p?hengst
p?hengst
Reduces a complex Hermitian-definite generalized eigenproblem to standard form.
Syntax
void pchengst
(
const
MKL_INT*
ibtype
,
const
char*
uplo
,
const
MKL_INT*
n
,
MKL_Complex8*
a
,
const
MKL_INT*
ia
,
const
MKL_INT*
ja
,
const
MKL_INT*
desca
,
const
MKL_Complex8*
b
,
const
MKL_INT*
ib
,
const
MKL_INT*
jb
,
const
MKL_INT*
descb
,
float*
scale
,
MKL_Complex8*
work
,
const
MKL_INT*
lwork
,
MKL_INT*
info
);
void pzhengst
(
const
MKL_INT*
ibtype
,
const
char*
uplo
,
const
MKL_INT*
n
,
MKL_Complex16*
a
,
const
MKL_INT*
ia
,
const
MKL_INT*
ja
,
const
MKL_INT*
desca
,
const
MKL_Complex16*
b
,
const
MKL_INT*
ib
,
const
MKL_INT*
jb
,
const
MKL_INT*
descb
,
double*
scale
,
MKL_Complex16*
work
,
const
MKL_INT*
lwork
,
MKL_INT*
info
);
Include Files
- mkl_scalapack.h
Description
p?hengst
reduces a complex Hermitian-definite generalized eigenproblem to standard form.p?hengst
performs the same function as p?hegst
, but is based on rank 2K updates, which are faster and more scalable than triangular solves (the basis of p?hengst
).p?hengst
calls p?hegst
when uplo
='U', hence p?hengst
provides improved performance only when uplo
='L' and ibtype
=1.p?hengst
also calls p?hegst
when insufficient workspace is provided, hence p?hengst
provides improved performance only when lwork
is sufficient (as described in the parameter descriptions).In the following sub(
A
) denotes the submatrix A
( ia
:ia
+n
-1, ja
:ja
+n
-1 ) and sub( B
) denotes the submatrix B
( ib
:ib
+n
-1, jb
:jb
+n
-1 ).If )*sub( )
ibtype
= 1, the problem is sub( A
)*x = lambda*sub( B
)*x, and sub( A
) is overwritten by inv(U
H
A
)*inv(U
) or inv(L
)*sub( A
)*inv(L
H
If or *sub(
ibtype
= 2 or 3, the problem is sub( A
)*sub( B
)*x = lambda*x or sub( B
)*sub( A
)*x = lambda*x, and sub( A
) is overwritten by U
*sub( A
)*U
H
L
H
A
)*L
.sub( * by
B
) must have been previously factorized as U
H
U
or L
*L
H
p?potrf
.Input Parameters
- ibtype
- (global)= 1: compute inv(U)*sub(HA)*inv(U) or inv(L)*sub(A)*inv(L);H= 2 or 3: computeU*sub(A)*UorHL*sub(HA)*L.
- uplo
- (global)= 'U': Upper triangle of sub(A) is stored and sub(B) is factored asU*HU;= 'L': Lower triangle of sub(A) is stored and sub(B) is factored asL*L.H
- n
- (global)The order of the matrices sub(A) and sub(B).n>= 0.
- a
- (local)Pointer into the local memory to an array of size.lld_a*LOCc(ja+n-1)On entry, this array contains the local pieces of then-by-nHermitian distributed matrix sub(A). Ifuplo= 'U', the leadingn-by-nupper triangular part of sub(A) contains the upper triangular part of the matrix, and its strictly lower triangular part is not referenced. Ifuplo= 'L', the leadingn-by-nlower triangular part of sub(A) contains the lower triangular part of the matrix, and its strictly upper triangular part is not referenced.
- ia
- (global)Global row index of matrixA, which points to the beginning of the submatrix on which to operate.
- ja
- (global)Global column index of matrixA, which points to the beginning of the submatrix on which to operate.
- desca
- (global and local)Array of sizedlen_.The array descriptor for the distributed matrixA.
- b
- (local)Pointer into the local memory to an array of size.lld_b*LOCc(jb+n-1)
- ib
- (global)Global row index of matrixB, which points to the beginning of the submatrix on which to operate.
- jb
- (global)Global column index of matrixB, which points to the beginning of the submatrix on which to operate.
- descb
- (global and local)Array of sizedlen_.The array descriptor for the distributed matrixB.
- work
- (local)Array, size (lwork)On exit,work( 1 ) returns the minimal and optimallwork.
- lwork
- (local)The size of the arraywork.lworkis local input and must be at least.lwork>= MAX( NB * ( NP0 +1 ), 3 * NB )Whenibtype= 1 anduplo= 'L',p?hengstprovides improved performance whenlwork>= 2 *NP0*NB+NQ0*NB+NB*NB, whereNB=mb_a=nb_a,NP0=numroc(n,NB, 0, 0,NPROW),NQ0=numroc(n,NB, 0, 0,NPROW), andnumrocis a ScaLAPACK tool function.MYROW,MYCOL,NPROWandNPCOLcan be determined by calling the subroutineblacs_gridinfo.Iflwork= -1, thenlworkis global input and a workspace query is assumed; the routine only calculates the optimal size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message is issued bypxerbla.
Output Parameters
- a
- On exit, ifinfo= 0, the transformed matrix, stored in the same format as sub(A).
- scale
- (global)Amount by which the eigenvalues should be scaled to compensate for the scaling performed in this routine.scaleis always returned as 1.0.
- work
- On exit,work[0]returns the minimal and optimallwork.
- info
- (global)= 0: successful exit< 0: If thei-th argument is an array and thej-entry had an illegal value, theninfo= -(i*100+j), if thei-th argument is a scalar and had an illegal value, theninfo= -i.