TESTING/EIG/cunt03.f(3)

💅 NAME 💅

TESTING/EIG/cunt03.f — yep, that's the whole name, bestie. This is the TESTING/EIG/cunt03.f(3) page from the Library Functions Manual, and we are about to get into it.

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine cunt03 (rc, mu, mv, n, k, u, ldu, v, ldv, work, lwork, rwork, result, info) — CUNT03

🦋 Function/Subroutine Documentation 🦋

subroutine cunt03 (character*( * ) rc, integer mu, integer mv, integer n,
     integer k, complex, dimension( ldu, * ) u, integer ldu, complex,
     dimension( ldv, * ) v, integer ldv, complex, dimension( * ) work,
     integer lwork, real, dimension( * ) rwork, real result, integer info)

CUNT03

🌸 Parameters 🌸

• RC — RC is CHARACTER*1. If RC = 'R' the rows of U and V are to be compared. If RC = 'C' the columns of U and V are to be compared.
• MU — MU is INTEGER. The number of rows of U if RC = 'R', and the number of columns if RC = 'C'. If MU = 0 CUNT03 does nothing. MU must be at least zero.
• MV — MV is INTEGER. The number of rows of V if RC = 'R', and the number of columns if RC = 'C'. If MV = 0 CUNT03 does nothing. MV must be at least zero.
• N — N is INTEGER. If RC = 'R', the number of columns in the matrices U and V, and if RC = 'C', the number of rows in U and V. If N = 0 CUNT03 does nothing. N must be at least zero.
• K — K is INTEGER. The number of rows or columns of U and V to compare. 0 <= K <= max(MU,MV).
• U — U is COMPLEX array, dimension (LDU,N). The first matrix to compare. If RC = 'R', U is MU by N, and if RC = 'C', U is N by MU.
• LDU — LDU is INTEGER. The leading dimension of U. If RC = 'R', LDU >= max(1,MU), and if RC = 'C', LDU >= max(1,N).
• V — V is COMPLEX array, dimension (LDV,N). The second matrix to compare. If RC = 'R', V is MV by N, and if RC = 'C', V is N by MV.
• LDV — LDV is INTEGER. The leading dimension of V. If RC = 'R', LDV >= max(1,MV), and if RC = 'C', LDV >= max(1,N).
• WORK — WORK is COMPLEX array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The length of the array WORK. For best performance, LWORK should be at least N*N if RC = 'C' or M*M if RC = 'R', but the tests will be done even if LWORK is 0.
• RWORK — RWORK is REAL array, dimension (max(MV,N)).
• RESULT — RESULT is REAL. The value computed by the test described above. RESULT is limited to 1/ulp to avoid overflow.
• INFO — INFO is INTEGER. 0 indicates a successful exit. -k indicates the k-th parameter had an illegal value.

🧚 Purpose 🧚

CUNT03 compares two unitary matrices U and V to see if their corresponding rows or columns span the same spaces. The rows are checked if RC = 'R', and the columns are checked if RC = 'C'.

RESULT is the maximum of

   | V*V' - I | / ( MV ulp ), if RC = 'R', or

   | V'*V - I | / ( MV ulp ), if RC = 'C',

and the maximum over rows (or columns) 1 to K of

   | U(i) - S*V(i) |/ ( N ulp )

where abs(S) = 1 (chosen to minimize the expression), U(i) is the i-th row (column) of U, and V(i) is the i-th row (column) of V.

Bestie, this is the math-y vibe check: it's checking whether the rows or columns line up in the same space, and RESULT tells you how far off they are. Slay. 💅

👑 Author 👑

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

Definition at line 160 of file cunt03.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole iconic page, bestie. It's from LAPACK Version 3.12.0, and the footer energy is literally TESTING/EIG/cunt03.f(3). Mwah 💋✨