---
name: "cgbt01.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/cgbt01.f"
---

# cgbt01.f(3)

## NAME

TESTING/LIN/cgbt01.f

## SYNOPSIS

### Functions/Subroutines

subroutine **cgbt01** (m, n, kl, ku, a, lda, afac, ldafac, ipiv, work, resid)\
 **CGBT01**

## Function/Subroutine Documentation

### subroutine cgbt01 (integer m, integer n, integer kl, integer ku, complex, dimension( lda, \* ) a, integer lda, complex, dimension( ldafac, \* ) afac, integer ldafac, integer, dimension( \* ) ipiv, complex, dimension( \* ) work, real resid)

**CGBT01**

**Purpose:**

```
!>
!> CGBT01 reconstructs a band matrix A from its L*U factorization and
!> computes the residual:
!>    norm(L*U - A) / ( N * norm(A) * EPS ),
!> where EPS is the machine epsilon.
!>
!> The expression L*U - A is computed one column at a time, so A and
!> AFAC are not modified.
!>
```

**Parameters**

*M*

```
!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.
!>
```

*N*

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

*KL*

```
!>          KL is INTEGER
!>          The number of subdiagonals within the band of A.  KL >= 0.
!>
```

*KU*

```
!>          KU is INTEGER
!>          The number of superdiagonals within the band of A.  KU >= 0.
!>
```

*A*

```
!>          A is COMPLEX array, dimension (LDA,N)
!>          The original matrix A in band storage, stored in rows 1 to
!>          KL+KU+1.
!>
```

*LDA*

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

*AFAC*

```
!>          AFAC is COMPLEX array, dimension (LDAFAC,N)
!>          The factored form of the matrix A.  AFAC contains the banded
!>          factors L and U from the L*U factorization, as computed by
!>          CGBTRF.  U is stored as an upper triangular band matrix with
!>          KL+KU superdiagonals in rows 1 to KL+KU+1, and the
!>          multipliers used during the factorization are stored in rows
!>          KL+KU+2 to 2*KL+KU+1.  See CGBTRF for further details.
!>
```

*LDAFAC*

```
!>          LDAFAC is INTEGER
!>          The leading dimension of the array AFAC.
!>          LDAFAC >= max(1,2*KL*KU+1).
!>
```

*IPIV*

```
!>          IPIV is INTEGER array, dimension (min(M,N))
!>          The pivot indices from CGBTRF.
!>
```

*WORK*

```
!>          WORK is COMPLEX array, dimension (2*KL+KU+1)
!>
```

*RESID*

```
!>          RESID is REAL
!>          norm(L*U - A) / ( N * norm(A) * EPS )
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **124** of file **cgbt01.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.