ZCSDTS(3)

✨ ZCSDTS(3) ✨

Okay bestie, this is the zcsdts.f(3) page from the Library Functions Manual — manual name folded in right here so we don’t have to copy that whole header line. It’s a LAPACK test routine and it’s here to vibe-check some CSD behavior. 💅

🎀 NAME 🎀

The NAME section is literally just a path, and it is exactly:

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

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

Here’s the synopsis, no cap:

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

💖 Function/Subroutine Documentation 💖

The full signature is giving main character energy:

   subroutine ZCSDTS (integer m, integer p, integer q, complex*16, dimension(
       ldx, * ) x, complex*16, dimension( ldx, * ) xf, integer ldx, complex*16,
       dimension( ldu1, * ) u1, integer ldu1, complex*16, dimension( ldu2, * )
       u2, integer ldu2, complex*16, dimension( ldv1t, * ) v1t, integer ldv1t,
       complex*16, dimension( ldv2t, * ) v2t, integer ldv2t, double precision,
       dimension( * ) theta, integer, dimension( * ) iwork, complex*16,
       dimension( lwork ) work, integer lwork, double precision, dimension( * )
       rwork, double precision, dimension( 15 ) result)
       ZCSDTS

✨ Purpose ✨

Ok so ZCSDTS tests ZUNCSD. Given an M-by-M partitioned unitary matrix X, where the partition is literally:

              Q  M-Q
       X = [ X11 X12 ] P   ,
           [ X21 X22 ] M-P

ZUNCSD computes the CSD, and it lands like this:

       [ 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 ]

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 — M is INTEGER. It’s the number of rows of the matrix X, and M >= 0. 💖
• P — P is INTEGER. It’s the number of rows of the matrix X11, and P >= 0.
• Q — Q is INTEGER. It’s the number of columns of the matrix X11, and Q >= 0.
• X — X is COMPLEX*16 array, dimension (LDX,M). It’s the M-by-M matrix X.
• XF — XF is COMPLEX*16 array, dimension (LDX,M). Details of the CSD of X, as returned by ZUNCSD; see ZUNCSD for further details.
• LDX — LDX is INTEGER. The leading dimension of the arrays X and XF. LDX >= max( 1,M ).
• U1 — U1 is COMPLEX*16 array, dimension(LDU1,P). The P-by-P unitary matrix U1.
• LDU1 — LDU1 is INTEGER. The leading dimension of the array U1. LDU >= max(1,P). Yes, it says LDU, bestie. 🫶
• U2 — U2 is COMPLEX*16 array, dimension(LDU2,M-P). The (M-P)-by-(M-P) unitary matrix U2.
• LDU2 — LDU2 is INTEGER. The leading dimension of the array U2. LDU >= max(1,M-P).
• V1T — V1T is COMPLEX*16 array, dimension(LDV1T,Q). The Q-by-Q unitary matrix V1T.
• LDV1T — LDV1T is INTEGER. The leading dimension of the array V1T. LDV1T >= max(1,Q).
• V2T — V2T is COMPLEX*16 array, dimension(LDV2T,M-Q). The (M-Q)-by-(M-Q) unitary matrix V2T.
• LDV2T — LDV2T is INTEGER. The leading dimension of the array V2T. LDV2T >= max(1,M-Q).
• THETA — THETA is DOUBLE PRECISION 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 ZUNCSD for details.
• IWORK — IWORK is INTEGER array, dimension (M).
• WORK — WORK is COMPLEX*16 array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The dimension of the array WORK.
• RWORK — RWORK is DOUBLE PRECISION array.
• RESULT — RESULT is DOUBLE PRECISION array, dimension (15). The test ratios are giving:

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 zcsdts.f.

📜 Author (auto-generated) 📜

Generated automatically by Doxygen for LAPACK from the source code.

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And that’s the page, bestie! Footer vibe check: it’s LAPACK, Version 3.12.0, and the file is /home/abui...IG/zcsdts.f(3). Slay. 💅✨