1SSPTRD(1) LAPACK routine (version 3.2) SSPTRD(1)
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6 SSPTRD - reduces a real symmetric matrix A stored in packed form to
7 symmetric tridiagonal form T by an orthogonal similarity transformation
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10 SUBROUTINE SSPTRD( UPLO, N, AP, D, E, TAU, INFO )
11 CHARACTER UPLO
13 INTEGER INFO, N
15 REAL AP( * ), D( * ), E( * ), TAU( * )
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19 SSPTRD reduces a real symmetric matrix A stored in packed form to sym‐
20 metric tridiagonal form T by an orthogonal similarity transformation:
21 Q**T * A * Q = T.
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24 UPLO (input) CHARACTER*1
25 = 'U': Upper triangle of A is stored;
26 = 'L': Lower triangle of A is stored.
27 N (input) INTEGER
29 The order of the matrix A. N >= 0.
30 AP (input/output) REAL array, dimension (N*(N+1)/2)
32 On entry, the upper or lower triangle of the symmetric matrix
33 A, packed columnwise in a linear array. The j-th column of A
34 is stored in the array AP as follows: if UPLO = 'U', AP(i +
35 (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +
36 (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, if UPLO = 'U',
37 the diagonal and first superdiagonal of A are overwritten by
38 the corresponding elements of the tridiagonal matrix T, and the
39 elements above the first superdiagonal, with the array TAU,
40 represent the orthogonal matrix Q as a product of elementary
41 reflectors; if UPLO = 'L', the diagonal and first subdiagonal
42 of A are over- written by the corresponding elements of the
43 tridiagonal matrix T, and the elements below the first subdiag‐
44 onal, with the array TAU, represent the orthogonal matrix Q as
45 a product of elementary reflectors. See Further Details. D
46 (output) REAL array, dimension (N) The diagonal elements of the
47 tridiagonal matrix T: D(i) = A(i,i).
48 E (output) REAL array, dimension (N-1)
50 The off-diagonal elements of the tridiagonal matrix T: E(i) =
51 A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
52 TAU (output) REAL array, dimension (N-1)
54 The scalar factors of the elementary reflectors (see Further
55 Details).
56 INFO (output) INTEGER
58 = 0: successful exit
59 < 0: if INFO = -i, the i-th argument had an illegal value
60
62 If UPLO = 'U', the matrix Q is represented as a product of elementary
63 reflectors
64 Q = H(n-1) . . . H(2) H(1).
65 Each H(i) has the form
66 H(i) = I - tau * v * v'
67 where tau is a real scalar, and v is a real vector with
68 v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP, overwrit‐
69 ing A(1:i-1,i+1), and tau is stored in TAU(i).
70 If UPLO = 'L', the matrix Q is represented as a product of elementary
71 reflectors
72 Q = H(1) H(2) . . . H(n-1).
73 Each H(i) has the form
74 H(i) = I - tau * v * v'
75 where tau is a real scalar, and v is a real vector with
76 v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP, overwrit‐
77 ing A(i+2:n,i), and tau is stored in TAU(i).
78 LAPACK routine (version 3.2) November 2008 SSPTRD(1)