SRC/dorm22.f(3)

🌸 NAME 🌸

okay so this is the Library Functions Manual page for SRC/dorm22.f(3), and the actual NAME is SRC/dorm22.f — yes bestie, that’s the whole name section. 💅

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine dorm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work,
    lwork, info)

DORM22 multiplies a general matrix by a banded orthogonal matrix.

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💅 Function/Subroutine Documentation 💅

subroutine dorm22 (character side, character trans, integer m, integer n,
    integer n1, integer n2, double precision, dimension( ldq, * ) q, integer
    ldq, double precision, dimension( ldc, * ) c, integer ldc, double
    precision, dimension( * ) work, integer lwork, integer info)

DORM22 multiplies a general matrix by a banded orthogonal matrix.

🎀 Purpose 🎀

So here’s the tea, bestie: DORM22 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'.

The orthogonal matrix Q processes a 2-by-2 block structure:

        [  Q11  Q12  ]
    Q = [            ]
        [  Q21  Q22  ],

where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an N2-by-N2 upper triangular matrix. That’s the whole shape of it. 🌸

🍓 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': apply Q (No transpose);
• = 'C': apply Q**T (Conjugate transpose).

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.

N1, N2

N1 is INTEGER N2 is INTEGER

The dimension of Q12 and Q21, respectively. N1, N2 >= 0.

The following requirement must be satisfied: N1 + N2 = M if SIDE = 'L' and N1 + N2 = N if SIDE = 'R'.

Q

Q is DOUBLE PRECISION array, dimension (LDQ,M) if SIDE = 'L' (LDQ,N) if SIDE = 'R'

LDQ

LDQ is INTEGER

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

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 >= M*N.

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 161 of file dorm22.f.

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🫶 Author 🫶

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💖 That’s the whole page, bestie — source/version: LAPACK Version 3.12.0, page: SRC/dorm22.f(3). Date: not shown in this footer, and I’m not inventing one, periodt. 🫶