469 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.va_shiftappend	(		vectarray,
			v_new
	)

Definition at line 476 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.value_to_str	(		value,
			format = "%.3f"
	)

Definition at line 114 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.values_to_str	(		list_of_vals,
			format = "%.3f"
	)

parametrized usage of sprintf

Definition at line 120 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.vector_element_multiply_old	(		v1,
			v2
	)

elementwise multiplication of two vectors. 

!!! http://www.scipy.org/NumPy_for_Matlab_Users !!!     

Definition at line 285 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.vector_to_str	(		vector,
			format = "%.3f"
	)

previous name: format_vector
parametrized usage of sprintf

Definition at line 129 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.vectors_angle	(		v1,
			v2,
			in_degrees = False,
			positive_direction = np.zeros(3)
	)

Returns the angle between two vectors. The positive direction, specifies which halfspace is used as positive vectors for the cross product of u and v
if not specified, the returned angle will be always positive. 
If specified, then if the sign of the returned angle is the same as the inner product of positive_direction and crossproduct(v1,v2)

Definition at line 248 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.weighted_dls_inverse	(		M,
			W = None,
			k = 0.0
	)

Definition at line 399 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.weighted_pseudo_inverse	(		M,
			W
	)

Definition at line 396 of file vectors_and_matrices.py.

def math_tools.algebra.vectors_and_matrices.which	(		v,
			condition,
			value
	)

Returns the positions of those elements of vector v which satisfy the given condition with the given value
condition is a string and must be in: '>', '>=', '<', '=='

Definition at line 154 of file vectors_and_matrices.py.

Variable Documentation

int err_code = 0

Definition at line 87 of file vectors_and_matrices.py.