# cpbt01.f - Man Page

TESTING/LIN/cpbt01.f

## Synopsis

### Functions/Subroutines

subroutine cpbt01 (uplo, n, kd, a, lda, afac, ldafac, rwork, resid)
CPBT01

## Function/Subroutine Documentation

### subroutine cpbt01 (character uplo, integer n, integer kd, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldafac, * ) afac, integer ldafac, real, dimension( * ) rwork, real resid)

CPBT01

Purpose:

``` CPBT01 reconstructs a Hermitian positive definite band matrix A from
its L*L' or U'*U factorization and computes the residual
norm( L*L' - A ) / ( N * norm(A) * EPS ) or
norm( U'*U - A ) / ( N * norm(A) * EPS ),
where EPS is the machine epsilon, L' is the conjugate transpose of
L, and U' is the conjugate transpose of U.```
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

```          N is INTEGER
The number of rows and columns of the matrix A.  N >= 0.```

KD

```          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.```

A

```          A is COMPLEX array, dimension (LDA,N)
The original Hermitian band matrix A.  If UPLO = 'U', the
upper triangular part of A is stored as a band matrix; if
UPLO = 'L', the lower triangular part of A is stored.  The
columns of the appropriate triangle are stored in the columns
of A and the diagonals of the triangle are stored in the rows
of A.  See CPBTRF for further details.```

LDA

```          LDA is INTEGER.
The leading dimension of the array A.  LDA >= max(1,KD+1).```

AFAC

```          AFAC is COMPLEX array, dimension (LDAFAC,N)
The factored form of the matrix A.  AFAC contains the factor
L or U from the L*L' or U'*U factorization in band storage
format, as computed by CPBTRF.```

LDAFAC

```          LDAFAC is INTEGER
The leading dimension of the array AFAC.
LDAFAC >= max(1,KD+1).```

RWORK

`          RWORK is REAL array, dimension (N)`

RESID

```          RESID is REAL
If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 118 of file cpbt01.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cpbt01(3) is an alias of cpbt01.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK