---
name: "ztbt03.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/ztbt03.f"
---

# ztbt03.f(3)

## NAME

TESTING/LIN/ztbt03.f

## SYNOPSIS

### Functions/Subroutines

subroutine **ztbt03** (uplo, trans, diag, n, kd, nrhs, ab, ldab, scale, cnorm, tscal, x, ldx, b, ldb, work, resid)\
 **ZTBT03**

## Function/Subroutine Documentation

### subroutine ztbt03 (character uplo, character trans, character diag, integer n, integer kd, integer nrhs, complex\*16, dimension( ldab, \* ) ab, integer ldab, double precision scale, double precision, dimension( \* ) cnorm, double precision tscal, complex\*16, dimension( ldx, \* ) x, integer ldx, complex\*16, dimension( ldb, \* ) b, integer ldb, complex\*16, dimension( \* ) work, double precision resid)

**ZTBT03**

**Purpose:**

```
!>
!> ZTBT03 computes the residual for the solution to a scaled triangular
!> system of equations  A*x = s*b,  A**T *x = s*b,  or  A**H *x = s*b
!> when A is a triangular band matrix.  Here A**T  denotes the transpose
!> of A, A**H denotes the conjugate transpose of A, s is a scalar, and
!> x and b are N by NRHS matrices.  The test ratio is the maximum over
!> the number of right hand sides of
!>    norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
!> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the matrix A is upper or lower triangular.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>
```

*TRANS*

```
!>          TRANS is CHARACTER*1
!>          Specifies the operation applied to A.
!>          = 'N':  A *x = s*b     (No transpose)
!>          = 'T':  A**T *x = s*b  (Transpose)
!>          = 'C':  A**H *x = s*b  (Conjugate transpose)
!>
```

*DIAG*

```
!>          DIAG is CHARACTER*1
!>          Specifies whether or not the matrix A is unit triangular.
!>          = 'N':  Non-unit triangular
!>          = 'U':  Unit triangular
!>
```

*N*

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

*KD*

```
!>          KD is INTEGER
!>          The number of superdiagonals or subdiagonals of the
!>          triangular band matrix A.  KD >= 0.
!>
```

*NRHS*

```
!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrices X and B.  NRHS >= 0.
!>
```

*AB*

```
!>          AB is COMPLEX*16 array, dimension (LDAB,N)
!>          The upper or lower triangular band matrix A, stored in the
!>          first kd+1 rows of the array. The j-th column of A is stored
!>          in the j-th column of the array AB as follows:
!>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
!>
```

*LDAB*

```
!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KD+1.
!>
```

*SCALE*

```
!>          SCALE is DOUBLE PRECISION
!>          The scaling factor s used in solving the triangular system.
!>
```

*CNORM*

```
!>          CNORM is DOUBLE PRECISION array, dimension (N)
!>          The 1-norms of the columns of A, not counting the diagonal.
!>
```

*TSCAL*

```
!>          TSCAL is DOUBLE PRECISION
!>          The scaling factor used in computing the 1-norms in CNORM.
!>          CNORM actually contains the column norms of TSCAL*A.
!>
```

*X*

```
!>          X is COMPLEX*16 array, dimension (LDX,NRHS)
!>          The computed solution vectors for the system of linear
!>          equations.
!>
```

*LDX*

```
!>          LDX is INTEGER
!>          The leading dimension of the array X.  LDX >= max(1,N).
!>
```

*B*

```
!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          The right hand side vectors for the system of linear
!>          equations.
!>
```

*LDB*

```
!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>
```

*WORK*

```
!>          WORK is COMPLEX*16 array, dimension (N)
!>
```

*RESID*

```
!>          RESID is DOUBLE PRECISION
!>          The maximum over the number of right hand sides of
!>          norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **174** of file **ztbt03.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.