# ctpsv.f - Man Page

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

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK