SRC/cgesvdx.f(3)

🌸 NAME 🌸

SRC/cgesvdx.f — bestie, this is the manual page for SRC/cgesvdx.f from the Library Functions Manual. It's all about the cgesvdx subroutine, and yes, it's giving linear algebra main character energy. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

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

CGESVDX computes the singular value decomposition (SVD) for GE matrices — iconic behavior, no cap. 🫶

💖 Function/Subroutine Documentation 💖

🎀 subroutine cgesvdx 🎀

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

CGESVDX computes the singular value decomposition (SVD) for GE matrices. 🦋

🌈 Purpose 🌈

Okay so CGESVDX computes the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing 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 which 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 are returned in descending order. The first min(m,n) columns of U and V are the left and right singular vectors of A. ✨

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

⚠️ Note that the routine returns V**T, not V. Like, important detail, bestie. 💀

🎀 Parameters 🎀

• 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 — 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 — 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 — is INTEGER. The number of rows of the input matrix A. M >= 0.
• N — is INTEGER. The number of columns of the input matrix A. N >= 0.
• A — is COMPLEX array, dimension (LDA,N). On entry, the M-by-N matrix A. On exit, the contents of A are destroyed. 💀
• LDA — is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• VL — is REAL. 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 — is REAL. 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 — 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 — 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 — 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 — is REAL array, dimension (min(M,N)). The singular values of A, sorted so that S(i) >= S(i+1). 🌸
• U — is COMPLEX 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 — is INTEGER. The leading dimension of the array U. LDU >= 1; if JOBU = 'V', LDU >= M.
• VT — is COMPLEX 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 — is INTEGER. The leading dimension of the array VT. LDVT >= 1; if JOBVT = 'V', LDVT >= NS (see above).
• WORK — is COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal 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 — is REAL array, dimension (MAX(1,LRWORK)). LRWORK >= MIN(M,N)*(MIN(M,N)*2+15*MIN(M,N)).
• 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 SBDSVDX/SSTEVX.
• 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 SBDSVDX/SSTEVX. if INFO = N*2 + 1, an internal error occurred in SBDSVDX

👑 Author 👑

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

Definition at line 267 of file cgesvdx.f.

👑 Author 👑

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💖 Cute sign-off: this page is LAPACK Version 3.12.0, page SRC/cgesvdx.f(3) — that's the footer vibe, bestie. periodt. 💅