sptsv (l) - Linux Manuals

sptsv: computes the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices

NAME

SPTSV - computes the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices

SYNOPSIS

SUBROUTINE SPTSV(
N, NRHS, D, E, B, LDB, INFO )

    
INTEGER INFO, LDB, N, NRHS

    
REAL B( LDB, * ), D( * ), E( * )

PURPOSE

SPTSV computes the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices. A is factored as A = L*D*L**T, and the factored form of A is then used to solve the system of equations.

ARGUMENTS

N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
D (input/output) REAL array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix A. On exit, the n diagonal elements of the diagonal matrix D from the factorization A = L*D*L**T.
E (input/output) REAL array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A. On exit, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**T factorization of A. (E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U**T*D*U factorization of A.)
B (input/output) REAL array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not positive definite, and the solution has not been computed. The factorization has not been completed unless i = N.

Pages related to sptsv

  • sptsv (3)
  • sptsvx (l) - uses the factorization A = L*D*L**T to compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix and X and B are N-by-NRHS matrices
  • sptcon (l) - computes the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by SPTTRF
  • spteqr (l) - computes all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF, and then calling SBDSQR to compute the singular values of the bidiagonal factor
  • sptrfs (l) - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
  • spttrf (l) - computes the L*D*Laq factorization of a real symmetric positive definite tridiagonal matrix A
  • spttrs (l) - solves a tridiagonal system of the form A * X = B using the L*D*Laq factorization of A computed by SPTTRF
  • sptts2 (l) - solves a tridiagonal system of the form A * X = B using the L*D*Laq factorization of A computed by SPTTRF
  • spbcon (l) - estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF