TESTING/EIG/cstt21.f(3)

TESTING/EIG/cstt21.f(3) 💅

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NAME 💖

TESTING/EIG/cstt21.f

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine cstt21 (n, kband, ad, ae, sd, se, u, ldu, work, rwork,
    result)

CSTT21

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💫 Function/Subroutine Documentation 💫

🌟 subroutine signature

   subroutine cstt21 (integer n, integer kband, real, dimension( * ) ad, real,
       dimension( * ) ae, real, dimension( * ) sd, real, dimension( * ) se,
       complex, dimension( ldu, * ) u, integer ldu, complex, dimension( * )
       work, real, dimension( * ) rwork, real, dimension( 2 ) result)

CSTT21

🎯 Purpose

okay so CSTT21 checks a decomposition of the form

A = U S U**H

where **H means conjugate transpose, A is real symmetric tridiagonal, U is unitary, and S is real and diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1). Two tests are performed:

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

RESULT(2) = | I - U U**H | / ( n ulp )

🧾 Parameters

• N — N is INTEGER. The size of the matrix. If it is zero, CSTT21 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 real 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 real (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 COMPLEX array, dimension (LDU, N). The unitary matrix in the decomposition.
• LDU — LDU is INTEGER. The leading dimension of U. LDU must be at least N.
• WORK — WORK is COMPLEX array, dimension (N**2).
• RWORK — RWORK is REAL array, dimension (N).
• 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

Definition at line 131 of file cstt21.f.

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🫶 Author

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