ctpsv (l) - Linux Manuals

ctpsv: solves one of the systems of equations A*x = b, or Aaq*x = b, or conjg( Aaq )*x = b,

NAME

CTPSV - solves one of the systems of equations A*x = b, or Aaq*x = b, or conjg( Aaq )*x = b,

SYNOPSIS

SUBROUTINE CTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)

    
INTEGER INCX,N

    
CHARACTER DIAG,TRANS,UPLO

    
COMPLEX AP(*),X(*)

PURPOSE

CTPSV solves one of the systems of equations

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.

ARGUMENTS

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

UPLO = aqUaq or aquaq A is an upper triangular matrix.

UPLO = aqLaq or aqlaq A is a lower triangular matrix.

Unchanged on exit.

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

TRANS = aqNaq or aqnaq A*x = b.

TRANS = aqTaq or aqtaq Aaq*x = b.

TRANS = aqCaq or aqcaq conjg( Aaq )*x = b.

Unchanged on exit.

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

DIAG = aqUaq or aquaq A is assumed to be unit triangular.

DIAG = aqNaq or aqnaq A is not assumed to be unit triangular.

Unchanged on exit.

N - INTEGER.
On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit.
AP - COMPLEX array of DIMENSION at least
( ( n*( n + 1 ) )/2 ). Before entry with UPLO = aqUaq or aquaq, 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 = aqLaq or aqlaq, 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 = aqUaq or aquaq, the diagonal elements of A are not referenced, but are assumed to be unity. Unchanged on exit.
X - COMPLEX array of 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 - INTEGER.
On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.

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.

Pages related to ctpsv

  • ctpsv (3)
  • ctpcon (l) - estimates the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm
  • ctpmv (l) - performs one of the matrix-vector operations x := A*x, or x := Aaq*x, or x := conjg( Aaq )*x,
  • ctprfs (l) - provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
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  • ctpttr (l) - copies a triangular matrix A from standard packed format (TP) to standard full format (TR)
  • ctbcon (l) - estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm