LinearAlgebra`BLAS`

LinearAlgebra`BLAS`

HERK

HERK[ul,ts,α,a,β,b]

computes the Hermitian rank-k update α op_ts[a].ConjugateTranspose[op_ts[a]]+β b and resets the appropriate part of b to the result.

Details and Options

To use HERK, you first need to load the BLAS Package using Needs["LinearAlgebra`BLAS`"].
The following arguments must be given:

	ul	input string	upper/lower triangular string
	ts	input string	transposition string
	α	input expression	scalar mutliple
	a	input expression	rectangular matrix
	β	input expression	scalar multiple
	b	input/output symbol	square matrix; the symbol value is modified in place

The upper/lower triangular string ul may be specified as:
"U" update the upper triangular part of b

"L" update the lower triangular part of b
The transposition strings describe the operators op_ts and may be specified as:
"N" no transposition

"T" transpose

"C" conjugate transpose
The main diagonal elements of b are assumed to be real-valued.
Dimensions of the matrix arguments must be such that the dot product and addition are well defined.

Examples

open allclose all

Basic Examples (1)Summary of the most common use cases

Load the BLAS package:

In[1]:=1

✖

https://wolfram.com/xid/0bhc98c1kbm7gspvbqvdz48i-nluht4

Apply Hermitian rank-2 update to the upper triangular part of a matrix:

In[2]:=2

✖

https://wolfram.com/xid/0bhc98c1kbm7gspvbqvdz48i-w56aik

Out[5]=5

Scope (4)Survey of the scope of standard use cases

Real matrices:

In[1]:=1

✖

https://wolfram.com/xid/0bhc98c1kbm7gspvbqvdz48i-bkwhxt

Out[4]=4

Complex matrices:

In[1]:=1

✖

https://wolfram.com/xid/0bhc98c1kbm7gspvbqvdz48i-dmgqnm

Out[1]=1

Arbitrary-precision matrices:

In[1]:=1

✖

https://wolfram.com/xid/0bhc98c1kbm7gspvbqvdz48i-0ujex7

Out[1]=1

Integer-symbolic matrices:

In[1]:=1

✖

https://wolfram.com/xid/0bhc98c1kbm7gspvbqvdz48i-xhyowv

Out[1]=1

Properties & Relations (1)Properties of the function, and connections to other functions

HERK["U","N",α,a,β,b] is equivalent to b=α a.ConjugateTranspose[a]+β b applied to the upper triangular part of b:

In[1]:=1

✖

https://wolfram.com/xid/0bhc98c1kbm7gspvbqvdz48i-yvw11k

Out[7]=7

The strictly lower triangular part of b is unchanged:

In[8]:=8

✖

https://wolfram.com/xid/0bhc98c1kbm7gspvbqvdz48i-879rta

Out[8]=8

Possible Issues (2)Common pitfalls and unexpected behavior

The last argument must be a symbol:

In[1]:=1

✖

https://wolfram.com/xid/0bhc98c1kbm7gspvbqvdz48i-raalz5

Out[1]=1

The last argument must be initialized to a matrix, otherwise an error message is issued:

In[1]:=1

✖

https://wolfram.com/xid/0bhc98c1kbm7gspvbqvdz48i-vsg3yk

Out[1]=1

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