slags2 (l) - Linux Manuals

slags2: 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

SLAGS2 - 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 SLAGS2(
UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ )

    
LOGICAL UPPER

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

PURPOSE

SLAGS2 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) REAL
A2 (input) REAL A3 (input) REAL On entry, A1, A2 and A3 are elements of the input 2-by-2 upper (lower) triangular matrix A.
B1 (input) REAL
B2 (input) REAL B3 (input) REAL On entry, B1, B2 and B3 are elements of the input 2-by-2 upper (lower) triangular matrix B.
CSU (output) REAL
SNU (output) REAL The desired orthogonal matrix U.
CSV (output) REAL
SNV (output) REAL The desired orthogonal matrix V.
CSQ (output) REAL
SNQ (output) REAL The desired orthogonal matrix Q.

Pages related to slags2

  • slags2 (3)
  • slag2 (l) - computes the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow
  • slag2d (l) - converts a SINGLE PRECISION matrix, SA, to a DOUBLE PRECISION matrix, A
  • slagtf (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,
  • slagtm (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
  • slagts (l) - may be used to solve one of the systems of equations (T - lambda*I)*x = y or (T - lambda*I)aq*x = y,
  • slagv2 (l) - computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular
  • sla_gbamv (l) - performs one of the matrix-vector operations y := alpha*abs(A)*abs(x) + beta*abs(y),