Man page - lasq2(3)

Packages contains this manual

Manual

lasq2

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine dlasq2 (integer n, double precision, dimension( * ) z, integerinfo)
subroutine slasq2 (integer n, real, dimension( * ) z, integer info)
Author

NAME

lasq2 - lasq2: dqds step

SYNOPSIS

Functions

subroutine dlasq2 (n, z, info)
DLASQ2 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.
subroutine slasq2 (n, z, info)
SLASQ2 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.

Detailed Description

Function Documentation

subroutine dlasq2 (integer n, double precision, dimension( * ) z, integerinfo)

DLASQ2 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.

Purpose:

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.

Parameters

N

N is INTEGER
The number of rows and columns in the matrix. N >= 0.

Z

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/NINˆ2, and Z( 2*N+5 ) holds the percentage of
shifts that failed.

INFO

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)

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

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).

subroutine slasq2 (integer n, real, dimension( * ) z, integer info)

SLASQ2 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.

Purpose:

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.

Parameters

N

N is INTEGER
The number of rows and columns in the matrix. N >= 0.

Z

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/NINˆ2, and Z( 2*N+5 ) holds the percentage of
shifts that failed.

INFO

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)

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

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).

Author

Generated automatically by Doxygen for LAPACK from the source code.