TESTING/EIG/dstt22.f(3)

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🌈 TESTING/EIG/dstt22.f(3) 🌈

okay bestie, this is the Library Functions Manual page for TESTING/EIG/dstt22.f, and we are getting into it 💅✨

✨ NAME ✨

TESTING/EIG/dstt22.f

🦋 SYNOPSIS 🦋

Functions/Subroutines

       subroutine dstt22 (n, m, kband, ad, ae, sd, se, u, ldu, work, ldwork,
           result)
           DSTT22

💅 Function/Subroutine Documentation 💅

   subroutine dstt22 (integer n, integer m, integer kband, double precision,
       dimension( * ) ad, double precision, dimension( * ) ae, double
       precision, dimension( * ) sd, double precision, dimension( * ) se,
       double precision, dimension( ldu, * ) u, integer ldu, double precision,
       dimension( ldwork, * ) work, integer ldwork, double precision,
       dimension( 2 ) result)
       DSTT22

🎯 Purpose 🎯

okay so DSTT22 checks a set of M eigenvalues and eigenvectors, like this:

A U = U S

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

  • RESULT(1) = | U' A U - S | / ( |A| m ulp )
  • RESULT(2) = | I - U'U | / ( m ulp )

🧸 Parameters 🧸

N

N is INTEGER — the size of the matrix, bestie. If it is zero, DSTT22 does nothing. It must be at least zero.

M

M is INTEGER — the number of eigenpairs to check. If it is zero, DSTT22 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 is DOUBLE PRECISION array, dimension (N) — the diagonal of the original (unfactored) matrix A. A is assumed to be symmetric tridiagonal.

AE

AE is DOUBLE PRECISION array, dimension (N) — the off-diagonal of the original (unfactored) matrix A. A is assumed to be symmetric tridiagonal. AE(1) is ignored, AE(2) is the (1,2) and (2,1) element, etc.

SD

SD is DOUBLE PRECISION array, dimension (N) — the diagonal of the (symmetric tri-) diagonal matrix S.

SE

SE is DOUBLE PRECISION array, dimension (N) — the off-diagonal of the (symmetric tri-) diagonal matrix S. Not referenced if KBSND=0. If KBAND=1, then AE(1) is ignored, SE(2) is the (1,2) and (2,1) element, etc.

yes bestie, KBSND=0 is literally what it says — we are preserving the original spelling, no cap 🙈

U

U is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDWORK, M+1)

LDWORK

LDWORK is INTEGER — the leading dimension of WORK. LDWORK must be at least max(1,M).

RESULT

RESULT is DOUBLE PRECISION array, dimension (2) — the values computed by the two tests described above. The values are currently limited to 1/ulp, to avoid overflow.

🫶 Author 🫶

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

Definition at line 137 of file dstt22.f.

💜 Author 💜

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