SRC/cgelst.f(3)

💖 NAME 💖

SRC/cgelst.f — the Library Functions Manual page for the cgelst subroutine, bestie. It's giving “solver with main character energy,” and we're gonna get through every single detail together. 💅

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✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

subroutine cgelst (character trans, integer m, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer info)

CGELST solves overdetermined or underdetermined systems for GE matrices using QR or LQ factorization with compact WY representation of Q.

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🦋 Function/Subroutine Documentation 🦋

🎀 subroutine cgelst 🎀

subroutine cgelst (character trans, integer m, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer info)

CGELST solves overdetermined or underdetermined systems for GE matrices using QR or LQ factorization with compact WY representation of Q.

🧠 Purpose 🧠

CGELST solves overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A with compact WY representation of Q.

It is assumed that A has full rank, and only a rudimentary protection against rank-deficient matrices is provided. This subroutine only detects exact rank-deficiency, where a diagonal element of the triangular factor of A is exactly zero.

It is conceivable for one (or more) of the diagonal elements of the triangular factor of A to be subnormally tiny numbers without this subroutine signalling an error. The solutions computed for such almost-rank-deficient matrices may be less accurate due to a loss of numerical precision.

The following options are provided:

1. If TRANS = 'N' and m >= n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem minimize || B - A*X ||.
2. If TRANS = 'N' and m < n: find the minimum norm solution of an underdetermined system A * X = B.
3. If TRANS = 'C' and m >= n: find the minimum norm solution of an underdetermined system A**T * X = B.
4. If TRANS = 'C' and m < n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem minimize || B - A**T * X ||.

Several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix X.

💜 Parameters 💜

• TRANS — is CHARACTER*1:
  • = 'N': the linear system involves A;
  • = 'C': the linear system involves A**H.
• M — is INTEGER: the number of rows of the matrix A. M >= 0.
• N — is INTEGER: the number of columns of the matrix A. N >= 0.
• NRHS — is INTEGER: the number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >=0.
• A — is COMPLEX array, dimension (LDA,N): on entry, the M-by-N matrix A. On exit:
  • if M >= N, A is overwritten by details of its QR factorization as returned by CGEQRT;
  • if M < N, A is overwritten by details of its LQ factorization as returned by CGELQT.
• LDA — is INTEGER: the leading dimension of the array A. LDA >= max(1,M).
• B — is COMPLEX array, dimension (LDB,NRHS): on entry, the matrix B of right hand side vectors, stored columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS if TRANS = 'C'. On exit, if INFO = 0, B is overwritten by the solution vectors, stored columnwise:
  • if TRANS = 'N' and m >= n, rows 1 to n of B contain the least squares solution vectors; the residual sum of squares for the solution in each column is given by the sum of squares of modulus of elements N+1 to M in that column;
  • if TRANS = 'N' and m < n, rows 1 to N of B contain the minimum norm solution vectors;
  • if TRANS = 'C' and m >= n, rows 1 to M of B contain the minimum norm solution vectors;
  • if TRANS = 'C' and m < n, rows 1 to M of B contain the least squares solution vectors; the residual sum of squares for the solution in each column is given by the sum of squares of the modulus of elements M+1 to N in that column.
• LDB — is INTEGER: the leading dimension of the array B. LDB >= MAX(1,M,N).
• 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, MN + max( MN, NRHS ) ). For optimal performance, LWORK >= max( 1, (MN + max( MN, NRHS ))*NB ), where MN = min(M,N) and NB is the optimum block size. 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 — is INTEGER:
  • = 0: successful exit;
  • < 0: if INFO = -i, the i-th argument had an illegal value;
  • > 0: if INFO = i, the i-th diagonal element of the triangular factor of A is exactly zero, so that A does not have full rank; the least squares solution could not be computed.

👑 Author 👑

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

🌟 Contributors 🌟

November 2022, Igor Kozachenko, Computer Science Division, University of California, Berkeley

Definition at line 201 of file cgelst.f.

🖨️ Author 🖨️

Generated automatically by Doxygen for LAPACK from the source code.

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