 LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
chbtrd.f File Reference

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Functions/Subroutines

subroutine chbtrd (VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
CHBTRD

Function/Subroutine Documentation

 subroutine chbtrd ( character VECT, character UPLO, integer N, integer KD, complex, dimension( ldab, * ) AB, integer LDAB, real, dimension( * ) D, real, dimension( * ) E, complex, dimension( ldq, * ) Q, integer LDQ, complex, dimension( * ) WORK, integer INFO )

CHBTRD

Purpose:
CHBTRD reduces a complex Hermitian band matrix A to real symmetric
tridiagonal form T by a unitary similarity transformation:
Q**H * A * Q = T.
Parameters:
 [in] VECT VECT is CHARACTER*1 = 'N': do not form Q; = 'V': form Q; = 'U': update a matrix X, by forming X*Q. [in] UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. [in] N N is INTEGER The order of the matrix A. N >= 0. [in] KD KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. [in,out] AB AB is COMPLEX array, dimension (LDAB,N) On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). On exit, the diagonal elements of AB are overwritten by the diagonal elements of the tridiagonal matrix T; if KD > 0, the elements on the first superdiagonal (if UPLO = 'U') or the first subdiagonal (if UPLO = 'L') are overwritten by the off-diagonal elements of T; the rest of AB is overwritten by values generated during the reduction. [in] LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1. [out] D D is REAL array, dimension (N) The diagonal elements of the tridiagonal matrix T. [out] E E is REAL array, dimension (N-1) The off-diagonal elements of the tridiagonal matrix T: E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'. [in,out] Q Q is COMPLEX array, dimension (LDQ,N) On entry, if VECT = 'U', then Q must contain an N-by-N matrix X; if VECT = 'N' or 'V', then Q need not be set. On exit: if VECT = 'V', Q contains the N-by-N unitary matrix Q; if VECT = 'U', Q contains the product X*Q; if VECT = 'N', the array Q is not referenced. [in] LDQ LDQ is INTEGER The leading dimension of the array Q. LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'. [out] WORK WORK is COMPLEX array, dimension (N) [out] INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Date:
November 2011
Further Details:
Modified by Linda Kaufman, Bell Labs.

Definition at line 163 of file chbtrd.f.

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