The insert_row method does this:
sage: m = identity_matrix(3)
sage: m
[1 0 0]
[0 1 0]
[0 0 1]
sage: m2= m.insert_row(2, [3,3,3])
sage: m2
[1 0 0]
[0 1 0]
[3 3 3]
[0 0 1]
sage: m # original matrix is unchanged
[1 0 0]
[0 1 0]
[0 0 1]
To insert a column, take the transpose, insert a row, and take the transpose again.
Another option:
sage: m = identity_matrix(3)
sage: m.rows()
[(1, 0, 0), (0, 1, 0), (0, 0, 1)]
sage: L = m.rows()
sage: L[2:2] = [(3,3,3)]
sage: L
[(1, 0, 0), (0, 1, 0), (3, 3, 3), (0, 0, 1)]
sage: matrix(L)
[1 0 0]
[0 1 0]
[3 3 3]
[0 0 1]
There is also a columns method.
I don't actually know how efficient these procedures are, but you can test them out using %timeit, for example.
There is a feature request to implement this for general matrices here: http://trac.sagemath.org/ticket/15965.
def insert_row(M,k,row):
return matrix(M.rows()[:k]+[row]+M.rows()[k:])
With m=identity_matrix(3) and row=[3,3,3], running %timeit m2 = matrix(m.rows()[:2] + [row] + m.rows()[2:]) takes about 40 microseconds, while %timeit m2 = m.insert_row(2, row) takes about 3 microseconds.
The stack and augment methods of matrices provide a workaround.
If a and b have same number of columns, a.stack(b) is
a stacked on top of ba with extra rows from bIf a and c have same number of rows, a.augment(c) is
a augmented to the right by ca with extra columns from cFor adding rows, one can use thestack method.
sage: a = identity_matrix(3)
sage: b = matrix([[3, 3, 3]])
sage: a[:2, :].stack(b).stack(a[2:, :])
[1 0 0]
[0 1 0]
[3 3 3]
[0 0 1]
This works over any ring.
sage: aa = a.change_ring(GF(5))
sage: bb = b.change_ring(GF(5))
sage: aa[:, :2].stack(bb).stack(aa[:, 2:])
[1 0 0]
[0 1 0]
[3 3 3]
[0 0 1]
For adding columns, one can similarly use the augment method.
sage: a = identity_matrix(3)
sage: c = matrix([[3], [3], [3]])
sage: a[:, :2].augment(c).augment(a[:, 2:])
[1 0 3 0]
[0 1 3 0]
[0 0 3 1]
This also works over any ring.
sage: aa = a.change_ring(GF(5))
sage: cc = c.change_ring(GF(5))
sage: aa[:, :2].augment(cc).augment(aa[:, 2:])
[1 0 3 0]
[0 1 3 0]
[0 0 3 1]
Asked: 2015-12-22 14:41:09 +0100
Seen: 13,237 times
Last updated: Dec 15 '21
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