DSPTRD 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.

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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)


          The diagonal elements of the tridiagonal matrix T:


          D(i) = A(i,i).

E

          E is DOUBLE PRECISION 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 DOUBLE PRECISION 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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2011

  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).