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 * 1 VECT, UPLO
  INTEGER N, KD, LDAB, LDQ, INFO
  REAL AB(LDAB,*), D(*), E(*), Q(LDQ,*), WORK(*)

  SUBROUTINE SSBTRD_64( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, 
 *      WORK, INFO)
  CHARACTER * 1 VECT, UPLO
  INTEGER*8 N, KD, LDAB, LDQ, INFO
  REAL AB(LDAB,*), D(*), E(*), Q(LDQ,*), WORK(*)

F95 INTERFACE

  SUBROUTINE SBTRD( VECT, UPLO, [N], KD, AB, [LDAB], D, E, Q, [LDQ], 
 *       [WORK], [INFO])
  CHARACTER(LEN=1) :: VECT, UPLO
  INTEGER :: N, KD, LDAB, LDQ, INFO
  REAL, DIMENSION(:) :: D, E, WORK
  REAL, DIMENSION(:,:) :: AB, Q

  SUBROUTINE SBTRD_64( VECT, UPLO, [N], KD, AB, [LDAB], D, E, Q, [LDQ], 
 *       [WORK], [INFO])
  CHARACTER(LEN=1) :: VECT, UPLO
  INTEGER(8) :: N, KD, LDAB, LDQ, INFO
  REAL, DIMENSION(:) :: D, E, WORK
  REAL, DIMENSION(:,:) :: AB, Q

C INTERFACE

#include <sunperf.h>

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

void ssbtrd_64(char vect, char uplo, long n, long kd, float *ab, long ldab, float *d, float *e, float *q, long ldq, long *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)

 = 'N':  do not form Q;

 = 'V':  form Q;

 = 'U':  update a matrix X, by forming X*Q.

UPLO (input)

 = 'U':  Upper triangle of A is stored;

 = 'L':  Lower triangle of A is stored.

N (input)
The order of the matrix A. N > = 0.
KD (input)
The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD > = 0.
AB (input/output)
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)
The leading dimension of the array AB. LDAB > = KD+1.
D (output)
The diagonal elements of the tridiagonal matrix T.
E (output)
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)
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)
The leading dimension of the array Q. LDQ > = 1, and LDQ > = N if VECT = 'V' or 'U'.
WORK (workspace)
dimension(N)

INFO (output)

 = 0:  successful exit

 < 0:  if INFO  = -i, the i-th argument had an illegal value

FURTHER DETAILS

Modified by Linda Kaufman, Bell Labs.