# ctrsv.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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ctrsv.f

## SYNOPSIS

### Functions/Subroutines

subroutine ctrsv (UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
CTRSV

## Function/Subroutine Documentation

### subroutine ctrsv (character UPLO, character TRANS, character DIAG, integer N, complex, dimension(lda,*) A, integer LDA, complex, dimension(*) X, integer INCX)

CTRSV

Purpose:

``` CTRSV  solves one of the systems of equations

A*x = b,   or   A**T*x = b,   or   A**H*x = b,

where b and x are n element vectors and A is an n by n unit, or
non-unit, upper or lower triangular matrix.

No test for singularity or near-singularity is included in this
routine. Such tests must be performed before calling this routine.
```

Parameters:

UPLO

```          UPLO is CHARACTER*1
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:

UPLO = 'U' or 'u'   A is an upper triangular matrix.

UPLO = 'L' or 'l'   A is a lower triangular matrix.
```

TRANS

```          TRANS is CHARACTER*1
On entry, TRANS specifies the equations to be solved as
follows:

TRANS = 'N' or 'n'   A*x = b.

TRANS = 'T' or 't'   A**T*x = b.

TRANS = 'C' or 'c'   A**H*x = b.
```

DIAG

```          DIAG is CHARACTER*1
On entry, DIAG specifies whether or not A is unit
triangular as follows:

DIAG = 'U' or 'u'   A is assumed to be unit triangular.

DIAG = 'N' or 'n'   A is not assumed to be unit
triangular.
```

N

```          N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.
```

A

```          A is COMPLEX array, dimension ( LDA, N )
Before entry with  UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when  DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
```

LDA

```          LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
```

X

```          X is COMPLEX array, dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element right-hand side vector b. On exit, X is overwritten
with the solution vector x.
```

INCX

```          INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

December 2016

Further Details:

```  Level 2 Blas routine.

-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
```

Definition at line 151 of file ctrsv.f.

## Author

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