CPBSV man page on Oracle

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```cpbsv.f(3)			    LAPACK			    cpbsv.f(3)

NAME
cpbsv.f -

SYNOPSIS
Functions/Subroutines
subroutine cpbsv (UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO)
CPBSV computes the solution to system of linear equations A * X =
B for OTHER matrices

Function/Subroutine Documentation
subroutine cpbsv (characterUPLO, integerN, integerKD, integerNRHS, complex,
dimension( ldab, * )AB, integerLDAB, complex, dimension( ldb, * )B,
integerLDB, integerINFO)
CPBSV computes the solution to system of linear equations A * X = B
for OTHER matrices

Purpose:

CPBSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite band matrix and X
and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as
A = U**H * U,  if UPLO = 'U', or
A = L * L**H,  if UPLO = 'L',
where U is an upper triangular band matrix, and L is a lower
triangular band matrix, with the same number of superdiagonals or
subdiagonals as A.	The factored form of A is then used to solve the
system of equations A * X = B.

Parameters:
UPLO

UPLO is CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

N

N is INTEGER
The number of linear equations, i.e., the order of the
matrix A.	N >= 0.

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B.  NRHS >= 0.

AB

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).
See below for further details.

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.

B

B is COMPLEX array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.

LDB

LDB is INTEGER
The leading dimension of the array B.  LDB >= max(1,N).

INFO

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i, the leading minor of order i of A is not
positive definite, so the factorization could not be
completed, and the solution has not been computed.

Author:
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:
November 2011

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 165 of file cpbsv.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2			Tue Sep 25 2012			    cpbsv.f(3)
```
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