# slatrs3.f - Man Page

SRC/slatrs3.f

## Synopsis

### Functions/Subroutines

subroutine slatrs3 (uplo, trans, diag, normin, n, nrhs, a, lda, x, ldx, scale, cnorm, work, lwork, info)
SLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow.

## Function/Subroutine Documentation

### subroutine slatrs3 (character uplo, character trans, character diag, character normin, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldx, * ) x, integer ldx, real, dimension( * ) scale, real, dimension( * ) cnorm, real, dimension( * ) work, integer lwork, integer info)

SLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow.

Purpose:

``` SLATRS3 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (LWORK).
On exit, if INFO = 0, WORK(1) returns the optimal size of
WORK.```

LWORK LWORK is INTEGER 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.

Parameters

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 227 of file slatrs3.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page slatrs3(3) is an alias of slatrs3.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK