table of contents
/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/ssptrd.f(3) | Library Functions Manual | /home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/ssptrd.f(3) |
NAME¶
/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/ssptrd.f
SYNOPSIS¶
Functions/Subroutines¶
subroutine SSPTRD (uplo, n, ap, d, e, tau, info)
SSPTRD
Function/Subroutine Documentation¶
subroutine SSPTRD (character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) d, real, dimension( * ) e, real, dimension( * ) tau, integer info)¶
SSPTRD
Purpose:
!> !> SSPTRD reduces a real symmetric matrix A stored in packed form to !> symmetric tridiagonal form T by an orthogonal similarity !> transformation: Q**T * A * Q = T. !>
Parameters
UPLO
!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !>
N
!> N is INTEGER !> The order of the matrix A. N >= 0. !>
AP
!> AP is REAL array, dimension (N*(N+1)/2) !> On entry, the upper or lower triangle of the symmetric matrix !> A, packed columnwise in a linear array. The j-th column of A !> is stored in the array AP as follows: !> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; !> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. !> On exit, if UPLO = 'U', the diagonal and first superdiagonal !> of A are overwritten by the corresponding elements of the !> tridiagonal matrix T, and the elements above the first !> superdiagonal, with the array TAU, represent the orthogonal !> matrix Q as a product of elementary reflectors; if UPLO !> = 'L', the diagonal and first subdiagonal of A are over- !> written by the corresponding elements of the tridiagonal !> matrix T, and the elements below the first subdiagonal, with !> the array TAU, represent the orthogonal matrix Q as a product !> of elementary reflectors. See Further Details. !>
D
!> D is REAL array, dimension (N) !> The diagonal elements of the tridiagonal matrix T: !> D(i) = A(i,i). !>
E
!> E is REAL array, dimension (N-1) !> The off-diagonal elements of the tridiagonal matrix T: !> E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. !>
TAU
!> TAU is REAL array, dimension (N-1) !> The scalar factors of the elementary reflectors (see Further !> Details). !>
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:
!> !> If UPLO = 'U', the matrix Q is represented as a product of elementary !> reflectors !> !> Q = H(n-1) . . . H(2) H(1). !> !> Each H(i) has the form !> !> H(i) = I - tau * v * v**T !> !> where tau is a real scalar, and v is a real vector with !> v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP, !> overwriting A(1:i-1,i+1), and tau is stored in TAU(i). !> !> If UPLO = 'L', the matrix Q is represented as a product of elementary !> reflectors !> !> Q = H(1) H(2) . . . H(n-1). !> !> Each H(i) has the form !> !> H(i) = I - tau * v * v**T !> !> where tau is a real scalar, and v is a real vector with !> v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP, !> overwriting A(i+2:n,i), and tau is stored in TAU(i). !>
Definition at line 149 of file ssptrd.f.
Author¶
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