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LinearAlgebra`BLAS`
LinearAlgebra`BLAS`

GER

GER[α,x,y,a]

computes the rank-one update a+αOuter[Times,x,y] and resets a to the result.

Details and Options

  • To use GER, you first need to load the BLAS Package using Needs["LinearAlgebra`BLAS`"].
  • The following arguments must be given:
  • αinput expressionscalar mutliple
    xinput expressionvector
    yinput expressionvector
    a
  • input/output symbol
    		• matrix; the symbol value is modified in place
  • Dimensions of the matrix and vector 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/08shha0bp8ic869sfwh-nluht4

Apply a rank-one update to a matrix:

In[2]:=2
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https://wolfram.com/xid/08shha0bp8ic869sfwh-w56aik
Out[2]=2

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

Real matrix and vectors:

In[1]:=1
✖
https://wolfram.com/xid/08shha0bp8ic869sfwh-bkwhxt
Out[1]=1

Complex matrix and vectors:

In[1]:=1
✖
https://wolfram.com/xid/08shha0bp8ic869sfwh-dmgqnm
Out[1]=1

Arbitrary-precision matrix and vectors:

In[1]:=1
✖
https://wolfram.com/xid/08shha0bp8ic869sfwh-0ujex7
Out[1]=1

Integer-symbolic matrix and vectors:

In[1]:=1
✖
https://wolfram.com/xid/08shha0bp8ic869sfwh-xhyowv
Out[1]=1

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

GER[α,x,y,a] is equivalent to a=a+αOuter[Times,x,y]:

In[17]:=17
✖
https://wolfram.com/xid/08shha0bp8ic869sfwh-yvw11k
Out[22]=22

This can also be expressed as a=a+αTranspose[{x}].{y}:

In[23]:=23
✖
https://wolfram.com/xid/08shha0bp8ic869sfwh-7ea2da
Out[23]=23

Possible Issues  (2)Common pitfalls and unexpected behavior

The last argument must be a symbol:

In[24]:=24
✖
https://wolfram.com/xid/08shha0bp8ic869sfwh-raalz5
Out[24]=24

The last argument must be initialized to a matrix:

In[1]:=1
✖
https://wolfram.com/xid/08shha0bp8ic869sfwh-vsg3yk
Out[1]=1
Wolfram Research (2017), GER, Wolfram Language function, https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GER.html.
✖
Wolfram Research (2017), GER, Wolfram Language function, https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GER.html.

Text

Wolfram Research (2017), GER, Wolfram Language function, https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GER.html.

✖
Wolfram Research (2017), GER, Wolfram Language function, https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GER.html.

CMS

Wolfram Language. 2017. "GER." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GER.html.

✖
Wolfram Language. 2017. "GER." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GER.html.

APA

Wolfram Language. (2017). GER. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GER.html

✖
Wolfram Language. (2017). GER. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GER.html

BibTeX

@misc{reference.wolfram_2024_ger, author="Wolfram Research", title="{GER}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GER.html}", note=[Accessed: 22-April-2025 ]}

✖
@misc{reference.wolfram_2024_ger, author="Wolfram Research", title="{GER}", year="2017", howpublished="\url{https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GER.html}", note=[Accessed: 22-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2024_ger, organization={Wolfram Research}, title={GER}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GER.html}, note=[Accessed: 22-April-2025 ]}

✖
@online{reference.wolfram_2024_ger, organization={Wolfram Research}, title={GER}, year={2017}, url={https://reference.wolfram.com/language/LowLevelLinearAlgebra/ref/GER.html}, note=[Accessed: 22-April-2025 ]}