## Developer Reference

• 2020.2
• 07/15/2020
• Public Content
Contents

# ?lals0

Applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by
?gelsd
.

## Syntax

Include Files
• mkl.fi
Description
The routine applies back the multiplying factors of either the left or right singular vector matrix of a diagonal matrix appended by a row to the right hand side matrix
B
in solving the least squares problem using the divide-and-conquer SVD approach.
For the left singular vector matrix, three types of orthogonal matrices are involved:
(1L) Givens rotations: the number of such rotations is
givptr
;the pairs of columns/rows they were applied to are stored in
givcol
;and the
c
- and
s
-values of these rotations are stored in
givnum
.
(2L) Permutation. The (
nl
+1)-st row of
B
is to be moved to the first row, and for j=2:
n
,
perm
(
j
)-th row of
B
is to be moved to the
j
-th row.
(3L) The left singular vector matrix of the remaining matrix.
For the right singular vector matrix, four types of orthogonal matrices are involved:
(1R) The right singular vector matrix of the remaining matrix.
(2R) If
sqre
= 1
, one extra Givens rotation to generate the right null space.
(3R) The inverse transformation of (2L).
(4R) The inverse transformation of (1L).
Input Parameters
icompq
INTEGER
. Specifies whether singular vectors are to be computed in factored form:
If
icompq
= 0
: Left singular vector matrix.
If
icompq
= 1
: Right singular vector matrix.
nl
INTEGER
. The row dimensio