WOLFRAM SYSTEM MODELER

# dtrsm

Solve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where A is triangular matrix. BLAS routine

# Wolfram Language

In[1]:=
`SystemModel["Modelica.Math.Matrices.LAPACK.dtrsm"]`
Out[1]:=

# Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

```Lapack documentation
Purpose
=======

DTRSM solves one of the matrix equations

op( A )*X = alpha*B,   or   X*op( A ) = alpha*B,

where alpha is a scalar, X and B are m by n matrices, A is a unit, or
non-unit,  upper or lower triangular matrix  and  op( A )  is one  of

op( A ) = A   or   op( A ) = A'.

The matrix X is overwritten on B.

Arguments
==========

SIDE   - CHARACTER*1.
On entry, SIDE specifies whether op( A ) appears on the left
or right of X as follows:

SIDE = 'L' or 'l'   op( A )*X = alpha*B.

SIDE = 'R' or 'r'   X*op( A ) = alpha*B.

Unchanged on exit.

UPLO   - CHARACTER*1.
On entry, UPLO specifies whether the matrix A is an upper or
lower triangular matrix as follows:

UPLO = 'U' or 'u'   A is an upper triangular matrix.

UPLO = 'L' or 'l'   A is a lower triangular matrix.

Unchanged on exit.

TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:

TRANSA = 'N' or 'n'   op( A ) = A.

TRANSA = 'T' or 't'   op( A ) = A'.

TRANSA = 'C' or 'c'   op( A ) = A'.

Unchanged on exit.

DIAG   - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit triangular
as follows:

DIAG = 'U' or 'u'   A is assumed to be unit triangular.

DIAG = 'N' or 'n'   A is not assumed to be unit
triangular.

Unchanged on exit.

M      - INTEGER.
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.

N      - INTEGER.
On entry, N specifies the number of columns of B.  N must be
at least zero.
Unchanged on exit.

ALPHA  - DOUBLE PRECISION.
On entry,  ALPHA specifies the scalar  alpha. When  alpha is
zero then  A is not referenced and  B need not be set before
entry.
Unchanged on exit.

A      - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
upper triangular part of the array  A must contain the upper
triangular matrix  and the strictly lower triangular part of
A is not referenced.
Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
lower triangular part of the array  A must contain the lower
triangular matrix  and the strictly upper triangular part of
A is not referenced.
Note that when  DIAG = 'U' or 'u',  the diagonal elements of
A  are not referenced either,  but are assumed to be  unity.
Unchanged on exit.

LDA    - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
then LDA must be at least max( 1, n ).
Unchanged on exit.

B      - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
Before entry,  the leading  m by n part of the array  B must
contain  the  right-hand  side  matrix  B,  and  on exit  is
overwritten by the solution matrix  X.

LDB    - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in  the  calling  (sub)  program.   LDB  must  be  at  least
max( 1, m ).
Unchanged on exit.

Level 3 Blas routine.```

# Syntax

X = dtrsm(A, B, alpha, right, upper, trans, unitTriangular)

# Inputs (7)

A Type: Real[:,:] Description: Input matrix A Type: Real[:,:] Description: Input matrix B Default Value: 1 Type: Real Description: Factor alpha Default Value: true Type: Boolean Description: = true, if A is right multiplication Default Value: true Type: Boolean Description: = true, if A is upper triangular Default Value: false Type: Boolean Description: = true, if op(A) means transposed(A) Default Value: false Type: Boolean Description: = true, if A is unit triangular, i.e., all diagonal elements of A are equal to 1

# Outputs (1)

X Default Value: B Type: Real[size(B, 1),size(B, 2)] Description: Matrix Bout=alpha*op( A )*B, or B := alpha*B*op( A )