Specifies whether the matrix

A

is upper or lower triangular.

=

'U'

: Upper triangular

=

'L'

: Lower triangular

Specifies the operation applied to

Ax

.

=

'N'

: Solve

Ax

=

s*b

(no transpose)

=

'T'

: Solve

A

T

x

=

s*b

(

transpose)

=

'C'

: Solve

A

H

x

=

s*b

(conjugate transpose),

where

s

- is a scale factor

Specifies whether or not the matrix

A

is unit triangular.

=

'N'

: Non-unit triangular

=

'U'

: Unit triangular

Specifies whether

cnorm

has been set or not.

=

'Y'

:

cnorm

contains the column norms on entry;

=

'N'

:

cnorm

is not set on entry. On exit, the norms will be computed and stored in

cnorm

.

The order of the matrix

A

.

n

≥

0

Array of size

lda

*

n

. Contains the triangular matrix

A

.

If

uplo

=

U

, the leading

n

-by-

n

upper triangular part of the array

a

contains the upper triangular matrix, and the strictly lower triangular part of

a

is not referenced.

If

uplo

=

'L'

, the leading

n

-by-

n

lower triangular part of the array

a

contains the lower triangular matrix, and the strictly upper triangular part of

a

is not referenced.

If

diag

=

'U'

, the diagonal elements of

a

are also not referenced and are assumed to be 1.

(global) The row and column indices in the global matrix

A

indicating the first row and the first column of the submatrix

A

, respectively.

(global and local) array of size

dlen_

. The array descriptor for the distributed matrix

A

.

Array of size

n

. On entry, the right hand side

b

of the triangular system.

(global).The row index in the global matrix

X

indicating the first row of sub(

x

).

(global)

The column index in the global matrix

X

indicating the first column of sub(

X

).

(global and local)

Array of size

dlen_

. The array descriptor for the distributed matrix

X

.

Array of size

n

. If

normin

=

'Y'

,

cnorm

is an input argument and

cnorm

[

j

]

contains the norm of the off-diagonal part of the

(

j

+1)

-th column of

the matrix

A

,

j

=0, 1, ...,

n

-1

. If

trans

=

'N'

,

cnorm

[

j

]

must be greater than or equal to the infinity-norm, and if

trans

=

'T'

or

'C'

,

cnorm

[

j

]

must be greater than or equal to the 1-norm.

(local).

Temporary workspace.

On exit,

x

is overwritten by the solution vector

x

.

Array of size

lda

*

n

. The scaling factor

s

for the triangular system as described above.

If

scale

= 0

, the matrix

A

is singular or badly scaled, and the vector

x

is an exact or approximate solution to

Ax

= 0

.

If

normin

=

'N'

,

cnorm

is an output argument and

cnorm

[

j

]

returns the 1-norm of the off-diagonal part of the

(

j

+1)-th

column of

A

,

j

=0, 1, ...,

n

-1

.