Parameters

uplo

Type: System..::..String

On entry: specifies whether $A$ is upper or lower triangular.

$\mathbf{uplo}=\text{"U"}$

$A$ is upper triangular.

$\mathbf{uplo}=\text{"L"}$

$A$ is lower triangular.

Constraint: $\mathbf{uplo}=\text{"U"}$ or $\text{"L"}$.

trans

Type: System..::..String

On entry: specifies the operation to be performed.

$\mathbf{trans}=\text{"N"}$

$x\leftarrow A^{-1}x$.

$\mathbf{trans}=\text{"T"}$ or $\text{"C"}$

$x\leftarrow A^{-\mathrm{T}}x$.

Constraint: $\mathbf{trans}=\text{"N"}$, $\text{"T"}$ or $\text{"C"}$.

diag

Type: System..::..String

On entry: specifies whether $A$ has nonunit or unit diagonal elements.

$\mathbf{diag}=\text{"N"}$

The diagonal elements are stored explicitly.

$\mathbf{diag}=\text{"U"}$

The diagonal elements are assumed to be $1$, and are not referenced.

Constraint: $\mathbf{diag}=\text{"N"}$ or $\text{"U"}$.

n

Type: System..::..Int32

On entry: $n$, the order of the matrix $A$.

Constraint: $\mathbf{n}\ge 0$.

a

Type: array<System..::..Double,2>[,](,)[,][,]

An array of size [dim1, dim2]

Note: dim1 must satisfy the constraint: $\mathrm{dim1}\ge \max \left(1,\mathbf{n}\right)$

Note: the second dimension of the array a must be at least $\mathbf{n}$.

On entry: the $n$ by $n$ triangular matrix $A$.

• If $\mathbf{uplo}=\text{"U"}$, $A$ is upper triangular and the elements of the array below the diagonal are not referenced.
• If $\mathbf{uplo}=\text{"L"}$, $A$ is lower triangular and the elements of the array above the diagonal are not referenced.
• If $\mathbf{diag}=\text{"U"}$, the diagonal elements of $A$ are assumed to be $1$, and are not referenced.

x

Type: array<System..::..Double>[]()[][]

An array of size [dim1]

Note: the dimension of the array x must be at least $\max \left(1,1+\left(\mathbf{n}-1\right)\times \left|\mathbf{incx}\right|\right)$.

On entry: the $n$-element vector $x$.

If $\mathbf{incx}>0$, $x_{\mathit{i}}$ must be stored in $\mathbf{x}\left[1+\left(\mathit{i}–1\right)\times \mathbf{incx}-1\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

If $\mathbf{incx}<0$, $x_{\mathit{i}}$ must be stored in $\mathbf{x}\left[1–\left(\mathbf{n}–\mathit{i}\right)\times \mathbf{incx}-1\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

On exit: the updated vector $x$ stored in the array elements used to supply the original vector $x$.

incx

Type: System..::..Int32

On entry: the increment in the subscripts of x between successive elements of $x$.

Constraint: $\mathbf{incx}\ne 0$.

ifail

Type: System..::..Int32%

On exit: $\mathbf{ifail}=0$ unless the method detects an error (see [Error Indicators and Warnings]).