SRC/dgesvd.f(3)

✨ SRC/dgesvd.f(3) ✨

From the Library Functions Manual — okay bestie, this is a LAPACK page and it's giving main-character Fortran energy. 💅

🎀 NAME

SRC/dgesvd.f

🌸 SYNOPSIS

💫 Functions/Subroutines

• subroutine dgesvd (jobu, jobvt, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, info) — DGESVD computes the singular value decomposition (SVD) for GE matrices

🔥 Function/Subroutine Documentation

subroutine dgesvd (character jobu, character jobvt, integer m, integer n,
    double precision, dimension( lda, * ) a, integer lda, 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 info)

DGESVD computes the singular value decomposition (SVD) for GE matrices

🦋 Purpose

Okay so DGESVD computes the SVD of a real M-by-N matrix A, optionally computing left and/or right singular vectors. The SVD is written as:

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 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.

Note that the routine returns V**T, not V. That's important, bestie. 💜

💅 Parameters

• JOBU — JOBU is CHARACTER*1. It specifies options for computing all or part of the matrix U:
  • = 'A': all M columns of U are returned in array U;
  • = 'S': the first min(m,n) columns of U (the left singular vectors) are returned in the array U;
  • = 'O': the first min(m,n) columns of U (the left singular vectors) are overwritten on the array A;
  • = 'N': no columns of U (no left singular vectors) are computed.
• JOBVT — JOBVT is CHARACTER*1. It specifies options for computing all or part of the matrix V**T:
  • = 'A': all N rows of V**T are returned in the array VT;
  • = 'S': the first min(m,n) rows of V**T (the right singular vectors) are returned in the array VT;
  • = 'O': the first min(m,n) rows of V**T (the right singular vectors) are overwritten on the array A;
  • = 'N': no rows of V**T (no right singular vectors) are computed.

⚠️ Warning, icon: JOBVT and JOBU cannot both be 'O'. That combo is a no. 💀

• 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:
  • if JOBU = 'O', A is overwritten with the first min(m,n) columns of U (the left singular vectors, stored columnwise);
  • if JOBVT = 'O', A is overwritten with the first min(m,n) rows of V**T (the right singular vectors, stored rowwise);
  • if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A are destroyed.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• 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 DOUBLE PRECISION array, dimension (LDU,UCOL) — (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'.
  • If JOBU = 'A', U contains the M-by-M orthogonal matrix U;
  • if JOBU = 'S', U contains the first min(m,n) columns of U (the left singular vectors, stored columnwise);
  • if JOBU = 'N' or 'O', U is not referenced.
• LDU — LDU is INTEGER. The leading dimension of the array U. LDU >= 1; if JOBU = 'S' or 'A', LDU >= M.
• VT — VT is DOUBLE PRECISION array, dimension (LDVT,N).
  • If JOBVT = 'A', VT contains the N-by-N orthogonal matrix V**T;
  • if JOBVT = 'S', VT contains the first min(m,n) rows of V**T (the right singular vectors, stored rowwise);
  • if JOBVT = 'N' or 'O', VT is not referenced.
• LDVT — LDVT is INTEGER. The leading dimension of the array VT. LDVT >= 1; if JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N).
• WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK; if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged superdiagonal elements of an upper bidiagonal matrix B whose diagonal is in S (not necessarily sorted). B satisfies A = U * B * VT, so it has the same singular values as A, and singular vectors related by U and VT.
• LWORK — LWORK is INTEGER. The dimension of the array WORK.
  • LWORK >= MAX(1,5*MIN(M,N)) for the paths (see comments inside code):
    • PATH 1 (M much larger than N, JOBU='N')
    • PATH 1t (N much larger than M, JOBVT='N')
  • LWORK >= MAX(1,3*MIN(M,N) + MAX(M,N),5*MIN(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.

• INFO — INFO is INTEGER.
  • = 0: successful exit.
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • > 0: if DBDSQR did not converge, INFO specifies how many superdiagonals of an intermediate bidiagonal form B did not converge to zero. See the description of WORK above for details.

👑 Author

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

Definition at line 209 of file dgesvd.f.

🪄 Author

Generated automatically by Doxygen for LAPACK from the source code.

---

Okay bestie, that's the whole page: LAPACK Version 3.12.0, source SRC/dgesvd.f(3) — no date on the footer, just SVD excellence. Mwah. 💋✨