table of contents
| laed9(3) | LAPACK | laed9(3) |
NAME¶
laed9 - laed9: D&C step: secular equation
SYNOPSIS¶
Functions¶
subroutine dlaed9 (k, kstart, kstop, n, d, q, ldq, rho,
dlambda, w, s, lds, info)
DLAED9 used by DSTEDC. Finds the roots of the secular equation and
updates the eigenvectors. Used when the original matrix is dense. subroutine
slaed9 (k, kstart, kstop, n, d, q, ldq, rho, dlambda, w, s, lds,
info)
SLAED9 used by SSTEDC. Finds the roots of the secular equation and
updates the eigenvectors. Used when the original matrix is dense.
Detailed Description¶
Function Documentation¶
subroutine dlaed9 (integer k, integer kstart, integer kstop, integer n, double precision, dimension( * ) d, double precision, dimension( ldq, * ) q, integer ldq, double precision rho, double precision, dimension( * ) dlambda, double precision, dimension( * ) w, double precision, dimension( lds, * ) s, integer lds, integer info)¶
DLAED9 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.
Purpose:
DLAED9 finds the roots of the secular equation, as defined by the
values in D, Z, and RHO, between KSTART and KSTOP. It makes the
appropriate calls to DLAED4 and then stores the new matrix of
eigenvectors for use in calculating the next level of Z vectors.
Parameters
K is INTEGER
The number of terms in the rational function to be solved by
DLAED4. K >= 0.
KSTART
KSTART is INTEGER
KSTOP
KSTOP is INTEGER
The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP
are to be computed. 1 <= KSTART <= KSTOP <= K.
N
N is INTEGER
The number of rows and columns in the Q matrix.
N >= K (delation may result in N > K).
D
D is DOUBLE PRECISION array, dimension (N)
D(I) contains the updated eigenvalues
for KSTART <= I <= KSTOP.
Q
Q is DOUBLE PRECISION array, dimension (LDQ,N)
LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max( 1, N ).
RHO
RHO is DOUBLE PRECISION
The value of the parameter in the rank one update equation.
RHO >= 0 required.
DLAMBDA
DLAMBDA is DOUBLE PRECISION array, dimension (K)
The first K elements of this array contain the old roots
of the deflated updating problem. These are the poles
of the secular equation.
W
W is DOUBLE PRECISION array, dimension (K)
The first K elements of this array contain the components
of the deflation-adjusted updating vector.
S
S is DOUBLE PRECISION array, dimension (LDS, K)
Will contain the eigenvectors of the repaired matrix which
will be stored for subsequent Z vector calculation and
multiplied by the previously accumulated eigenvectors
to update the system.
LDS
LDS is INTEGER
The leading dimension of S. LDS >= max( 1, K ).
INFO
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = 1, an eigenvalue did not converge
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
subroutine slaed9 (integer k, integer kstart, integer kstop, integer n, real, dimension( * ) d, real, dimension( ldq, * ) q, integer ldq, real rho, real, dimension( * ) dlambda, real, dimension( * ) w, real, dimension( lds, * ) s, integer lds, integer info)¶
SLAED9 used by SSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.
Purpose:
SLAED9 finds the roots of the secular equation, as defined by the
values in D, Z, and RHO, between KSTART and KSTOP. It makes the
appropriate calls to SLAED4 and then stores the new matrix of
eigenvectors for use in calculating the next level of Z vectors.
Parameters
K is INTEGER
The number of terms in the rational function to be solved by
SLAED4. K >= 0.
KSTART
KSTART is INTEGER
KSTOP
KSTOP is INTEGER
The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP
are to be computed. 1 <= KSTART <= KSTOP <= K.
N
N is INTEGER
The number of rows and columns in the Q matrix.
N >= K (delation may result in N > K).
D
D is REAL array, dimension (N)
D(I) contains the updated eigenvalues
for KSTART <= I <= KSTOP.
Q
Q is REAL array, dimension (LDQ,N)
LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max( 1, N ).
RHO
RHO is REAL
The value of the parameter in the rank one update equation.
RHO >= 0 required.
DLAMBDA
DLAMBDA is REAL array, dimension (K)
The first K elements of this array contain the old roots
of the deflated updating problem. These are the poles
of the secular equation.
W
W is REAL array, dimension (K)
The first K elements of this array contain the components
of the deflation-adjusted updating vector.
S
S is REAL array, dimension (LDS, K)
Will contain the eigenvectors of the repaired matrix which
will be stored for subsequent Z vector calculation and
multiplied by the previously accumulated eigenvectors
to update the system.
LDS
LDS is INTEGER
The leading dimension of S. LDS >= max( 1, K ).
INFO
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = 1, an eigenvalue did not converge
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Author¶
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