SRC/dormhr.f(3)

💖 SRC/dormhr.f 💖

okay so you opened SRC/dormhr.f(3) from the Library Functions Manual, and this is the whole glow-up on the DORMHR subroutine. no cap, every parameter and every condition is staying right here. 💅

🎀 NAME 🎀

SRC/dormhr.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

       subroutine dormhr (side, trans, m, n, ilo, ihi, a, lda, tau, c, ldc,
           work, lwork, info)
           DORMHR

💅 FUNCTION/SUBROUTINE DOCUMENTATION 💅

   subroutine dormhr (character side, character trans, integer m, integer n,
       integer ilo, integer ihi, double precision, dimension( lda, * ) a,
       integer lda, double precision, dimension( * ) tau, double precision,
       dimension( ldc, * ) c, integer ldc, double precision, dimension( * )
       work, integer lwork, integer info)
       DORMHR

🎯 Purpose 🎯

DORMHR 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 IHI-ILO elementary reflectors, as returned by DGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-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.

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.

ILO

ILO is INTEGER

IHI

IHI is INTEGER

ILO and IHI must have the same values as in the previous call of DGEHRD. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi).

If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and ILO = 1 and IHI = 0, if M = 0; if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and ILO = 1 and IHI = 0, if N = 0.

A

A is DOUBLE PRECISION array, dimension

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

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

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 DOUBLE PRECISION 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 DGEHRD.

C

C is DOUBLE PRECISION 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 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. 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.

bestie, special-case alert 🚨 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 176 of file dormhr.f.

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👑 AUTHOR 👑

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