TESTING/EIG/sstt21.f(3)

🌸 NAME 🌸

Bestie, this page is TESTING/EIG/sstt21.f, and it lives in the Library Functions Manual — that's the manual name, iykyk. 💅

✨ SYNOPSIS ✨

Functions/Subroutines 🛠️

subroutine sstt21 (n, kband, ad, ae, sd, se, u, ldu, work, result)
           SSTT21

📚 Function/Subroutine Documentation 📚

subroutine sstt21 (integer n, integer kband, real, dimension( * ) ad, real,
       dimension( * ) ae, real, dimension( * ) sd, real, dimension( * ) se,
       real, dimension( ldu, * ) u, integer ldu, real, dimension( * ) work,
       real, dimension( 2 ) result)
       SSTT21

Purpose 🎯

Ok so SSTT21 checks a decomposition of the form

A = U S U'

where ' means transpose, A is symmetric tridiagonal, U is orthogonal, and S is diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1). Two tests are performed:

RESULT(1) = | A - U S U' | / ( |A| n ulp )

RESULT(2) = | I - UU' | / ( n ulp )

Parameters 🧮

• N — N is INTEGER. The size of the matrix. If it is zero, SSTT21 does nothing. It must be at least zero.
• KBAND — KBAND is INTEGER. The bandwidth of the matrix S. It may only be zero or one. If zero, then S is diagonal, and SE is not referenced. If one, then S is symmetric tri-diagonal.
• AD — AD is REAL array, dimension (N). The diagonal of the original (unfactored) matrix A. A is assumed to be symmetric tridiagonal.
• AE — AE is REAL array, dimension (N-1). The off-diagonal of the original (unfactored) matrix A. A is assumed to be symmetric tridiagonal. AE(1) is the (1,2) and (2,1) element, AE(2) is the (2,3) and (3,2) element, etc.
• SD — SD is REAL array, dimension (N). The diagonal of the (symmetric tri-) diagonal matrix S.
• SE — SE is REAL array, dimension (N-1). The off-diagonal of the (symmetric tri-) diagonal matrix S. Not referenced if KBSND=0. If KBAND=1, then AE(1) is the (1,2) and (2,1) element, SE(2) is the (2,3) and (3,2) element, etc.
• U — U is REAL array, dimension (LDU, N). The orthogonal matrix in the decomposition.
• LDU — LDU is INTEGER. The leading dimension of U. LDU must be at least N.
• WORK — WORK is REAL array, dimension (N*(N+1)).
• RESULT — RESULT is REAL array, dimension (2). The values computed by the two tests described above. The values are currently limited to 1/ulp, to avoid overflow. RESULT(1) is always modified.

Author 🏛️

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 125 of file sstt21.f.

🤖 Author 🤖

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