# ?tpsv

Solves a system of linear equations whose coefficients are in a triangular packed matrix.

## Syntax

FORTRAN 77:

call stpsv(uplo, trans, diag, n, ap, x, incx )

call dtpsv(uplo, trans, diag, n, ap, x, incx )

call ctpsv(uplo, trans, diag, n, ap, x, incx )

call ztpsv(uplo, trans, diag, n, ap, x, incx )

Fortran 95:

call tpsv(a, x [,uplo] [, trans] [,diag])

## Description

The ?tpsv routines solve one of the following systems of equations

`A*x = b`, or `A'*x = b`, or `conjg(A')*x = b`,

where:

b and x are n-element vectors,

A is an n-by-n unit, or non-unit, upper or lower triangular matrix, supplied in packed form.

This routine does not test for singularity or near-singularity.

Such tests must be performed before calling this routine.

## Input Parameters

uplo

  CHARACTER*1. Specifies whether the matrix A is upper or lower triangular:

  if `uplo = 'U'` or 'u', then the matrix is upper triangular;

  if `uplo = 'L'` or 'l', then the matrix is low triangular.

trans

  CHARACTER*1. Specifies the system of equations:

  if `trans = 'N'` or `'n'`, then `A*x = b`;

  if `trans = 'T'` or `'t'`, then `A'*x = b`;

  if `trans = 'C'` or `'c'`, then `conjg(A')*x = b`.

diag

  CHARACTER*1. Specifies whether the matrix A is unit triangular:

  if `diag = 'U'` or 'u' then the matrix is unit triangular;

  if `diag = 'N'` or 'n', then the matrix is not unit triangular.

n

  INTEGER. Specifies the order of the matrix A. The value of n must be at least zero.

ap

  REAL for stpsv

  DOUBLE PRECISION for dtpsv

  COMPLEX for ctpsv

  DOUBLE COMPLEX for ztpsv

  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.

  When `diag = 'U'` or 'u', the diagonal elements of a are not referenced, but are assumed to be unity.

x

  REAL for stpsv

  DOUBLE PRECISION for dtpsv

  COMPLEX for ctpsv

  DOUBLE COMPLEX for ztpsv

  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.

incx

  INTEGER. Specifies the increment for the elements of x.

  The value of incx must not be zero.

## Output Parameters

x

  Overwritten with the solution vector x.

## Fortran 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see Fortran 95 Interface Conventions.

Specific details for the routine tpsv interface are the following:

a

  Holds the array a of size (n*(n+1)/2).

x

  Holds the vector of length (n).

uplo

  Must be 'U' or 'L'. The default value is 'U'.

trans

  Must be 'N', 'C', or 'T'.

  The default value is 'N'.

diag

  Must be 'N' or 'U'. The default value is 'N'.

Parent topic: BLAS Level 2 Routines