LinearAlgebra`BLAS`

LinearAlgebra`BLAS`

TRMV

TRMV[ul,ts,dg,a,b]

computes the triangular matrix-vector multiplication op_ts[a].b and resets b to the result.

Details and Options

To use TRMV, 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
	dg	input string	diagonal ones string
	a	input expression	rectangular matrix
	b	input/output symbol	vector; the symbol value is modified in place

The upper/lower triangular string ul may be specified as:
"U" the upper triangular part of a is to be used

"L" the lower triangular part of a is to be used
The transposition string ts describes the operator op_ts and may be specified as:
"N" no transposition

"T" transpose

"C" conjugate transpose
The diagonal ones string dg may be specified as:
"U" the main diagonal of a is assumed to contain only ones

"N" the actual values of the main diagonal of a are used
Dimensions of the matrix and vector arguments must be such that the dot product is 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/0k109sy3smikwv6jb15z81b-nluht4

Compute UpperTriangularize[a].b and save it in b:

In[2]:=2

✖

https://wolfram.com/xid/0k109sy3smikwv6jb15z81b-qr0g3w

Out[2]=2

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

Real matrix and vectors:

In[1]:=1

✖

https://wolfram.com/xid/0k109sy3smikwv6jb15z81b-fbzaue

Out[4]=4

Complex matrix and vectors:

In[1]:=1

✖

https://wolfram.com/xid/0k109sy3smikwv6jb15z81b-n2l34m

Out[1]=1

Arbitrary-precision matrix and vectors:

In[1]:=1

✖

https://wolfram.com/xid/0k109sy3smikwv6jb15z81b-v1s878

Out[1]=1

Symbolic matrix and vectors:

In[1]:=1

✖

https://wolfram.com/xid/0k109sy3smikwv6jb15z81b-vep7c3

Out[1]=1

Properties & Relations (4)Properties of the function, and connections to other functions

TRMV["U","N","N",a,b] is equivalent to b=UpperTriangularize[a].b:

In[1]:=1

✖

https://wolfram.com/xid/0k109sy3smikwv6jb15z81b-qdy9hg

Out[4]=4

TRMV["L","T","N",a,b] is equivalent to b=Transpose[LowerTriangularize[a]].b:

In[1]:=1

✖

https://wolfram.com/xid/0k109sy3smikwv6jb15z81b-b1z0fq

Out[1]=1

Note this is not TRMV["U","N","N",a,b] as the lower triangular part is used for the transpose:

In[2]:=2

✖

https://wolfram.com/xid/0k109sy3smikwv6jb15z81b-03m87w

Out[2]=2

If dg="U", the diagonal values of a are assumed to be ones:

In[1]:=1

✖

https://wolfram.com/xid/0k109sy3smikwv6jb15z81b-gf3jxd

Out[1]=1

The diagonal has been effectively replaced by ones:

In[2]:=2

✖

https://wolfram.com/xid/0k109sy3smikwv6jb15z81b-sfyy0p

Out[2]=2

If a is a rectangular matrix then only the leading upper or lower triangular part of a is used:

In[1]:=1

✖

https://wolfram.com/xid/0k109sy3smikwv6jb15z81b-udaosp

Out[1]=1

The matrix a is effectively truncated to its upper left corner:

In[2]:=2

✖

https://wolfram.com/xid/0k109sy3smikwv6jb15z81b-vkfp57

Out[2]=2

Possible Issues (2)Common pitfalls and unexpected behavior

The last argument must be a symbol:

In[1]:=1

✖

https://wolfram.com/xid/0k109sy3smikwv6jb15z81b-b2kczm

Out[2]=2

The last argument must be initialized to a vector:

In[1]:=1

✖

https://wolfram.com/xid/0k109sy3smikwv6jb15z81b-dx0fph

Out[1]=1

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