TESTING/EIG/sort03.f(3)

✨ NAME ✨

TESTING/EIG/sort03.f — that’s the file, bestie 💅. This page lives in the Library Functions Manual, and it’s all about the SORT03 subroutine.

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🦋 SYNOPSIS 🦋

💖 Functions/Subroutines 💖

   Functions/Subroutines
       subroutine sort03 (rc, mu, mv, n, k, u, ldu, v, ldv, work, lwork,
           result, info)
           SORT03

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💅 Function/Subroutine Documentation 💅

   subroutine sort03 (character*( * ) rc, integer mu, integer mv, integer n,
       integer k, real, dimension( ldu, * ) u, integer ldu, real, dimension(
       ldv, * ) v, integer ldv, real, dimension( * ) work, integer lwork, real
       result, integer info)

SORT03 — yes, that’s the subroutine’s name, and she is the main character here 👑.

🎯 Purpose 🎯

SORT03 compares two orthogonal 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 S is +-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 💖.

📝 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, SORT03 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, SORT03 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, SORT03 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 REAL 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 REAL 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 REAL 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.
• 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.

👑 Author 👑

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

Definition at line 154 of file sort03.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, that’s the whole page 🫶. Source/version vibes: LAPACK, Version 3.12.0, generated automatically by Doxygen for LAPACK from the source code. Byeee ✨💅🎀