Matrix Feedback - mkraska/meclib GitHub Wiki

Feedback for matrix (vector) answers checks every element and reports only the wrong elements, each with a label such as "x-component" or "Row 2, column 1". Two functions from fb_value.mac do this:

Answer	Function	Result
numbers	fb_unit_matrix()	[txt, isOK]: feedback text and a complete numeric check
expressions	fb_vars_matrix()	txt: feedback text only

Both are bilingual (German and English, chosen by the question's language like all meclib feedback). For the question text (a table row with label, input, unit and validation) see Matrix input.

Input

Field	Value
Input type	Matrix
Model answer	matrix variable, e.g. A: matrix([2.5], [-1.2]); (its size sets the size of the input)
Students must verify	Yes
Show validation	Yes, compact

PRT for numeric answers

Field	Value
Feedback variables	[txt, isOK]: fb_unit_matrix(S_A, A, 0.005);
Answer test	AlgEquiv
SAns	isOK
TAns	true
Quiet	Yes
Feedback (true and false)	{@txt@}

isOK is true only if every element is within the relative tolerance (as in fb_unit), so no NumRelative test on a list of components is needed.

PRT for symbolic answers

Field	Value
Feedback variables	txt: fb_vars_matrix(S_A, A, []);
Answer test	AlgEquiv
SAns	S_A
TAns	A
Quiet	Yes
Feedback (true and false)	{@txt@}

The third argument is the list of variables whose terms are checked, as in fb_vars. fb_vars_matrix() has no flag: no message does not prove that the answer is correct, so the answer test compares the whole matrix.

Labels

Without a label argument:

• vectors with up to 3 elements: x-component, y-component, z-component
• longer vectors: Element 1, Element 2, ...
• matrices: Row 1, column 2

Other labels:

fb_unit_matrix(S_A, A, 0.005, "index")            /* Element 1, Element 2, ... */
fb_unit_matrix(S_A, A, 0.005, ['N, 'Q_y, 'Q_z])   /* formulas N, Q_y, Q_z, row by row */
fb_vars_matrix(S_A, A, [], ['x_A, 'y_A])          /* formulas x_A, y_A */

Quote symbol labels ('x_A), so that a question variable of the same name is not substituted.

Example

Model answer A: matrix([2.5], [-1.2]), labels ['x_B, 'y_B], student's answer [25, -1.0]. Feedback (each element on its own line):

• x_B: The mantissa is correct but the value is off by at least one order of magnitude. Check your unit conversion.
• y_B: The value is too small by at least 10%.

The Meclib Workbench creates input, PRT and question text with its input dialog (types "vector / matrix of numbers" and "vector / matrix of expressions").

Older questions

Questions written before these functions compare the components with NumRelative on a list and add one fb_unit or fb_vars line per component to the feedback:

toList(m):= args(transpose(m))[1];      /* feedback variables */
SAns: toList(S_A)   TAns: toList(A)     /* NumRelative, quiet */

They keep working; toList covers column vectors only.