---
name: "cpbt01.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/cpbt01.f"
---

# cpbt01.f(3)

## NAME

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.