# zgbt01.f - Man Page

TESTING/LIN/zgbt01.f

## Synopsis

### Functions/Subroutines

subroutine **zgbt01** (m, n, kl, ku, a, lda, afac, ldafac, ipiv, work, resid)**ZGBT01**

## Function/Subroutine Documentation

### subroutine zgbt01 (integer m, integer n, integer kl, integer ku, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldafac, * ) afac, integer ldafac, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, double precision resid)

**ZGBT01**

**Purpose:**

ZGBT01 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*16 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*16 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 ZGBTRF. 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 ZGBTRF 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 ZGBTRF.

*WORK*WORK is COMPLEX*16 array, dimension (2*KL+KU+1)

*RESID*RESID is DOUBLE PRECISION 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 **zgbt01.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zgbt01(3) is an alias of zgbt01.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK