Parameters

uplo

Type: System..::..String

On entry: specifies whether the upper or lower triangular part of $A$ is stored and how $A$ is to be factorized.

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

The upper triangular part of $A$ is stored and $A$ is factorized as $U^{\mathrm{T}}U$, where $U$ is upper triangular.

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

The lower triangular part of $A$ is stored and $A$ is factorized as $L{L}^{\mathrm{T}}$, where $L$ is lower triangular.

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

n

Type: System..::..Int32

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

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

kd

Type: System..::..Int32

On entry: $k_d$, the number of superdiagonals or subdiagonals of the matrix $A$.

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

ab

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

An array of size [dim1, dim2]

Note: dim1 must satisfy the constraint: $\mathrm{dim1}\ge \mathbf{kd}+1$

Note: the second dimension of the array ab must be at least $\max \left(1,\mathbf{n}\right)$.

On entry: the $n$ by $n$ symmetric positive definite band matrix $A$.

The matrix is stored in rows $1$ to $k_d+1$, more precisely,

• if $\mathbf{uplo}=\text{"U"}$, the elements of the upper triangle of $A$ within the band must be stored with element $A_{ij}$ in $\mathbf{ab}[k_d+1+i-j,j]\text{ for }\max \left(1,j-k_d\right)\le i\le j$;
• if $\mathbf{uplo}=\text{"L"}$, the elements of the lower triangle of $A$ within the band must be stored with element $A_{ij}$ in $\mathbf{ab}[1+i-j,j]\text{ for }j\le i\le \min \left(n,j+k_d\right)\text{.}$

On exit: the upper or lower triangle of $A$ is overwritten by the Cholesky factor $U$ or $L$ as specified by uplo, using the same storage format as described above.

info

Type: System..::..Int32%

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