SRC/slasd0.f(3)

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✨ NAME ✨

SRC/slasd0.f

🦋 SYNOPSIS 🦋

Functions/Subroutines

• subroutine slasd0 — SLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.

subroutine slasd0 (n, sqre, d, e, u, ldu, vt, ldvt, smlsiz, iwork, work,
    info)

💫 Function/Subroutine Documentation 💫

subroutine slasd0

subroutine slasd0 (integer n, integer sqre, real, dimension( * ) d, real,
    dimension( * ) e, real, dimension( ldu, * ) u, integer ldu, real,
    dimension( ldvt, * ) vt, integer ldvt, integer smlsiz, integer,
    dimension( * ) iwork, real, dimension( * ) work, integer info)

SLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.

🌸 Purpose 🌸

Using a divide and conquer approach, SLASD0 computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE. The algorithm computes orthogonal matrices U and VT such that B = U * S * VT. The singular values S are overwritten on D.

A related subroutine, SLASDA, computes only the singular values, and optionally, the singular vectors in compact form.

🎀 Parameters 🎀

• N — N is INTEGER. On entry, the row dimension of the upper bidiagonal matrix. This is also the dimension of the main diagonal array D.
• SQRE — SQRE is INTEGER. Specifies the column dimension of the bidiagonal matrix.
  • = 0: The bidiagonal matrix has column dimension M = N;
  • = 1: The bidiagonal matrix has column dimension M = N+1;
• D — D is REAL array, dimension (N). On entry D contains the main diagonal of the bidiagonal matrix. On exit D, if INFO = 0, contains its singular values.
• E — E is REAL array, dimension (M-1). Contains the subdiagonal entries of the bidiagonal matrix. On exit, E has been destroyed.
• U — U is REAL array, dimension (LDU, N). On exit, U contains the left singular vectors, if U passed in as (N, N) Identity.
• LDU — LDU is INTEGER. On entry, leading dimension of U.
• VT — VT is REAL array, dimension (LDVT, M). On exit, VT**T contains the right singular vectors, if VT passed in as (M, M) Identity.
• LDVT — LDVT is INTEGER. On entry, leading dimension of VT.
• SMLSIZ — SMLSIZ is INTEGER. On entry, maximum size of the subproblems at the bottom of the computation tree.
• IWORK — IWORK is INTEGER array, dimension (8*N)
• WORK — WORK is REAL array, dimension (3*M**2+2*M)
• INFO — INFO is INTEGER
  • = 0: successful exit.
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • > 0: if INFO = 1, a singular value 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 at line 150 of file slasd0.f.

🌈 Author 🌈

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