lasdq(3)

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version 3.12.1 · 9 versions
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💅 lasdq — the D&C step that does the leaf using bdsqr

okay bestie, welcome to lasdq(3) from the Library Functions Manual ✨ this is a LAPACK internal-ish page (it says "Library Functions Manual" up top, and the whole thing is the D&C step: leaf using bdsqr — that's the NAME line, you're welcome, we folded it in here so it looks cute 🎀).

✨ NAME ✨

lasdq — lasdq: D&C step: leaf using bdsqr

like… that's it, that's the name. short, iconic, to the point 💅

🌸 SYNOPSIS 🌸

Functions

  • subroutine dlasdq (uplo, sqre, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, work, info) — DLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.
  • subroutine slasdq (uplo, sqre, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, work, info) — SLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.

two flavors, same vibe: d = double precision, s = single precision. pick your fighter 🥊

🦋 Detailed Description 🦋

no cap, this section is basically just a title card — the actual tea is all in Function Documentation below 👇

👑 Function Documentation 👑

🍓 subroutine dlasdq

here's the full signature, character for character, don't @ me:

subroutine dlasdq (character uplo, integer sqre, integer n, integer ncvt,
    integer nru, integer ncc, double precision, dimension( * ) d, double
    precision, dimension( * ) e, double precision, dimension( ldvt, * ) vt,
    integer ldvt, double precision, dimension( ldu, * ) u, integer ldu,
    double precision, dimension( ldc, * ) c, integer ldc, double precision,
    dimension( * ) work, integer info)
DLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.

💖 Purpose:

okay so, the actual purpose text, unrolled for you:

DLASDQ computes the singular value decomposition (SVD) of a real (upper or lower) bidiagonal matrix with diagonal D and offdiagonal E, accumulating the transformations if desired. Letting B denote the input bidiagonal matrix, the algorithm computes orthogonal matrices Q and P such that B = Q * S * P**T (P**T denotes the transpose of P). The singular values S are overwritten on D.

literally the entire plot right there 🔥 and then the side quests:

The input matrix U is changed to U * Q if desired. The input matrix VT is changed to P**T * VT if desired. The input matrix C is changed to Q**T * C if desired.

and for the full lore drop:

See by J. Demmel and W. Kahan, LAPACK Working Note #3, for a detailed description of the algorithm.

(yes, the reference is missing its title in the original — I'm not making that up, that's just how the page ships 🙈)

🌈 Parameters

  • UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the input bidiagonal matrix is upper or lower bidiagonal, and whether it is square are not. (that's the original's wording, I'm not fixing it 😭)
    • UPLO = 'U' or 'u' → B is upper bidiagonal.
    • UPLO = 'L' or 'l' → B is lower bidiagonal.
  • SQRE — SQRE is INTEGER.
    • = 0: then the input matrix is N-by-N.
    • = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and (N+1)-by-N if UPLU = 'L'. (again — UPLU is what the page says, keep it moving 💀)
    • The bidiagonal matrix has N = NL + NR + 1 rows and M = N + SQRE >= N columns.
  • N — N is INTEGER. On entry, N specifies the number of rows and columns in the matrix. N must be at least 0.
  • NCVT — NCVT is INTEGER. On entry, NCVT specifies the number of columns of the matrix VT. NCVT must be at least 0.
  • NRU — NRU is INTEGER. On entry, NRU specifies the number of rows of the matrix U. NRU must be at least 0.
  • NCC — NCC is INTEGER. On entry, NCC specifies the number of columns of the matrix C. NCC must be at least 0.
  • D — D is DOUBLE PRECISION array, dimension (N). On entry, D contains the diagonal entries of the bidiagonal matrix whose SVD is desired. On normal exit, D contains the singular values in ascending order. 🫶
  • E — E is DOUBLE PRECISION array. dimension is (N-1) if SQRE = 0 and N if SQRE = 1. On entry, the entries of E contain the offdiagonal entries of the bidiagonal matrix whose SVD is desired. On normal exit, E will contain 0. If the algorithm does not converge, D and E will contain the diagonal and superdiagonal entries of a bidiagonal matrix orthogonally equivalent to the one given as input. (so no cap: non-convergence still leaves you something coherent, just not the answer you wanted 😭)
  • VT — VT is DOUBLE PRECISION array, dimension (LDVT, NCVT). On entry, contains a matrix which on exit has been premultiplied by P**T, dimension N-by-NCVT if SQRE = 0 and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0).
  • LDVT — LDVT is INTEGER. On entry, LDVT specifies the leading dimension of VT as declared in the calling (sub) program. LDVT must be at least 1. If NCVT is nonzero LDVT must also be at least N.
  • U — U is DOUBLE PRECISION array, dimension (LDU, N). On entry, contains a matrix which on exit has been postmultiplied by Q, dimension NRU-by-N if SQRE = 0 and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0).
  • LDU — LDU is INTEGER. On entry, LDU specifies the leading dimension of U as declared in the calling (sub) program. LDU must be at least max( 1, NRU ).
  • C — C is DOUBLE PRECISION array, dimension (LDC, NCC). On entry, contains an N-by-NCC matrix which on exit has been premultiplied by Q**T dimension N-by-NCC if SQRE = 0 and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0).
  • LDC — LDC is INTEGER. On entry, LDC specifies the leading dimension of C as declared in the calling (sub) program. LDC must be at least 1. If NCC is nonzero, LDC must also be at least N.
  • WORK — WORK is DOUBLE PRECISION array, dimension (4*N). Workspace. Only referenced if one of NCVT, NRU, or NCC is nonzero, and if N is at least 2.
  • INFO — INFO is INTEGER. On exit, a value of 0 indicates a successful exit. If INFO < 0, argument number -INFO is illegal. If INFO > 0, the algorithm did not converge, and INFO specifies how many superdiagonals did not converge. 💀 (that's your "oof" signal, bestie — write it down)

🌟 Author

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

🧚 Contributors:

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

📍 Definition at line 209 of file dlasdq.f.

💜 subroutine slasdq

same energy, single precision version. signature:

subroutine slasdq (character uplo, integer sqre, integer n, integer ncvt,
    integer nru, integer ncc, real, dimension( * ) d, real, dimension( * )
    e, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( ldu, *
    ) u, integer ldu, real, dimension( ldc, * ) c, integer ldc, real,
    dimension( * ) work, integer info)
SLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.

💖 Purpose:

SLASDQ computes the singular value decomposition (SVD) of a real (upper or lower) bidiagonal matrix with diagonal D and offdiagonal E, accumulating the transformations if desired. Letting B denote the input bidiagonal matrix, the algorithm computes orthogonal matrices Q and P such that B = Q * S * P**T (P**T denotes the transpose of P). The singular values S are overwritten on D.
The input matrix U is changed to U * Q if desired. The input matrix VT is changed to P**T * VT if desired. The input matrix C is changed to Q**T * C if desired.
See by J. Demmel and W. Kahan, LAPACK Working Note #3, for a detailed description of the algorithm.

🌈 Parameters

  • UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the input bidiagonal matrix is upper or lower bidiagonal, and whether it is square are not.
    • UPLO = 'U' or 'u' → B is upper bidiagonal.
    • UPLO = 'L' or 'l' → B is lower bidiagonal.
  • SQRE — SQRE is INTEGER.
    • = 0: then the input matrix is N-by-N.
    • = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and (N+1)-by-N if UPLU = 'L'.
    • The bidiagonal matrix has N = NL + NR + 1 rows and M = N + SQRE >= N columns.
  • N — N is INTEGER. On entry, N specifies the number of rows and columns in the matrix. N must be at least 0.
  • NCVT — NCVT is INTEGER. On entry, NCVT specifies the number of columns of the matrix VT. NCVT must be at least 0.
  • NRU — NRU is INTEGER. On entry, NRU specifies the number of rows of the matrix U. NRU must be at least 0.
  • NCC — NCC is INTEGER. On entry, NCC specifies the number of columns of the matrix C. NCC must be at least 0.
  • D — D is REAL array, dimension (N). On entry, D contains the diagonal entries of the bidiagonal matrix whose SVD is desired. On normal exit, D contains the singular values in ascending order.
  • E — E is REAL array. dimension is (N-1) if SQRE = 0 and N if SQRE = 1. On entry, the entries of E contain the offdiagonal entries of the bidiagonal matrix whose SVD is desired. On normal exit, E will contain 0. If the algorithm does not converge, D and E will contain the diagonal and superdiagonal entries of a bidiagonal matrix orthogonally equivalent to the one given as input.
  • VT — VT is REAL array, dimension (LDVT, NCVT). On entry, contains a matrix which on exit has been premultiplied by P**T, dimension N-by-NCVT if SQRE = 0 and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0).
  • LDVT — LDVT is INTEGER. On entry, LDVT specifies the leading dimension of VT as declared in the calling (sub) program. LDVT must be at least 1. If NCVT is nonzero LDVT must also be at least N.
  • U —

(( part 2 picks up right there at U, bestie — don't go anywhere 💖 ))

  • U — U is a REAL array, dimension (LDU, N). On entry, it contains a matrix which on exit has been postmultiplied by Q; dimension is NRU-by-N if SQRE = 0 and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0). 💅
  • LDU — LDU is INTEGER. On entry, LDU specifies the leading dimension of U as declared in the calling (sub) program. LDU must be at least max( 1, NRU ). 🫶
  • C — C is a REAL array, dimension (LDC, NCC). On entry, it contains an N-by-NCC matrix which on exit has been premultiplied by Q**T; dimension N-by-NCC if SQRE = 0 and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0). ✨
  • LDC — LDC is INTEGER. On entry, LDC specifies the leading dimension of C as declared in the calling (sub) program. LDC must be at least 1. If NCC is nonzero, LDC must also be at least N. 🎀
  • WORK — WORK is a REAL array, dimension (4*N). It’s workspace. Only referenced if one of NCVT, NRU, or NCC is nonzero, and if N is at least 2. 🧚
  • INFO — INFO is INTEGER. On exit, a value of 0 indicates a successful exit. If INFO < 0, argument number -INFO is illegal. If INFO > 0, the algorithm did not converge, and INFO specifies how many superdiagonals did not converge. 💀

👑 AUTHOR

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

💖 CONTRIBUTORS

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA 🫶

🧵 DEFINITION

Definition at line 209 of file slasdq.f. — that’s where the source lives, bestie. 🔥

🤖 AUTHOR (THE AUTO-GENERATED BIT)

Generated automatically by Doxygen for LAPACK from the source code. That’s the official stamp. 🫡

Bye bestie! 💖 Footer check: this is LAPACK, Version 3.12.0, page lasdq(3) — source/version/date realness, periodt. ✨🎀

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