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

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgesvdx.f

Yep bestie, that's the file. This page lives in the Library Functions Manual, and the main-character routine is ZGESVDX. The header/footer file path shows up as /home/abui.../zgesvdx.f(3) — we love a truncated path moment 💅.

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine ZGESVDX (jobu, jobvt, range, m, n, a, lda, vl, vu, il, iu,
    ns, s, u, ldu, vt, ldvt, work, lwork, rwork, iwork, info)
     ZGESVDX computes the singular value decomposition (SVD) for GE
    matrices

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🦋 Function/Subroutine Documentation 🦋

subroutine ZGESVDX (character jobu, character jobvt, character range,
    integer m, integer n, complex*16, dimension( lda, * ) a, integer lda,
    double precision vl, double precision vu, integer il, integer iu,
    integer ns, double precision, dimension( * ) s, complex*16, dimension(
    ldu, * ) u, integer ldu, complex*16, dimension( ldvt, * ) vt, integer
    ldvt, complex*16, dimension( * ) work, integer lwork, double precision,
    dimension( * ) rwork, integer, dimension( * ) iwork, integer info)

The one-liner is literally: ZGESVDX computes the singular value decomposition (SVD) for GE matrices.

✨ Purpose ✨

Okay so here's the tea, bestie: ZGESVDX computes the singular value decomposition (SVD) of a complex M-by-N matrix A, and you can optionally compute the left and/or right singular vectors. The SVD is written like this:

A = U * SIGMA * transpose(V)

where SIGMA is an M-by-N matrix that is zero except for its min(m,n) diagonal elements, U is an M-by-M unitary matrix, and V is an N-by-N unitary matrix. The diagonal elements of SIGMA are the singular values of A; they are real and non-negative, and they're returned in descending order. The first min(m,n) columns of U and V are the left and right singular vectors of A. Iconic behavior, honestly ✨.

ZGESVDX 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: the routine returns V**T, not V 🫶.

🌈 Parameters 🌈

Bestie, here is every single parameter — no skips, no cap:

• 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 COMPLEX*16 array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit, the contents of A are destroyed.
• 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).
• U — U is COMPLEX*16 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.
• LDU — LDU is INTEGER. The leading dimension of the array U. LDU >= 1; if JOBU = 'V', LDU >= M.
• VT — VT is COMPLEX*16 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.
• LDVT — LDVT is INTEGER. The leading dimension of the array VT. LDVT >= 1; if JOBVT = 'V', LDVT >= NS (see above).
• WORK — WORK is COMPLEX*16 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.

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.

• RWORK — RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)). LRWORK >= MIN(M,N)*(MIN(M,N)*2+15*MIN(M,N)).
• 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.
• INFO — INFO is INTEGER: = 0: successful exit; < 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 at line 267 of file zgesvdx.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, that's the whole page 💅. The footer source/version vibes are LAPACK Version 3.12.0, and the page file is /home/abui.../zgesvdx.f(3). Mwah 💖