chbtrd-f(3)

chbtrd.f –

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine chbtrd (characterVECT, characterUPLO, integerN, integerKD, complex, dimension( ldab, * )AB, integerLDAB, real, dimension( * )D, real, dimension( * )E, complex, dimension( ldq, * )Q, integerLDQ, complex, dimension( * )WORK, integerINFO)

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:

VECT

 VECT is CHARACTER*1
 = 'N': do not form Q;
 = 'V': form Q;
 = 'U': update a matrix X, by forming X*Q.

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 matrix A. N >= 0.

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

LDAB

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

 D is REAL array, dimension (N)
 The diagonal elements of the tridiagonal matrix T.

 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'.

 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.

LDQ

 LDQ is INTEGER
 The leading dimension of the array Q.
 LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.

WORK

 WORK is COMPLEX 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

Further Details:

 Modified by Linda Kaufman, Bell Labs.

Definition at line 163 of file chbtrd.f.

Author

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