# 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

Univ. of Colorado Denver

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