## Developer Reference

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

# ?la_syrpvgrw

Computes the reciprocal pivot growth factor
norm(A)/norm(U)
for a symmetric indefinite matrix.

## Syntax

Include Files
• mkl.fi
Description
The
?la_syrpvgrw
routine computes the reciprocal pivot growth factor
norm(
A
)/norm(
U
)
. The max absolute element norm is used. If this is much less than 1, the stability of the
LU
factorization of the equilibrated matrix
A
could be poor. This also means that the solution
X
, estimated condition numbers, and error bounds could be unreliable.
Input Parameters
uplo
CHARACTER*1
. Must be
'U'
or
'L'
.
Specifies the triangle of A to store:
If
uplo
=
'U'
, the upper triangle of
A
is stored,
If
uplo
=
'L'
, the lower triangle of
A
is stored.
n
INTEGER
. The number of linear equations, the order of the matrix
A
;
n
0.
info
INTEGER
. The value of INFO returned from
?sytrf
, that is, the pivot in column
info
is exactly 0.
a
,
af
REAL
for
sla_syrpvgrw
DOUBLE PRECISION
for
dla_syrpvgrw
COMPLEX
for
cla_syrpvgrw
DOUBLE COMPLEX
for
zla_syrpvgrw
.
Arrays:
a
(
lda
,*)
,
af
(
ldaf
,*)
.
The array
a
contains the input
n
-by-
n
matrix
A
. The second dimension of
a
must be at least
max(1,
n
)
.
The array
af
contains the block diagonal matrix D and the multipliers used to obtain the factor
U
or
L
as computed by
?sytrf
.
The second dimension of
af
must be at least
max(1,
n
)
.
lda
INTEGER
a
;
lda
max(1,
n
)
.
ldaf
INTEGER
af
;
ldaf
max(1,
n
)
.
ipiv
INTEGER
.
Array,
DIMENSION
n
. Details of the interchanges and the block structure of D as determined by
?sytrf
.
work
REAL
for
sla_syrpvgrw
and
cla_syrpvgrw
DOUBLE PRECISION
for
dla_syrpvgrw
and
zla_syrpvgrw
.
Workspace array, dimension 2*
n
.