SRC/sormtr.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

✨ NAME ✨

okay so this is SRC/sormtr.f(3) — the Library Functions Manual page for SRC/sormtr.f — and it's giving very much "LAPACK routine who knows she's iconic" energy 👑. no cap, this is the real deal.

🛠 SYNOPSIS 🛠

🧩 Functions/Subroutines

subroutine sormtr (side, uplo, trans, m, n, a, lda, tau, c, ldc, work, lwork, info)
    SORMTR

📚 Function/Subroutine Documentation 📚

subroutine sormtr (character side, character uplo, character trans, integer
     m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension(
     * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * )
     work, integer lwork, integer info)
    SORMTR

🎯 Purpose 🎯

SORMTR overwrites the general real M-by-N matrix C with:

                SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'T':      Q**T * C       C * Q**T

where Q is a real orthogonal matrix of order nq, with nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of nq-1 elementary reflectors, as returned by SSYTRD:

  • if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
  • if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).

🌸 Parameters 🌸

🌟 SIDE

SIDE is CHARACTER*1

  • = 'L': apply Q or Q**T from the Left;
  • = 'R': apply Q or Q**T from the Right.

🌟 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.

🌟 TRANS

TRANS is CHARACTER*1

  • = 'N': No transpose, apply Q;
  • = 'T': Transpose, apply Q**T.

🌟 M

M is INTEGER

The number of rows of the matrix C. M >= 0.

🌟 N

N is INTEGER

The number of columns of the matrix C. N >= 0.

🌟 A

A is REAL array, dimension

  • (LDA,M) if SIDE = 'L'
  • (LDA,N) if SIDE = 'R'

The vectors which define the elementary reflectors, as returned by SSYTRD.

🌟 LDA

LDA is INTEGER

The leading dimension of the array A. LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.

🌟 TAU

TAU is REAL array, dimension

  • (M-1) if SIDE = 'L'
  • (N-1) if SIDE = 'R'

TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SSYTRD.

🌟 C

C is REAL array, dimension (LDC,N)

On entry, the M-by-N matrix C.

On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

🌟 LDC

LDC is INTEGER

The leading dimension of the array C. LDC >= max(1,M).

🌟 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.

  • If SIDE = 'L', LWORK >= max(1,N);
  • if SIDE = 'R', LWORK >= max(1,M).

For optimum performance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE = 'R', 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 at line 170 of file sormtr.f 📍

Definition at line 170 of file sormtr.f.

🤖 Author 🤖

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