?pbtf2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

Computes the Cholesky factorization of a symmetric/ Hermitian positive-definite band matrix (unblocked algorithm).

call spbtf2 ( uplo , n , kd , ab , ldab , info )

call dpbtf2 ( uplo , n , kd , ab , ldab , info )

call cpbtf2 ( uplo , n , kd , ab , ldab , info )

call zpbtf2 ( uplo , n , kd , ab , ldab , info )

The routine computes the Cholesky factorization of a real symmetric or complex Hermitian positive definite band matrix A .

The factorization has the form

A = U^{T}*U for real flavors, A = U^{H}*U for complex flavors if uplo = 'U' , or

A = L*L^{T} for real flavors, A = L*L^{H} for complex flavors if uplo = 'L' ,

where U is an upper triangular matrix, and L is lower triangular. This is the unblocked version of the algorithm, calling BLAS Level 2 Routines .

uplo: CHARACTER*1 . Specifies whether the upper or lower triangular part of the symmetric/Hermitian matrix A is stored: = ‘U’ : upper triangular = ‘L’ : lower triangular
n: INTEGER . The order of the matrix A . n≥ 0 .
kd: INTEGER . The number of super-diagonals of the matrix A if uplo = 'U' , or the number of sub-diagonals if uplo = 'L' . kd≥ 0 .
ab: REAL for spbtf2 DOUBLE PRECISION for dpbtf2 COMPLEX for cpbtf2 DOUBLE COMPLEX for zpbtf2 . Array, DIMENSION ( ldab , n ). On entry, the upper or lower triangle of the symmetric/ Hermitian band matrix A , stored in the first kd +1 rows of the array. The j -th column of A is stored in the j -th column of the array ab as follows: if uplo = 'U' , ab(kd+1+i-j,j) = A(i, j for max(1, j-kd) ≤ i ≤ j ; if uplo = 'L' , ab(1+i-j,j) = A(i, j for j ≤ i ≤ min( n , j + kd ).
ldab: INTEGER . The leading dimension of the array ab . ldab≥kd+1 .

ab: On exit, If info = 0 , the triangular factor U or L from the Cholesky factorization A=U^{T}*U ( A=U^{H}*U ), or A= L*L^{T} ( A = L*L^{H} ) of the band matrix A , in the same storage format as A .

info

INTEGER .

= 0: successful exit
< 0: if info = -k , the k- th argument had an illegal value
> 0: if info = k , the leading minor of order k is not positive definite, and the factorization could not be completed.