strsv (l) - Linux Manuals

strsv: solves one of the systems of equations A*x = b, or Aaq*x = b,

NAME

STRSV - solves one of the systems of equations A*x = b, or Aaq*x = b,

SYNOPSIS

SUBROUTINE STRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)

    
INTEGER INCX,LDA,N

    
CHARACTER DIAG,TRANS,UPLO

    
REAL A(LDA,*),X(*)

PURPOSE

STRSV 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.

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 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.
A - REAL array of DIMENSION ( LDA, n ).
Before entry with UPLO = aqUaq or aquaq, the leading n by n upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = aqLaq or aqlaq, the leading n by n lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = aqUaq or aquaq, the diagonal elements of A are not referenced either, but are assumed to be unity. Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). Unchanged on exit.
X - REAL 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 strsv

  • strsv (3)
  • strsen (l) - reorders the real Schur factorization of a real matrix A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T,
  • strsm (l) - solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B,
  • strsna (l) - estimates reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q orthogonal)
  • strsyl (l) - solves the real Sylvester matrix equation
  • strcon (l) - estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
  • strevc (l) - computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T
  • strexc (l) - reorders the real Schur factorization of a real matrix A = Q*T*Q**T, so that the diagonal block of T with row index IFST is moved to row ILST
  • strmm (l) - performs one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ),