NAME

ssbtrd - reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation

SYNOPSIS

SUBROUTINE SSBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO )

CHARACTER UPLO, VECT

INTEGER INFO, KD, LDAB, LDQ, N

REAL AB( LDAB, ∗ ), D( ∗ ), E( ∗ ), Q( LDQ, ∗ ), WORK( ∗ )

#include <sunperf.h>

void ssbtrd(char vect, char uplo, int n, int kd, float ∗sab, int ldab, float ∗d, float ∗e, float ∗q, int ldq, int ∗info) ;

PURPOSE

SSBTRD reduces a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation: Q∗∗T ∗ A ∗ Q = T. 
 

ARGUMENTS

VECT (input) CHARACTER∗1
= ’N’:  do not form Q;
= ’V’:  form Q;
= ’U’:  update a matrix X, by forming X∗Q.

UPLO (input) CHARACTER∗1
= ’U’:  Upper triangle of A is stored;
= ’L’:  Lower triangle of A is stored.

N (input) INTEGER
The order of the matrix A.  N >= 0.

KD (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = ’U’, or the number of subdiagonals if UPLO = ’L’.  KD >= 0.

AB (input/output) 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.

LDAB (input) INTEGER
The leading dimension of the array AB.  LDAB >= KD+1.

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

E (output) 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 (input/output) 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.

LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= 1, and LDQ >= N if VECT = ’V’ or ’U’.

WORK (workspace) REAL array, dimension (N)

INFO (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

SunOS WorkShop_5.0  —  Last change: 10 Dec 1998