?pttrsv

Syntax

Include Files

• C: mkl_scalapack.h

Description

The ?pttrsv routine solves one of the triangular systems:

L^T*X = B, or L*X = B for real flavors,

or

L*X = B, or L^H*X = B,

U*X = B, or U^H*X = B for complex flavors,

where L (or U for complex flavors) is the Cholesky factor of a Hermitian positive-definite tridiagonal matrix A such that

A = L*D*L^H (computed by spttrf/dpttrf)

or

A = U^H*D*U or A = L*D*L^H (computed by cpttrf/zpttrf).

Input Parameters

uplo

CHARACTER*1. Must be 'U' or 'L'.

Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix A is stored and the form of the factorization:

If uplo = 'U', e is the superdiagonal of U, and A = U^H*D*U or A = L*D*L^H;

if uplo = 'L', e is the subdiagonal of L, and A = L*D*L^H.

The two forms are equivalent, if A is real.

trans

CHARACTER.

Specifies the form of the system of equations:

for real flavors:

if trans = 'N': L*X = B (no transpose)

if trans = 'T': L^T*X = B (transpose)

for complex flavors:

if trans = 'N': U*X = B or L*X = B (no transpose)

if trans = 'C': U^H*X = B or L^H*X = B (conjugate transpose).

n

INTEGER. The order of the tridiagonal matrix A. n ≥ 0.

nrhs

INTEGER. The number of right hand sides, that is, the number of columns of the matrix B. nrhs ≥ 0.

d

REAL array, DIMENSION (n). The n diagonal elements of the diagonal matrix D from the factorization computed by ?pttrf.

e

COMPLEX array, DIMENSION(n-1). The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization computed by ?pttrf. See uplo.

b

COMPLEX array, DIMENSION (ldb, nrhs).

On entry, the right hand side matrix B.

ldb

INTEGER.

The leading dimension of the array b.

ldb ≥ max(1, n).

Output Parameters

b

On exit, the solution matrix X.

info

INTEGER.

= 0: successful exit

< 0: if info = -i, the i-th argument had an illegal value.