sposv (l) - Linux Manuals

sposv: computes the solution to a real system of linear equations A * X = B,

NAME

SPOSV - computes the solution to a real system of linear equations A * X = B,

SYNOPSIS

SUBROUTINE SPOSV(
UPLO, N, NRHS, A, LDA, B, LDB, INFO )

    
CHARACTER UPLO

    
INTEGER INFO, LDA, LDB, N, NRHS

    
REAL A( LDA, * ), B( LDB, * )

PURPOSE

SPOSV computes the solution to a real system of linear equations
A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as

A = U**T* U,  if UPLO = aqUaq, or

A = L * L**T,  if UPLO = aqLaq,
where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

ARGUMENTS

UPLO (input) CHARACTER*1
= aqUaq: Upper triangle of A is stored;
= aqLaq: Lower triangle of A is stored.
N (input) INTEGER
The number of linear equations, i.e., 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.
A (input/output) REAL array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = aqUaq, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = aqLaq, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
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 of A is not positive definite, so the factorization could not be completed, and the solution has not been computed.

Pages related to sposv

  • sposv (3)
  • sposvx (l) - uses the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,
  • sposvxx (l) - SPOSVXX use the Cholesky factorization A = U**T*U or A = L*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 matrix and X and B are N-by-NRHS matrices
  • spocon (l) - estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF
  • spoequ (l) - computes row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm)
  • spoequb (l) - computes row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm)
  • sporfs (l) - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite,
  • sporfsx (l) - SPORFSX improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, and provides error bounds and backward error estimates for the solution
  • spotf2 (l) - computes the Cholesky factorization of a real symmetric positive definite matrix A
  • dsposv (l) - computes the solution to a real system of linear equations A * X = B,