---
name: "dlatrs3.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/dlatrs3.f"
---

# dlatrs3.f(3)

## NAME

SRC/dlatrs3.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dlatrs3** (uplo, trans, diag, normin, n, nrhs, a, lda, x, ldx, scale, cnorm, work, lwork, info)\
 **DLATRS3** solves a triangular system of equations with the scale factors set to prevent overflow.

## Function/Subroutine Documentation

### subroutine dlatrs3 (character uplo, character trans, character diag, character normin, integer n, integer nrhs, double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( ldx, \* ) x, integer ldx, double precision, dimension( \* ) scale, double precision, dimension( \* ) cnorm, double precision, dimension( \* ) work, integer lwork, integer info)

**DLATRS3** solves a triangular system of equations with the scale factors set to prevent overflow.

**Purpose:**

```
!>
!> DLATRS3 solves one of the triangular systems
!>
!>    A * X = B * diag(scale)  or  A**T * X = B * diag(scale)
!>
!> with scaling to prevent overflow.  Here A is an upper or lower
!> triangular matrix, A**T denotes the transpose of A. X and B are
!> n by nrhs matrices and scale is an nrhs element vector of scaling
!> factors. A scaling factor scale(j) is usually less than or equal
!> to 1, chosen such that X(:,j) is less than the overflow threshold.
!> If the matrix A is singular (A(j,j) = 0 for some j), then
!> a non-trivial solution to A*X = 0 is returned. If the system is
!> so badly scaled that the solution cannot be represented as
!> (1/scale(k))*X(:,k), then x(:,k) = 0 and scale(k) is returned.
!>
!> This is a BLAS-3 version of LATRS for solving several right
!> hand sides simultaneously.
!>
!>
```

**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':  Solve A * x = s*b  (No transpose)
!>          = 'T':  Solve A**T* x = s*b  (Transpose)
!>          = 'C':  Solve A**T* 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
!>
```

*NORMIN*

```
!>          NORMIN is CHARACTER*1
!>          Specifies whether CNORM has been set or not.
!>          = 'Y':  CNORM contains the column norms on entry
!>          = 'N':  CNORM is not set on entry.  On exit, the norms will
!>                  be computed and stored in CNORM.
!>
```

*N*

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

*NRHS*

```
!>          NRHS is INTEGER
!>          The number of columns of X.  NRHS >= 0.
!>
```

*A*

```
!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          The triangular matrix A.  If UPLO = 'U', the leading n by n
!>          upper triangular part of the array A contains the upper
!>          triangular matrix, and the strictly lower triangular part of
!>          A is not referenced.  If UPLO = 'L', the leading n by n lower
!>          triangular part of the array A contains the lower triangular
!>          matrix, and the strictly upper triangular part of A is not
!>          referenced.  If DIAG = 'U', the diagonal elements of A are
!>          also not referenced and are assumed to be 1.
!>
```

*LDA*

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

*X*

```
!>          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
!>          On entry, the right hand side B of the triangular system.
!>          On exit, X is overwritten by the solution matrix X.
!>
```

*LDX*

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

*SCALE*

```
!>          SCALE is DOUBLE PRECISION array, dimension (NRHS)
!>          The scaling factor s(k) is for the triangular system
!>          A * x(:,k) = s(k)*b(:,k)  or  A**T* x(:,k) = s(k)*b(:,k).
!>          If SCALE = 0, the matrix A is singular or badly scaled.
!>          If A(j,j) = 0 is encountered, a non-trivial vector x(:,k)
!>          that is an exact or approximate solution to A*x(:,k) = 0
!>          is returned. If the system so badly scaled that solution
!>          cannot be presented as x(:,k) * 1/s(k), then x(:,k) = 0
!>          is returned.
!>
```

*CNORM*

```
!>          CNORM is DOUBLE PRECISION array, dimension (N)
!>
!>          If NORMIN = 'Y', CNORM is an input argument and CNORM(j)
!>          contains the norm of the off-diagonal part of the j-th column
!>          of A.  If TRANS = 'N', CNORM(j) must be greater than or equal
!>          to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j)
!>          must be greater than or equal to the 1-norm.
!>
!>          If NORMIN = 'N', CNORM is an output argument and CNORM(j)
!>          returns the 1-norm of the offdiagonal part of the j-th column
!>          of A.
!>
```

*WORK*

```
!>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)).
!>          On exit, if INFO = 0, WORK(1) returns the optimal size of
!>          WORK.
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!>
!>          If MIN(N,NRHS) = 0, LWORK >= 1, else
!>          LWORK >= MAX(1, 2*NBA * MAX(NBA, MIN(NRHS, 32)), where
!>          NBA = (N + NB - 1)/NB and NB is the optimal block size.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal dimensions of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -k, the k-th argument had an illegal value
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

Definition at line **232** of file **dlatrs3.f**.

## Author

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