ssbtrd (l) - Linux Manuals

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

NAME

SSBTRD - reduces 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( * )

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
= aqNaq: do not form Q;
= aqVaq: form Q;
= aqUaq: update a matrix X, by forming X*Q.
UPLO (input) CHARACTER*1

= aqUaq: Upper triangle of A is stored;
= aqLaq: 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 = aqUaq, or the number of subdiagonals if UPLO = aqLaq. 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 = aqUaq, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = aqLaq, 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 = aqUaq) or the first subdiagonal (if UPLO = aqLaq) 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 = aqUaq; E(i) = T(i+1,i) if UPLO = aqLaq.
Q (input/output) REAL array, dimension (LDQ,N)
On entry, if VECT = aqUaq, then Q must contain an N-by-N matrix X; if VECT = aqNaq or aqVaq, then Q need not be set. On exit: if VECT = aqVaq, Q contains the N-by-N orthogonal matrix Q; if VECT = aqUaq, Q contains the product X*Q; if VECT = aqNaq, the array Q is not referenced.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= 1, and LDQ >= N if VECT = aqVaq or aqUaq.
WORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

FURTHER DETAILS

Modified by Linda Kaufman, Bell Labs.

Pages related to ssbtrd

  • ssbtrd (3)
  • ssbev (l) - computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
  • ssbevd (l) - computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
  • ssbevx (l) - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
  • ssbgst (l) - reduces a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
  • ssbgv (l) - computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x
  • ssbgvd (l) - computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x
  • ssbgvx (l) - computes selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x