NAME

ctpsv - solve one of the systems of equations   A∗x = b, or A’∗x = b, or conjg( A’ )∗x = b

SYNOPSIS

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

void ctpsv(char uplo, char trans, char diag, long int n,
complex ∗cap, complex ∗cx, long int incx)

INTEGER INCX, N

CHARACTER∗1 DIAG, TRANS, UPLO

COMPLEX AP( ∗ ), X( ∗ )

PURPOSE

CTPSV  solves one of the systems of equations A∗x = b, or A’∗x = b, or conjg( A’ )∗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   - 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.
 
Unchanged on exit.

TRANS  - 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’∗x = b.
 
TRANS = ’C’ or ’c’   conjg( A’ )∗x = b.
 
Unchanged on exit.

DIAG   - 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.
 
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 = ’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. 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.

Sun, Inc.  —  Last change: 20 Sep 1996