SRC/ssytd2.f(3)

🎀 SRC/ssytd2.f(3) 🎀

hey bestie!! welcome to the Library Functions Manual page for SRC/ssytd2.f(3) — we're about to make a symmetric matrix tridiagonal and look cute doing it 💅✨

✨ NAME ✨

SRC/ssytd2.f — bestie, this is the manual page for the ssytd2 subroutine, and it's literally the unblocked glow-up that takes a real symmetric matrix to symmetric tridiagonal form. 🦋

🌸 SYNOPSIS 🌸

✨ Functions/Subroutines ✨

• subroutine ssytd2 (uplo, n, a, lda, d, e, tau, info) — SSYTD2 reduces a symmetric matrix to real symmetric tridiagonal form by an orthogonal similarity transformation (unblocked algorithm). 💅

💖 Function/Subroutine Documentation 💖

🦋 subroutine ssytd2 🦋

subroutine ssytd2 (character uplo, integer n, real, dimension( lda, * ) a,
    integer lda, real, dimension( * ) d, real, dimension( * ) e, real,
    dimension( * ) tau, integer info)

SSYTD2 reduces a symmetric matrix to real symmetric tridiagonal form by an orthogonal similarity transformation (unblocked algorithm). ✨

🌟 Purpose 🌟

okay so the purpose is literally this, no cap:

SSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation: Q**T * A * Q = T. 🔥

🦋 Parameters 🦋

• UPLO — UPLO is CHARACTER*1. It specifies whether the upper or lower triangular part of the symmetric matrix A is stored:
  • = 'U': Upper triangular 🦋
  • = 'L': Lower triangular 🦋
• N — N is INTEGER. The order of the matrix A. N >= 0. 💜
• A — A is REAL array, dimension (LDA,N). On entry, the symmetric matrix A. If UPLO = 'U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. 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 overwritten 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. 🌈
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). ✨
• 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 👑

these absolute icons, fr fr:

• 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 A(1:i-1,i+1), and tau 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 A(i+2:n,i), and tau in TAU(i).

The contents of A on exit are illustrated by the following examples with n = 5:

if UPLO = 'U':                       if UPLO = 'L':

  (  d   e   v2  v3  v4 )              (  d                  )
  (      d   e   v3  v4 )              (  e   d              )
  (          d   e   v4 )              (  v1  e   d          )
  (              d   e  )              (  v1  v2  e   d      )
  (                  d  )              (  v1  v2  v3  e   d  )

where d and e denote diagonal and off-diagonal elements of T, and vi denotes an element of the vector defining H(i).

📌 Definition at line 172 of file ssytd2.f. 📌

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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