chbgst-f(3)

chbgst.f –

Synopsis

Functions/Subroutines

subroutine chbgst (VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, RWORK, INFO)
CHBGST

Function/Subroutine Documentation

subroutine chbgst (characterVECT, characterUPLO, integerN, integerKA, integerKB, complex, dimension( ldab, * )AB, integerLDAB, complex, dimension( ldbb, * )BB, integerLDBB, complex, dimension( ldx, * )X, integerLDX, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)

CHBGST

Purpose:

 CHBGST reduces a complex Hermitian-definite banded generalized
 eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
 such that C has the same bandwidth as A.
 B must have been previously factorized as S**H*S by CPBSTF, using a
 split Cholesky factorization. A is overwritten by C = X**H*A*X, where
 X = S**(-1)*Q and Q is a unitary matrix chosen to preserve the
 bandwidth of A.

Parameters:

VECT

 VECT is CHARACTER*1
 = 'N': do not form the transformation matrix X;
 = 'V': form X.

UPLO

 UPLO is CHARACTER*1
 = 'U': Upper triangle of A is stored;
 = 'L': Lower triangle of A is stored.

 N is INTEGER
 The order of the matrices A and B. N >= 0.

 KA is INTEGER
 The number of superdiagonals of the matrix A if UPLO = 'U',
 or the number of subdiagonals if UPLO = 'L'. KA >= 0.

 KB is INTEGER
 The number of superdiagonals of the matrix B if UPLO = 'U',
 or the number of subdiagonals if UPLO = 'L'. KA >= KB >= 0.

 AB is COMPLEX array, dimension (LDAB,N)
 On entry, the upper or lower triangle of the Hermitian band
 matrix A, stored in the first ka+1 rows of the array. The
 j-th column of A is stored in the j-th column of the array AB
 as follows:
 if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
 if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
 On exit, the transformed matrix X**H*A*X, stored in the same
 format as A.

LDAB

 LDAB is INTEGER
 The leading dimension of the array AB. LDAB >= KA+1.

 BB is COMPLEX array, dimension (LDBB,N)
 The banded factor S from the split Cholesky factorization of
 B, as returned by CPBSTF, stored in the first kb+1 rows of
 the array.

LDBB

 LDBB is INTEGER
 The leading dimension of the array BB. LDBB >= KB+1.

 X is COMPLEX array, dimension (LDX,N)
 If VECT = 'V', the n-by-n matrix X.
 If VECT = 'N', the array X is not referenced.

LDX

 LDX is INTEGER
 The leading dimension of the array X.
 LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.

WORK

 WORK is COMPLEX array, dimension (N)

RWORK

 RWORK is REAL array, dimension (N)

INFO

 INFO is INTEGER
 = 0: successful exit
 < 0: if INFO = -i, the i-th argument had an illegal value.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 165 of file chbgst.f.

Author

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