ungtr(3)

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version 3.12.1 · 9 versions
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🎀 ungtr(3) — Library Functions Manual 🎀

okay so bestie, this is the ungtr(3) page, and the manual name is Library Functions Manual — folded in right here at the top instead of making you read a duplicated header line. 💅

✨ NAME ✨

ungtr — {un,or}gtr: generate Q from hetrd. That's the whole name vibe, periodt. 🦋

🌈 SYNOPSIS 🌈

💻 Functions 💻

  • subroutine cungtr (uplo, n, a, lda, tau, work, lwork, info) — this is the CUNGTR one, signature exactly as the page gives it. no cap. ✨
  • subroutine dorgtr (uplo, n, a, lda, tau, work, lwork, info) — and here's DORGTR, same arg-list energy. 💜
  • subroutine sorgtr (uplo, n, a, lda, tau, work, lwork, info) — SORGTR is in the group chat too. 🫶
  • subroutine zungtr (uplo, n, a, lda, tau, work, lwork, info) — plus ZUNGTR, right on cue. 🌸

💫 Detailed Description 💫

This is the Detailed Description section, and it's giving "the NAME line already spilled the tea." The page says ungtr is {un,or}gtr: generate Q from hetrd. That's the detailed-description vibe here, bestie — iconic, concise, and not doing extra. ✨

💫 Function Documentation 💫

Okay bestie, this is the function-docs part, and it’s giving “four routines, one mission”: build Q out of the elementary reflectors that CHETRD / DSYTRD / SSYTRD / ZHETRD handed you. Each routine gets the full treatment below, no skips. 🫶

💅 cungtr — CUNGTR 💅

   subroutine cungtr (character uplo, integer n, complex, dimension( lda, * )
       a, integer lda, complex, dimension( * ) tau, complex, dimension( * )
       work, integer lwork, integer info)

Purpose

CUNGTR generates a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by CHETRD:

if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),

if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).

Parameters

  • UPLO — UPLO is CHARACTER*1
    • = 'U': Upper triangle of A contains elementary reflectors from CHETRD;
    • = 'L': Lower triangle of A contains elementary reflectors from CHETRD.
  • N — N is INTEGER. The order of the matrix Q. N >= 0.
  • A — A is COMPLEX array, dimension (LDA,N). On entry, the vectors which define the elementary reflectors, as returned by CHETRD. On exit, the N-by-N unitary matrix Q.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= N.
  • TAU — TAU is COMPLEX array, dimension (N-1). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CHETRD.
  • WORK — WORK is COMPLEX 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 >= N-1. For optimum performance LWORK >= (N-1)*NB, where NB is the optimal blocksize. 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

Author

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

Definition

Definition at line 122 of file cungtr.f.

🌸 dorgtr — DORGTR 🌸

   subroutine dorgtr (character uplo, integer n, double precision, dimension(
       lda, * ) a, integer lda, double precision, dimension( * ) tau, double
       precision, dimension( * ) work, integer lwork, integer info)

Purpose

DORGTR generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by DSYTRD:

if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),

if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).

Parameters

  • UPLO — UPLO is CHARACTER*1
    • = 'U': Upper triangle of A contains elementary reflectors from DSYTRD;
    • = 'L': Lower triangle of A contains elementary reflectors from DSYTRD.
  • N — N is INTEGER. The order of the matrix Q. N >= 0.
  • A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry, the vectors which define the elementary reflectors, as returned by DSYTRD. On exit, the N-by-N orthogonal matrix Q.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • TAU — TAU is DOUBLE PRECISION array, dimension (N-1). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DSYTRD.
  • WORK — WORK is DOUBLE PRECISION 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,N-1). For optimum performance LWORK >= (N-1)*NB, where NB is the optimal blocksize. 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

Author

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

Definition

Definition at line 122 of file dorgtr.f.

🦋 sorgtr — SORGTR 🦋

   subroutine sorgtr (character uplo, integer n, real, dimension( lda, * ) a,
       integer lda, real, dimension( * ) tau, real, dimension( * ) work,
       integer lwork, integer info)

Purpose

SORGTR generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by SSYTRD:

if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),

if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).

Parameters

  • UPLO — UPLO is CHARACTER*1
    • = 'U': Upper triangle of A contains elementary reflectors from SSYTRD;
    • = 'L': Lower triangle of A contains elementary reflectors from SSYTRD.
  • N — N is INTEGER. The order of the matrix Q. N >= 0.
  • A — A is REAL array, dimension (LDA,N). On entry, the vectors which define the elementary reflectors, as returned by SSYTRD. On exit, the N-by-N orthogonal matrix Q.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • TAU — TAU is REAL array, dimension (N-1). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SSYTRD.
  • WORK — WORK is REAL 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,N-1). For optimum performance LWORK >= (N-1)*NB, where NB is the optimal blocksize. 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

Author

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

Definition

Definition at line 122 of file sorgtr.f.

🎀 zungtr — ZUNGTR 🎀

   subroutine zungtr (character uplo, integer n, complex*16, dimension( lda, *
       ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension(
       * ) work, integer lwork, integer info)

Purpose

ZUNGTR generates a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by ZHETRD:

if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),

if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).

Parameters

  • UPLO — UPLO is CHARACTER*1
    • = 'U': Upper triangle of A contains elementary reflectors from ZHETRD;
    • = 'L': Lower triangle of A contains elementary reflectors from ZHETRD.
  • N — N is INTEGER. The order of the matrix Q. N >= 0.
  • A — A is COMPLEX*16 array, dimension (LDA,N). On entry, the vectors which define the elementary reflectors, as returned by ZHETRD. On exit, the N-by-N unitary matrix Q.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= N.
  • TAU — TAU is COMPLEX*16 array, dimension (N-1). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZHETRD.
  • 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 >= N-1. For optimum performance LWORK >= (N-1)*NB, where NB is the optimal blocksize. 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

Author

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

Definition

Definition at line 122 of file zungtr.f.

✨ Author ✨

Generated automatically by Doxygen for LAPACK from the source code.

And that’s the whole function-docs moment, bestie — four routines, all documented, no crumbs left. This page’s footer energy is LAPACK Version 3.12.0 + ungtr(3) (no date in the footer, just vibes and version info). Go build your Q and slay. 💖✨

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