ung2l(3)

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version 3.12.1 · 9 versions
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🎀 NAME 🎀

okay bestie, welcome to ung2l(3) — the Library Functions Manual page for ung2l — {un,or}g2l: step in ungql.

✨ SYNOPSIS ✨

Functions

  • subroutine cung2l (m, n, k, a, lda, tau, work, info) — CUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm).
  • subroutine dorg2l (m, n, k, a, lda, tau, work, info) — DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).
  • subroutine sorg2l (m, n, k, a, lda, tau, work, info) — SORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).
  • subroutine zung2l (m, n, k, a, lda, tau, work, info) — ZUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm).

💅 Detailed Description 💅

the detailed tea is all below in Function Documentation. no cap, every routine is there with its full signature, purpose, parameters, author list, and definition line. 💖

🌸 Function Documentation 🌸

🧚 subroutine cung2l 🧚

subroutine cung2l (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm).

Purpose

bestie, CUNG2L generates an m by n complex matrix Q with orthonormal columns. Q is defined as the last n columns of a product of k elementary reflectors of order m:

Q  =  H(k) . . . H(2) H(1)

and all of that is as returned by CGEQLF. ✨

Parameters

  • M — INTEGER. The number of rows of the matrix Q. M >= 0.
  • N — INTEGER. The number of columns of the matrix Q. M >= N >= 0.
  • K — INTEGER. The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
  • A — COMPLEX array, dimension (LDA,N). On entry, the (n-k+i)-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGEQLF in the last k columns of its array argument A. On exit, the m-by-n matrix Q.
  • LDA — INTEGER. The first dimension of the array A. LDA >= max(1,M).
  • TAU — COMPLEX array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEQLF.
  • WORK — COMPLEX array, dimension (N).
  • INFO — INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument has an illegal value.

Author

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

Definition at line 113 of file cung2l.f.

🦋 subroutine dorg2l 🦋

subroutine dorg2l (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).

Purpose

DORG2L generates an m by n real matrix Q with orthonormal columns. Q is defined as the last n columns of a product of k elementary reflectors of order m:

Q  =  H(k) . . . H(2) H(1)

as returned by DGEQLF. 💖

Parameters

  • M — INTEGER. The number of rows of the matrix Q. M >= 0.
  • N — INTEGER. The number of columns of the matrix Q. M >= N >= 0.
  • K — INTEGER. The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
  • A — DOUBLE PRECISION array, dimension (LDA,N). On entry, the (n-k+i)-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGEQLF in the last k columns of its array argument A. On exit, the m by n matrix Q.
  • LDA — INTEGER. The first dimension of the array A. LDA >= max(1,M).
  • TAU — DOUBLE PRECISION array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGEQLF.
  • WORK — DOUBLE PRECISION array, dimension (N).
  • INFO — INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument has an illegal value.

Author

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

Definition at line 113 of file dorg2l.f.

🌈 subroutine sorg2l 🌈

subroutine sorg2l (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).

Purpose

SORG2L generates an m by n real matrix Q with orthonormal columns. Q is defined as the last n columns of a product of k elementary reflectors of order m:

Q  =  H(k) . . . H(2) H(1)

as returned by SGEQLF. 🫶

Parameters

  • M — INTEGER. The number of rows of the matrix Q. M >= 0.
  • N — INTEGER. The number of columns of the matrix Q. M >= N >= 0.
  • K — INTEGER. The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
  • A — REAL array, dimension (LDA,N). On entry, the (n-k+i)-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGEQLF in the last k columns of its array argument A. On exit, the m by n matrix Q.
  • LDA — INTEGER. The first dimension of the array A. LDA >= max(1,M).
  • TAU — REAL array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGEQLF.
  • WORK — REAL array, dimension (N).
  • INFO — INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument has an illegal value.

Author

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

Definition at line 113 of file sorg2l.f.

👑 subroutine zung2l 👑

subroutine zung2l (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

ZUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm).

Purpose

ZUNG2L generates an m by n complex matrix Q with orthonormal columns. Q is defined as the last n columns of a product of k elementary reflectors of order m:

Q  =  H(k) . . . H(2) H(1)

as returned by ZGEQLF. ⭐

Parameters

  • M — INTEGER. The number of rows of the matrix Q. M >= 0.
  • N — INTEGER. The number of columns of the matrix Q. M >= N >= 0.
  • K — INTEGER. The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
  • A — COMPLEX*16 array, dimension (LDA,N). On entry, the (n-k+i)-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGEQLF in the last k columns of its array argument A. On exit, the m-by-n matrix Q.
  • LDA — INTEGER. The first dimension of the array A. LDA >= max(1,M).
  • TAU — COMPLEX*16 array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZGEQLF.
  • WORK — COMPLEX*16 array, dimension (N).
  • INFO — INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument has an illegal value.

Author

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

Definition at line 113 of file zung2l.f.

🫶 Author 🫶

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