dlags2 (l) - Linux Manuals

dlags2: computes 2-by-2 orthogonal matrices U, V and Q, such that if ( UPPER ) then Uaq*A*Q = Uaq*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and Vaq*B*Q = Vaq*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then Uaq*A*Q = Uaq*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and Vaq*B*Q = Vaq*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) The rows of the transformed A and B are parallel, where U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) ( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ ) Zaq denotes the transpose of Z

NAME

DLAGS2 - computes 2-by-2 orthogonal matrices U, V and Q, such that if ( UPPER ) then Uaq*A*Q = Uaq*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and Vaq*B*Q = Vaq*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then Uaq*A*Q = Uaq*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and Vaq*B*Q = Vaq*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) The rows of the transformed A and B are parallel, where U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) ( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ ) Zaq denotes the transpose of Z

SYNOPSIS

SUBROUTINE DLAGS2(
UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ )

    
LOGICAL UPPER

    
DOUBLE PRECISION A1, A2, A3, B1, B2, B3, CSQ, CSU, CSV, SNQ, SNU, SNV

PURPOSE

DLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such that if ( UPPER ) then

ARGUMENTS

UPPER (input) LOGICAL
= .TRUE.: the input matrices A and B are upper triangular.
= .FALSE.: the input matrices A and B are lower triangular.
A1 (input) DOUBLE PRECISION
A2 (input) DOUBLE PRECISION A3 (input) DOUBLE PRECISION On entry, A1, A2 and A3 are elements of the input 2-by-2 upper (lower) triangular matrix A.
B1 (input) DOUBLE PRECISION
B2 (input) DOUBLE PRECISION B3 (input) DOUBLE PRECISION On entry, B1, B2 and B3 are elements of the input 2-by-2 upper (lower) triangular matrix B.
CSU (output) DOUBLE PRECISION
SNU (output) DOUBLE PRECISION The desired orthogonal matrix U.
CSV (output) DOUBLE PRECISION
SNV (output) DOUBLE PRECISION The desired orthogonal matrix V.
CSQ (output) DOUBLE PRECISION
SNQ (output) DOUBLE PRECISION The desired orthogonal matrix Q.

Pages related to dlags2

  • dlags2 (3)
  • dlag2 (l) - computes the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow
  • dlag2s (l) - converts a DOUBLE PRECISION matrix, SA, to a SINGLE PRECISION matrix, A
  • dlagtf (l) - factorizes the matrix (T - lambda*I), where T is an n by n tridiagonal matrix and lambda is a scalar, as T - lambda*I = PLU,
  • dlagtm (l) - performs a matrix-vector product of the form B := alpha * A * X + beta * B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1
  • dlagts (l) - may be used to solve one of the systems of equations (T - lambda*I)*x = y or (T - lambda*I)aq*x = y,
  • dlagv2 (l) - computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular
  • dla_gbamv (l) - performs one of the matrix-vector operations y := alpha*abs(A)*abs(x) + beta*abs(y),