TESTING/EIG/cstt22.f(3)

💅 TESTING/EIG/cstt22.f 💅

okay bestie, welcome to the TESTING/EIG/cstt22.f(3) page from the Library Functions Manual — this is the little test routine that checks a Hermitian tridiagonal eigen-decomposition, and we are obsessed with the details ✨💖

🌸 NAME 🌸

TESTING/EIG/cstt22.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

       subroutine cstt22 (n, m, kband, ad, ae, sd, se, u, ldu, work, ldwork,
           rwork, result)
           CSTT22

💖 Function/Subroutine Documentation 💖

🫶 subroutine cstt22 🫶

       subroutine cstt22 (integer n, integer m, integer kband, real, dimension( * )
           ad, real, dimension( * ) ae, real, dimension( * ) sd, real, dimension( *
           ) se, complex, dimension( ldu, * ) u, integer ldu, complex, dimension(
           ldwork, * ) work, integer ldwork, real, dimension( * ) rwork, real,
           dimension( 2 ) result)

CSTT22

🎀 Purpose 🎀

CSTT22 checks a set of M eigenvalues and eigenvectors, like this:

A U = U S

where A is Hermitian tridiagonal, the columns of U are unitary, and S is diagonal (if KBAND=0) or Hermitian 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. It's the size of the matrix. If it is zero, CSTT22 does nothing. It must be at least zero.
• M — M is INTEGER. The number of eigenpairs to check. If it is zero, CSTT22 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 Hermitian tri-diagonal.
• AD — AD is REAL array, dimension (N). The diagonal of the original (unfactored) matrix A. A is assumed to be Hermitian tridiagonal.
• AE — AE is REAL array, dimension (N). The off-diagonal of the original (unfactored) matrix A. A is assumed to be Hermitian tridiagonal. AE(1) is ignored, AE(2) is the (1,2) and (2,1) element, etc.
• SD — SD is REAL array, dimension (N). The diagonal of the (Hermitian tri-) diagonal matrix S.
• SE — SE is REAL array, dimension (N). The off-diagonal of the (Hermitian 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.
• U — U is REAL 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 (LDWORK, M+1).
• LDWORK — LDWORK is INTEGER. The leading dimension of WORK. LDWORK must be at least max(1,M).
• 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.

👑 Author 👑

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

Definition at line 143 of file cstt22.f.

🪄 Author 🪄

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 this page is LAPACK Version 3.12.0 for TESTING/EIG/cstt22.f(3), and the footer doesn't list a date — so no fake date from me, bestie 🫶✨