/home/abui.../dgesvdx.f(3)

💅 NAME

so the header up top says /home/abui.../dgesvdx.f(3) and this whole thing lives in the Library Functions Manual — bestie, we're looking at the source file /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgesvdx.f, which is giving "deep in the LAPACK source tree" energy 🫶

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine DGESVDX (jobu, jobvt, range, m, n, a, lda, vl, vu, il, iu,
    ns, s, u, ldu, vt, ldvt, work, lwork, iwork, info)

tl;dr: DGESVDX computes the singular value decomposition (SVD) for GE matrices. iconic. 🔥

🎀 FUNCTION/SUBROUTINE DOCUMENTATION 🎀

subroutine DGESVDX (character jobu, character jobvt, character range,
    integer m, integer n, double precision, dimension( lda, * ) a, integer
    lda, double precision vl, double precision vu, integer il, integer iu,
    integer ns, double precision, dimension( * ) s, double precision,
    dimension( ldu, * ) u, integer ldu, double precision, dimension( ldvt, *
    ) vt, integer ldvt, double precision, dimension( * ) work, integer
    lwork, integer, dimension( * ) iwork, integer info)

DGESVDX computes the singular value decomposition (SVD) for GE matrices ✨

🌸 Purpose 🌸

okay so, for real:

DGESVDX computes the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors. The SVD is written

A = U * SIGMA * transpose(V)

where SIGMA is an M-by-N matrix which is zero except for its min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA are the singular values of A — they are real and non-negative, and are returned in descending order. The first min(m,n) columns of U and V are the left and right singular vectors of A.

DGESVDX uses an eigenvalue problem for obtaining the SVD, which allows for the computation of a subset of singular values and vectors. See DBDSVDX for details.

⚠️ note that the routine returns V**T, not V. yes, transposed. don't come for me, that's just how it is 💀

💜 Parameters 💜

JOBU — JOBU is CHARACTER*1. Specifies options for computing all or part of the matrix U:
- = 'V': the first min(m,n) columns of U (the left singular vectors) or as specified by RANGE are returned in the array U;
- = 'N': no columns of U (no left singular vectors) are computed.
JOBVT — JOBVT is CHARACTER*1. Specifies options for computing all or part of the matrix V**T:
- = 'V': the first min(m,n) rows of V**T (the right singular vectors) or as specified by RANGE are returned in the array VT;
- = 'N': no rows of V**T (no right singular vectors) are computed.
RANGE — RANGE is CHARACTER*1:
- = 'A': all singular values will be found.
- = 'V': all singular values in the half-open interval (VL,VU] will be found.
- = 'I': the IL-th through IU-th singular values will be found.
M — M is INTEGER. The number of rows of the input matrix A. M >= 0.
N — N is INTEGER. The number of columns of the input matrix A. N >= 0.
A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit, the contents of A are destroyed. 😭 she ate and left no crumbs — your matrix is gone, that's the deal.
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
VL — VL is DOUBLE PRECISION. If RANGE='V', the lower bound of the interval to be searched for singular values. VU > VL. Not referenced if RANGE = 'A' or 'I'.
VU — VU is DOUBLE PRECISION. If RANGE='V', the upper bound of the interval to be searched for singular values. VU > VL. Not referenced if RANGE = 'A' or 'I'.
IL — IL is INTEGER. If RANGE='I', the index of the smallest singular value to be returned. 1 <= IL <= IU <= min(M,N), if min(M,N) > 0. Not referenced if RANGE = 'A' or 'V'.
IU — IU is INTEGER. If RANGE='I', the index of the largest singular value to be returned. 1 <= IL <= IU <= min(M,N), if min(M,N) > 0. Not referenced if RANGE = 'A' or 'V'.
NS — NS is INTEGER. The total number of singular values found, 0 <= NS <= min(M,N). If RANGE = 'A', NS = min(M,N); if RANGE = 'I', NS = IU-IL+1.
S — S is DOUBLE PRECISION array, dimension (min(M,N)). The singular values of A, sorted so that S(i) >= S(i+1). descending order, bestie, always descending 📉
U — U is DOUBLE PRECISION array, dimension (LDU,UCOL). If JOBU = 'V', U contains columns of U (the left singular vectors, stored columnwise) as specified by RANGE; if JOBU = 'N', U is not referenced.

note: the user must ensure that UCOL >= NS; if RANGE = 'V', the exact value of NS is not known in advance and an upper bound must be used. 👀 plan ahead, gorl.

LDU — LDU is INTEGER. The leading dimension of the array U. LDU >= 1; if JOBU = 'V', LDU >= M.
VT — VT is DOUBLE PRECISION array, dimension (LDVT,N). If JOBVT = 'V', VT contains the rows of V**T (the right singular vectors, stored rowwise) as specified by RANGE; if JOBVT = 'N', VT is not referenced.

note: the user must ensure that LDVT >= NS; if RANGE = 'V', the exact value of NS is not known in advance and an upper bound must be used. again. same warning. it's giving "read the room" 🙈

LDVT — LDVT is INTEGER. The leading dimension of the array VT. LDVT >= 1; if JOBVT = 'V', LDVT >= NS (see above).
WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= MAX(1,MIN(M,N)*(MIN(M,N)+4)) for the paths (see comments inside the code):
- PATH 1 (M much larger than N)
- PATH 1t (N much larger than M)

LWORK >= MAX(1,MIN(M,N)*2+MAX(M,N)) for the other paths. For good performance, LWORK should generally be larger. highkey always size up, it's the main character move 👑 If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

IWORK — IWORK is INTEGER array, dimension (12*MIN(M,N)). If INFO = 0, the first NS elements of IWORK are zero. If INFO > 0, then IWORK contains the indices of the eigenvectors that failed to converge in DBDSVDX/DSTEVX. lowkey the receipts of what went wrong 🧾
INFO — INFO is INTEGER:
- = 0: successful exit ✨ slay
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: if INFO = i, then i eigenvectors failed to converge in DBDSVDX/DSTEVX. if INFO = N*2 + 1, an internal error occurred in DBDSVDX

🦋 Author 🦋

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

⭐ Definition ⭐

Definition at line 260 of file dgesvdx.f.

🌈 Author 🌈

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