.TH "lasq2" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lasq2 \- lasq2: dqds step
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBdlasq2\fP (n, z, info)"
.br
.RI "\fBDLASQ2\fP computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high relative accuracy\&. Used by sbdsqr and sstegr\&. "
.ti -1c
.RI "subroutine \fBslasq2\fP (n, z, info)"
.br
.RI "\fBSLASQ2\fP computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high relative accuracy\&. Used by sbdsqr and sstegr\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine dlasq2 (integer n, double precision, dimension( * ) z, integer info)"

.PP
\fBDLASQ2\fP computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high relative accuracy\&. Used by sbdsqr and sstegr\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> DLASQ2 computes all the eigenvalues of the symmetric positive
!> definite tridiagonal matrix associated with the qd array Z to high
!> relative accuracy are computed to high relative accuracy, in the
!> absence of denormalization, underflow and overflow\&.
!>
!> To see the relation of Z to the tridiagonal matrix, let L be a
!> unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,\&.\&.) and
!> let U be an upper bidiagonal matrix with 1's above and diagonal
!> Z(1,3,5,,\&.\&.)\&. The tridiagonal is L*U or, if you prefer, the
!> symmetric tridiagonal to which it is similar\&.
!>
!> Note : DLASQ2 defines a logical variable, IEEE, which is true
!> on machines which follow ieee-754 floating-point standard in their
!> handling of infinities and NaNs, and false otherwise\&. This variable
!> is passed to DLASQ3\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>        The number of rows and columns in the matrix\&. N >= 0\&.
!> 
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
!>          Z is DOUBLE PRECISION array, dimension ( 4*N )
!>        On entry Z holds the qd array\&. On exit, entries 1 to N hold
!>        the eigenvalues in decreasing order, Z( 2*N+1 ) holds the
!>        trace, and Z( 2*N+2 ) holds the sum of the eigenvalues\&. If
!>        N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 )
!>        holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of
!>        shifts that failed\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>        = 0: successful exit
!>        < 0: if the i-th argument is a scalar and had an illegal
!>             value, then INFO = -i, if the i-th argument is an
!>             array and the j-entry had an illegal value, then
!>             INFO = -(i*100+j)
!>        > 0: the algorithm failed
!>              = 1, a split was marked by a positive value in E
!>              = 2, current block of Z not diagonalized after 100*N
!>                   iterations (in inner while loop)\&.  On exit Z holds
!>                   a qd array with the same eigenvalues as the given Z\&.
!>              = 3, termination criterion of outer while loop not met
!>                   (program created more than N unreduced blocks)
!> 
.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
\fBFurther Details:\fP
.RS 4

.PP
.nf
!>
!>  Local Variables: I0:N0 defines a current unreduced segment of Z\&.
!>  The shifts are accumulated in SIGMA\&. Iteration count is in ITER\&.
!>  Ping-pong is controlled by PP (alternates between 0 and 1)\&.
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB111\fP of file \fBdlasq2\&.f\fP\&.
.SS "subroutine slasq2 (integer n, real, dimension( * ) z, integer info)"

.PP
\fBSLASQ2\fP computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high relative accuracy\&. Used by sbdsqr and sstegr\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SLASQ2 computes all the eigenvalues of the symmetric positive
!> definite tridiagonal matrix associated with the qd array Z to high
!> relative accuracy are computed to high relative accuracy, in the
!> absence of denormalization, underflow and overflow\&.
!>
!> To see the relation of Z to the tridiagonal matrix, let L be a
!> unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,\&.\&.) and
!> let U be an upper bidiagonal matrix with 1's above and diagonal
!> Z(1,3,5,,\&.\&.)\&. The tridiagonal is L*U or, if you prefer, the
!> symmetric tridiagonal to which it is similar\&.
!>
!> Note : SLASQ2 defines a logical variable, IEEE, which is true
!> on machines which follow ieee-754 floating-point standard in their
!> handling of infinities and NaNs, and false otherwise\&. This variable
!> is passed to SLASQ3\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>        The number of rows and columns in the matrix\&. N >= 0\&.
!> 
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
!>          Z is REAL array, dimension ( 4*N )
!>        On entry Z holds the qd array\&. On exit, entries 1 to N hold
!>        the eigenvalues in decreasing order, Z( 2*N+1 ) holds the
!>        trace, and Z( 2*N+2 ) holds the sum of the eigenvalues\&. If
!>        N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 )
!>        holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of
!>        shifts that failed\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>        = 0: successful exit
!>        < 0: if the i-th argument is a scalar and had an illegal
!>             value, then INFO = -i, if the i-th argument is an
!>             array and the j-entry had an illegal value, then
!>             INFO = -(i*100+j)
!>        > 0: the algorithm failed
!>              = 1, a split was marked by a positive value in E
!>              = 2, current block of Z not diagonalized after 100*N
!>                   iterations (in inner while loop)\&.  On exit Z holds
!>                   a qd array with the same eigenvalues as the given Z\&.
!>              = 3, termination criterion of outer while loop not met
!>                   (program created more than N unreduced blocks)
!> 
.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
\fBFurther Details:\fP
.RS 4

.PP
.nf
!>
!>  Local Variables: I0:N0 defines a current unreduced segment of Z\&.
!>  The shifts are accumulated in SIGMA\&. Iteration count is in ITER\&.
!>  Ping-pong is controlled by PP (alternates between 0 and 1)\&.
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB111\fP of file \fBslasq2\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.