---
name: "dtpt03.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/dtpt03.f"
---

# dtpt03.f(3)

## NAME

TESTING/LIN/dtpt03.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dtpt03** (uplo, trans, diag, n, nrhs, ap, scale, cnorm, tscal, x, ldx, b, ldb, work, resid)\
 **DTPT03**

## Function/Subroutine Documentation

### subroutine dtpt03 (character uplo, character trans, character diag, integer n, integer nrhs, double precision, dimension( \* ) ap, double precision scale, double precision, dimension( \* ) cnorm, double precision tscal, double precision, dimension( ldx, \* ) x, integer ldx, double precision, dimension( ldb, \* ) b, integer ldb, double precision, dimension( \* ) work, double precision resid)

**DTPT03**

**Purpose:**

```
!>
!> DTPT03 computes the residual for the solution to a scaled triangular
!> system of equations A*x = s*b  or  A'*x = s*b  when the triangular
!> matrix A is stored in packed format.  Here A' is the 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 or A' 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'*x = s*b  (Transpose)
!>          = 'C':  A'*x = s*b  (Conjugate transpose = 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.
!>
```

*NRHS*

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

*AP*

```
!>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
!>          The upper or lower triangular matrix A, packed columnwise in
!>          a linear array.  The j-th column of A is stored in the array
!>          AP as follows:
!>          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
!>          if UPLO = 'L',
!>             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
!>
```

*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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 **159** of file **dtpt03.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.