cpbtf2-f(3)

cpbtf2.f –

Synopsis

Functions/Subroutines

subroutine cpbtf2 (UPLO, N, KD, AB, LDAB, INFO)
CPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

Function/Subroutine Documentation

subroutine cpbtf2 (characterUPLO, integerN, integerKD, complex, dimension( ldab, * )AB, integerLDAB, integerINFO)

CPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

Purpose:

 CPBTF2 computes the Cholesky factorization of a complex Hermitian
 positive definite band matrix A.
 The factorization has the form
 A = U**H * U , if UPLO = 'U', or
 A = L * L**H, if UPLO = 'L',
 where U is an upper triangular matrix, U**H is the conjugate transpose
 of U, and L is lower triangular.
 This is the unblocked version of the algorithm, calling Level 2 BLAS.

Parameters:

UPLO

 UPLO is CHARACTER*1
 Specifies whether the upper or lower triangular part of the
 Hermitian matrix A is stored:
 = 'U': Upper triangular
 = 'L': Lower triangular

 N is INTEGER
 The order of the matrix A. N >= 0.

 KD is 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 is COMPLEX array, dimension (LDAB,N)
 On entry, the upper or lower triangle of the 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).
 On exit, if INFO = 0, the triangular factor U or L from the
 Cholesky factorization A = U**H *U or A = L*L**H of the band
 matrix A, in the same storage format as A.

LDAB

 LDAB is INTEGER
 The leading dimension of the array AB. LDAB >= KD+1.

INFO

 INFO is 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.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Further Details:

 The band storage scheme is illustrated by the following example, when
 N = 6, KD = 2, and UPLO = 'U':
 On entry: On exit:
 * * a13 a24 a35 a46 * * u13 u24 u35 u46
 * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
 a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
 Similarly, if UPLO = 'L' the format of A is as follows:
 On entry: On exit:
 a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
 a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
 a31 a42 a53 a64 * * l31 l42 l53 l64 * *
 Array elements marked * are not used by the routine.

Definition at line 143 of file cpbtf2.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.