## Developer Reference

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

# Glossary

A
H
Denotes the conjugate transpose of a general matrix
A
.
conjugate matrix.
A
T
Denotes the transpose of a general matrix
A
.
transpose.
band matrix
A general
m
-by-
n
matrix
A
such that
a
ij
= 0
for
|
i
-
j
| >
l
, where
1 <
l
< min(
m
,
n
)
. For example, any tridiagonal matrix is a band matrix.
band storage
A special storage scheme for band matrices. A matrix is stored in a two-dimensional array: columns of the matrix are stored in the corresponding columns of the array, and diagonals of the matrix are stored in rows of the array.
BLAS
Abbreviation for Basic Linear Algebra Subprograms. These subprograms implement vector, matrix-vector, and matrix-matrix operations.
BRNG
Abbreviation for Basic Random Number Generator. Basic random number generators are pseudorandom number generators imitating i.i.d. random number sequences of uniform distribution. Distributions other than uniform are generated by applying different transformation techniques to the sequences of random numbers of uniform distribution.
BRNG registration
Standardized mechanism that allows a user to include a user-designed BRNG into the VSL and use it along with the predefined VSL basic generators.
Bunch-Kaufman factorization
Representation of a real symmetric or complex Hermitian matrix
A
in the form
A
=
PUDU
H
P
T
(or
A
=
PLDL
H
P
T
) where
P
is a permutation matrix,
U
and
L
are upper and lower triangular matrices with unit diagonal, and
D
is a Hermitian block-diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks.
U
and
L
have 2-by-2 unit diagonal blocks corresponding to the 2-by-2 blocks of
D
.
c
When found as the first letter of routine names,
c
indicates the usage of single-precision complex data type.
CBLAS
C interface to the BLAS.
See
BLAS.
CDF
Cumulative Distribution Function. The function that determines probability distribution for univariate or multivariate random variable
X
. For univariate distribution the cumulative distribution function is the function of real argument
x
, which for every
x
takes a value equal to probability of the event
A
:
X
x
. For multivariate distribution the cumulative distribution function is the function of a real vector
x
= (
x
1
,
x
2
, ...,
x
n
)
, which, for every
x
, takes a value equal to probability of the event
A
= (
X
1
x
1
&
X
2
x
2
, & ..., &
X
n
x
n
)
.
Cholesky factorization
Representation of a symmetric positive-definite or, for complex data, Hermitian positive-definite matrix
A
in the form
A
=
U
H
U
or
A
=
LL
H
, where
L
is a lower triangular matrix and
U
is an upper triangular matrix.
condition number
The number
κ
(
A
)
defined for a given square matrix
A
as follows:
κ
(
A
) = ||
A
|| ||
A
1
||
.
conjugate matrix
The matrix
A
H
defined for a given general matrix
A
as follows: (
A
H
)
ij
= (
a
ji
)
*
.
conjugate number
The conjugate of a complex number
z
=
a
+
bi
is
z
*
=
a
-
bi
.
d
When found as the first letter of routine names,
d
indicates the usage of double-precision real data type.
dot product
The number denoted
x
·
y
and defined for given vectors
x
and
y
as follows:
x
·
y
=
Σ
i
x
i
y
i
.
Here
x
i
and