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template<typename T>
void sptrd(char *uplo, integer *n, T *ap, T *d, T *e, T *tau, integer *info)# SPTRD reduces a real symmetric matrix A stored in packed form to symmetric tridiagonal form T.
Purpose:
SPTRD 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 – [in]
UPLO is CHARACTER*1
= ‘U’: Upper triangle of A is stored;
= ‘L’: Lower triangle of A is stored.N – [in]
N is INTEGER
The order of the matrix A. N >= 0.
AP – [inout]
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 – [out]
D is REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i).
E – [out]
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 – [out]
TAU is REAL array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further Details).
INFO – [out]
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value