CCSDTS(3)

📦 version 3.12.0, in opensuse-leap 16.0

🦋 CCSDTS(3) — Library Functions Manual 🦋

hey bestie, welcome to the glow-up of /home/abui...IG/ccsdts.f(3). this is the Library Functions Manual page for CCSDTS, and we’re gonna read it like a group chat. no cap, all the details stay. 💅

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/ccsdts.f

✨ SYNOPSIS ✨

Functions/Subroutines

       subroutine CCSDTS (m, p, q, x, xf, ldx, u1, ldu1, u2, ldu2, v1t, ldv1t,
           v2t, ldv2t, theta, iwork, work, lwork, rwork, result)
           CCSDTS

💅 Function/Subroutine Documentation 💅

       subroutine CCSDTS (integer m, integer p, integer q, complex, dimension( ldx,
           * ) x, complex, dimension( ldx, * ) xf, integer ldx, complex, dimension(
           ldu1, * ) u1, integer ldu1, complex, dimension( ldu2, * ) u2, integer
           ldu2, complex, dimension( ldv1t, * ) v1t, integer ldv1t, complex,
           dimension( ldv2t, * ) v2t, integer ldv2t, real, dimension( * ) theta,
           integer, dimension( * ) iwork, complex, dimension( lwork ) work, integer
           lwork, real, dimension( * ) rwork, real, dimension( 15 ) result)
       CCSDTS

✨ Purpose ✨

okay so CCSDTS is literally the test bestie for CUNCSD 🫶. given an M-by-M partitioned unitary matrix X, it computes the CSD. the diagrams are staying exactly as they are — math is math, bestie 💖.

CCSDTS tests CUNCSD, which, given an M-by-M partitioned unitary
matrix X,
             Q  M-Q
      X = [ X11 X12 ] P   ,
          [ X21 X22 ] M-P

computes the CSD

      [ U1    ]**T * [ X11 X12 ] * [ V1    ]
      [    U2 ]      [ X21 X22 ]   [    V2 ]

                            [  I  0  0 |  0  0  0 ]
                            [  0  C  0 |  0 -S  0 ]
                            [  0  0  0 |  0  0 -I ]
                          = [---------------------] = [ D11 D12 ] .
                            [  0  0  0 |  I  0  0 ]   [ D21 D22 ]
                            [  0  S  0 |  0  C  0 ]
                            [  0  0  I |  0  0  0 ]

and it also tests SORCSD2BY1, which, given:

         Q
      [ X11 ] P   ,
      [ X21 ] M-P

computes the 2-by-1 CSD:

                                    [  I  0  0 ]
                                    [  0  C  0 ]
                                    [  0  0  0 ]
      [ U1    ]**T * [ X11 ] * V1 = [----------] = [ D11 ] ,
      [    U2 ]      [ X21 ]        [  0  0  0 ]   [ D21 ]
                                    [  0  S  0 ]
                                    [  0  0  I ]

🍓 Parameters 🍓

  • M — INTEGER. the number of rows of the matrix X. M >= 0. 💖
  • P — INTEGER. the number of rows of the matrix X11. P >= 0. ✨
  • Q — INTEGER. the number of columns of the matrix X11. Q >= 0. 🎀
  • X — COMPLEX array, dimension (LDX,M). the M-by-M matrix X. 🦋
  • XF — COMPLEX array, dimension (LDX,M). details of the CSD of X, as returned by CUNCSD; see CUNCSD for further details. 🌸
  • LDX — INTEGER. the leading dimension of the arrays X and XF. LDX >= max( 1,M ). 💅
  • U1 — COMPLEX array, dimension(LDU1,P). the P-by-P unitary matrix U1. 🫶
  • LDU1 — INTEGER. the leading dimension of the array U1. LDU >= max(1,P). 😭
  • U2 — COMPLEX array, dimension(LDU2,M-P). the (M-P)-by-(M-P) unitary matrix U2. 🔥
  • LDU2 — INTEGER. the leading dimension of the array U2. LDU >= max(1,M-P). 👑
  • V1T — COMPLEX array, dimension(LDV1T,Q). the Q-by-Q unitary matrix V1T. 🌈
  • LDV1T — INTEGER. the leading dimension of the array V1T. LDV1T >= max(1,Q). ⭐
  • V2T — COMPLEX array, dimension(LDV2T,M-Q). the (M-Q)-by-(M-Q) unitary matrix V2T. 💀
  • LDV2T — INTEGER. the leading dimension of the array V2T. LDV2T >= max(1,M-Q). 🙈
  • THETA — REAL array, dimension MIN(P,M-P,Q,M-Q). the CS values of X; the essentially diagonal matrices C and S are constructed from THETA; see subroutine CUNCSD for details. 🍓
  • IWORK — INTEGER array, dimension (M). 🧚
  • WORK — COMPLEX array, dimension (LWORK). 💜
  • LWORK — INTEGER. the dimension of the array WORK. 💖
  • RWORK — REAL array. ✨
  • RESULT — REAL array, dimension (15). The test ratios:

First, the 2-by-2 CSD:

RESULT(1) = norm( U1'*X11*V1 - D11 ) / ( MAX(1,P,Q)*EPS2 )
RESULT(2) = norm( U1'*X12*V2 - D12 ) / ( MAX(1,P,M-Q)*EPS2 )
RESULT(3) = norm( U2'*X21*V1 - D21 ) / ( MAX(1,M-P,Q)*EPS2 )
RESULT(4) = norm( U2'*X22*V2 - D22 ) / ( MAX(1,M-P,M-Q)*EPS2 )
RESULT(5) = norm( I - U1'*U1 ) / ( MAX(1,P)*ULP )
RESULT(6) = norm( I - U2'*U2 ) / ( MAX(1,M-P)*ULP )
RESULT(7) = norm( I - V1T'*V1T ) / ( MAX(1,Q)*ULP )
RESULT(8) = norm( I - V2T'*V2T ) / ( MAX(1,M-Q)*ULP )
RESULT(9) = 0        if THETA is in increasing order and
                     all angles are in [0,pi/2]

                   = ULPINV   otherwise.

Then, the 2-by-1 CSD:

RESULT(10) = norm( U1'*X11*V1 - D11 ) / ( MAX(1,P,Q)*EPS2 )
RESULT(11) = norm( U2'*X21*V1 - D21 ) / ( MAX(1,M-P,Q)*EPS2 )
RESULT(12) = norm( I - U1'*U1 ) / ( MAX(1,P)*ULP )
RESULT(13) = norm( I - U2'*U2 ) / ( MAX(1,M-P)*ULP )
RESULT(14) = norm( I - V1T'*V1T ) / ( MAX(1,Q)*ULP )
RESULT(15) = 0        if THETA is in increasing order and
                      all angles are in [0,pi/2]

                   = ULPINV   otherwise.
( EPS2 = MAX( norm( I - X'*X ) / M, ULP ). )

Author

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

Definition at line 226 of file ccsdts.f.

👑 Author 👑

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