---
name: "ctpsv.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/ctpsv.f"
---

# ctpsv.f(3)

## NAME

BLAS/SRC/ctpsv.f

## SYNOPSIS

### Functions/Subroutines

subroutine **ctpsv** (uplo, trans, diag, n, ap, x, incx)\
 **CTPSV**

## Function/Subroutine Documentation

### subroutine ctpsv (character uplo, character trans, character diag, integer n, complex, dimension(\*) ap, complex, dimension(\*) x, integer incx)

**CTPSV**

**Purpose:**

```
!>
!> CTPSV  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, supplied in packed form.
!>
!> 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.
!>
```

*AP*

```
!>          AP is COMPLEX array, dimension at least
!>           ( ( n*( n + 1 ) )/2 ).
!>           Before entry with  UPLO = 'U' or 'u', the array AP must
!>           contain the upper triangular matrix packed sequentially,
!>           column by column, so that AP( 1 ) contains a( 1, 1 ),
!>           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
!>           respectively, and so on.
!>           Before entry with UPLO = 'L' or 'l', the array AP must
!>           contain the lower triangular matrix packed sequentially,
!>           column by column, so that AP( 1 ) contains a( 1, 1 ),
!>           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
!>           respectively, and so on.
!>           Note that when  DIAG = 'U' or 'u', the diagonal elements of
!>           A are not referenced, but are assumed to be unity.
!>
```

*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

Univ. of Colorado Denver

NAG Ltd.

**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 **143** of file **ctpsv.f**.

## Author

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