dtrsv (l) - Linux Manuals

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

NAME

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

SYNOPSIS

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

    
INTEGER INCX,LDA,N

    
CHARACTER DIAG,TRANS,UPLO

    
DOUBLE PRECISION A(LDA,*),X(*)

PURPOSE

DTRSV 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION 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.

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 dtrsv

  • dtrsv (3)
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  • dtrsm (l) - solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B,
  • dtrsna (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)
  • dtrsyl (l) - solves the real Sylvester matrix equation
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  • dtrevc (l) - computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T
  • dtrexc (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
  • dtrmm (l) - performs one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ),