Contents

# ?lasd3

Finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by
?bdsdc
.

## Syntax

Include Files
• mkl.h
Description
The routine
?lasd3
finds all the square roots of the roots of the secular equation, as defined by the values in
D
and
Z
.
It makes the appropriate calls to
?lasd4
and then updates the singular vectors by matrix multiplication.
The routine
?lasd3
is called from
?lasd1
.
Input Parameters
nl
The row dimension of the upper block.
nl
1
.
nr
The row dimension of the lower block.
nr
1
.
sqre
If
sqre
= 0
): the lower block is an
nr
-by-
nr
square matrix.
If
sqre
= 1
): the lower block is an
nr
-by-(
n
r
+1) rectangular matrix. The bidiagonal matrix has
n
=
nl
+
nr
+ 1
rows and
m
=
n
+
sqre
n
columns.
k
The size of the secular equation,
1 ≤
k
n
.
q
Workspace array,
DIMENSION
at least (
ldq
,
k
).
ldq
The leading dimension of the array
Q
.
ldq
k
.
dsigma
Array,
DIMENSION
(
k
). The first
k
elements of this array contain the old roots of the deflated updating problem. These are the poles of the secular equation.
ldu
The leading dimension of the array
u
.
ldu
n
.
u2
Array,
DIMENSION
(
ldu2
,
n
).
The first
k
columns of this matrix contain the non-deflated left singular vectors for the split problem.
ldu2
The leading dimension of the array
u2
.
ldu2
n
.
ldvt
The leading dimension of the array
vt
.
ldvt
n
.
vt2
Array,
DIMENSION
(
ldvt2
,
n
).
The first
k
columns of
vt2
' contain the non-deflated right singular vectors for the split problem.
ldvt2
The leading dimension of the array
vt2
.
ldvt2
n
.
idxc
Array,
DIMENSION
(
n
).
The permutation used to arrange the columns of
u
(and rows of
vt
) into three groups: the first group contains non-zero entries only at and above (or before)
nl
+1
; the second contains non-zero entries only at and below (or after)
nl
+2
; and the third is dense. The first column of
u
and the row of
vt
are treated separately, however. The rows of the singular vectors found by
?lasd4
must be likewise permuted before the matrix multiplies can take place.
ctot
Array,
DIMENSION
(4). A count of the total number of the various types of columns in
u
(or rows in
vt
), as described in
idxc
.
The fourth column type is any column which has been deflated.
z
Array,
DIMENSION
(
k
). The first
k
elements of this array contain the components of the deflation-adjusted updating row vector.
Output Parameters
d
Array,
DIMENSION
(
k
). On exit the square roots of the roots of the secular equation, in ascending order.
u
Array,
DIMENSION
(
ldu
,
n
).
The last
n
-
k
columns of this matrix contain the deflated left singular vectors.
vt
Array,
DIMENSION
(
ldvt
,
m
).
The last
m
-
k
columns of
vt
' contain the deflated right singular vectors.
vt2
Destroyed on exit.
z
Destroyed on exit.
info
If
info
= 0
): successful exit.
If
info
= -
i
< 0
, the
i
-th argument had an illegal value.
If
info
= 1
, an singular value did not converge.
Application Notes
This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.