.TH "TESTING/MATGEN/dlatm6.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
TESTING/MATGEN/dlatm6.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdlatm6\fP (type, n, a, lda, b, x, ldx, y, ldy, alpha, beta, wx, wy, s, dif)"
.br
.RI "\fBDLATM6\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dlatm6 (integer type, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( lda, * ) b, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( ldy, * ) y, integer ldy, double precision alpha, double precision beta, double precision wx, double precision wy, double precision, dimension( * ) s, double precision, dimension( * ) dif)"

.PP
\fBDLATM6\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> DLATM6 generates test matrices for the generalized eigenvalue
!> problem, their corresponding right and left eigenvector matrices,
!> and also reciprocal condition numbers for all eigenvalues and
!> the reciprocal condition numbers of eigenvectors corresponding to
!> the 1th and 5th eigenvalues\&.
!>
!> Test Matrices
!> =============
!>
!> Two kinds of test matrix pairs
!>
!>       (A, B) = inverse(YH) * (Da, Db) * inverse(X)
!>
!> are used in the tests:
!>
!> Type 1:
!>    Da = 1+a   0    0    0    0    Db = 1   0   0   0   0
!>          0   2+a   0    0    0         0   1   0   0   0
!>          0    0   3+a   0    0         0   0   1   0   0
!>          0    0    0   4+a   0         0   0   0   1   0
!>          0    0    0    0   5+a ,      0   0   0   0   1 , and
!>
!> Type 2:
!>    Da =  1   -1    0    0    0    Db = 1   0   0   0   0
!>          1    1    0    0    0         0   1   0   0   0
!>          0    0    1    0    0         0   0   1   0   0
!>          0    0    0   1+a  1+b        0   0   0   1   0
!>          0    0    0  -1-b  1+a ,      0   0   0   0   1 \&.
!>
!> In both cases the same inverse(YH) and inverse(X) are used to compute
!> (A, B), giving the exact eigenvectors to (A,B) as (YH, X):
!>
!> YH:  =  1    0   -y    y   -y    X =  1   0  -x  -x   x
!>         0    1   -y    y   -y         0   1   x  -x  -x
!>         0    0    1    0    0         0   0   1   0   0
!>         0    0    0    1    0         0   0   0   1   0
!>         0    0    0    0    1,        0   0   0   0   1 ,
!>
!> where a, b, x and y will have all values independently of each other\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fITYPE\fP 
.PP
.nf
!>          TYPE is INTEGER
!>          Specifies the problem type (see further details)\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          Size of the matrices A and B\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is DOUBLE PRECISION array, dimension (LDA, N)\&.
!>          On exit A N-by-N is initialized according to TYPE\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of A and of B\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is DOUBLE PRECISION array, dimension (LDA, N)\&.
!>          On exit B N-by-N is initialized according to TYPE\&.
!> 
.fi
.PP
.br
\fIX\fP 
.PP
.nf
!>          X is DOUBLE PRECISION array, dimension (LDX, N)\&.
!>          On exit X is the N-by-N matrix of right eigenvectors\&.
!> 
.fi
.PP
.br
\fILDX\fP 
.PP
.nf
!>          LDX is INTEGER
!>          The leading dimension of X\&.
!> 
.fi
.PP
.br
\fIY\fP 
.PP
.nf
!>          Y is DOUBLE PRECISION array, dimension (LDY, N)\&.
!>          On exit Y is the N-by-N matrix of left eigenvectors\&.
!> 
.fi
.PP
.br
\fILDY\fP 
.PP
.nf
!>          LDY is INTEGER
!>          The leading dimension of Y\&.
!> 
.fi
.PP
.br
\fIALPHA\fP 
.PP
.nf
!>          ALPHA is DOUBLE PRECISION
!> 
.fi
.PP
.br
\fIBETA\fP 
.PP
.nf
!>          BETA is DOUBLE PRECISION
!>
!>          Weighting constants for matrix A\&.
!> 
.fi
.PP
.br
\fIWX\fP 
.PP
.nf
!>          WX is DOUBLE PRECISION
!>          Constant for right eigenvector matrix\&.
!> 
.fi
.PP
.br
\fIWY\fP 
.PP
.nf
!>          WY is DOUBLE PRECISION
!>          Constant for left eigenvector matrix\&.
!> 
.fi
.PP
.br
\fIS\fP 
.PP
.nf
!>          S is DOUBLE PRECISION array, dimension (N)
!>          S(i) is the reciprocal condition number for eigenvalue i\&.
!> 
.fi
.PP
.br
\fIDIF\fP 
.PP
.nf
!>          DIF is DOUBLE PRECISION array, dimension (N)
!>          DIF(i) is the reciprocal condition number for eigenvector i\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB174\fP of file \fBdlatm6\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.