ssbtrd()

subroutine ssbtrd	(	character	vect,
		character	uplo,
		integer	n,
		integer	kd,
		real, dimension( ldab, * )	ab,
		integer	ldab,
		real, dimension( * )	d,
		real, dimension( * )	e,
		real, dimension( ldq, * )	q,
		integer	ldq,
		real, dimension( * )	work,
		integer	info )

SSBTRD

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Purpose:

!>
!> SSBTRD reduces a real symmetric band matrix A to symmetric
!> tridiagonal form T by an orthogonal similarity transformation:
!> Q**T * 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 REAL array, dimension (LDAB,N) !> On entry, the upper or lower triangle of the symmetric 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 REAL 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 orthogonal 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 REAL array, dimension (N) !>
[out]	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.

Further Details:

!>
!>  Modified by Linda Kaufman, Bell Labs.
!>