SRC/stprfb.f(3)

💅 NAME

SRC/stprfb.f — straight from the Library Functions Manual, bestie. This is the page for STPRFB, and it's giving "real matrix glow-up" energy. 💖

✨ SYNOPSIS

Functions/Subroutines

• subroutine stprfb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb, work, ldwork) — STPRFB applies a real "triangular-pentagonal" block reflector to a real matrix, which is composed of two blocks. 🫶

🦋 Function/Subroutine Documentation

subroutine stprfb (character side, character trans, character direct,
    character storev, integer m, integer n, integer k, integer l, real,
    dimension( ldv, * ) v, integer ldv, real, dimension( ldt, * ) t, integer
    ldt, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * )
    b, integer ldb, real, dimension( ldwork, * ) work, integer ldwork)

STPRFB applies a real "triangular-pentagonal" block reflector to a real matrix, which is composed of two blocks. 💫

✨ Purpose

STPRFB applies a real block reflector H or its transpose H**T to a real matrix C, which is composed of two blocks A and B, either from the left or right.

🌈 Parameters

SIDE

• SIDE is CHARACTER*1
• = 'L': apply H or H**T from the Left
• = 'R': apply H or H**T from the Right

TRANS

• TRANS is CHARACTER*1
• = 'N': apply H (No transpose)
• = 'T': apply H**T (Transpose)

DIRECT

• DIRECT is CHARACTER*1
• Indicates how H is formed from a product of elementary reflectors
• = 'F': H = H(1) H(2) . . . H(k) (Forward)
• = 'B': H = H(k) . . . H(2) H(1) (Backward)

STOREV

• STOREV is CHARACTER*1
• Indicates how the vectors which define the elementary reflectors are stored:
• = 'C': Columns
• = 'R': Rows

M

• M is INTEGER
• The number of rows of the matrix B.
• M >= 0.

N

• N is INTEGER
• The number of columns of the matrix B.
• N >= 0.

K

• K is INTEGER
• The order of the matrix T, i.e. the number of elementary reflectors whose product defines the block reflector.
• K >= 0.

L

• L is INTEGER
• The order of the trapezoidal part of V.
• K >= L >= 0. See Further Details.

V

• V is REAL array, dimension

(LDV,K) if STOREV = 'C'
(LDV,M) if STOREV = 'R' and SIDE = 'L'
(LDV,N) if STOREV = 'R' and SIDE = 'R'

• The pentagonal matrix V, which contains the elementary reflectors H(1), H(2), ..., H(K). See Further Details.

LDV

• LDV is INTEGER
• The leading dimension of the array V.
• If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
• if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
• if STOREV = 'R', LDV >= K.

T

• T is REAL array, dimension (LDT,K)
• The triangular K-by-K matrix T in the representation of the block reflector.

LDT

• LDT is INTEGER
• The leading dimension of the array T.
• LDT >= K.

A

• A is REAL array, dimension
• (LDA,N) if SIDE = 'L' or (LDA,K) if SIDE = 'R'
• On entry, the K-by-N or M-by-K matrix A.
• On exit, A is overwritten by the corresponding block of H*C or H**T*C or C*H or C*H**T. See Further Details.

LDA

• LDA is INTEGER
• The leading dimension of the array A.
• If SIDE = 'L', LDA >= max(1,K);
• If SIDE = 'R', LDA >= max(1,M).

B

• B is REAL array, dimension (LDB,N)
• On entry, the M-by-N matrix B.
• On exit, B is overwritten by the corresponding block of H*C or H**T*C or C*H or C*H**T. See Further Details.

LDB

• LDB is INTEGER
• The leading dimension of the array B.
• LDB >= max(1,M).

WORK

• WORK is REAL array, dimension
• (LDWORK,N) if SIDE = 'L',
• (LDWORK,K) if SIDE = 'R'.

LDWORK

• LDWORK is INTEGER
• The leading dimension of the array WORK.
• If SIDE = 'L', LDWORK >= K;
• if SIDE = 'R', LDWORK >= M.

👑 Author

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

🌸 Further Details

C is a composite matrix formed from blocks A and B. The block B is of size M-by-N; if SIDE = 'R', A is of size M-by-K, and if SIDE = 'L', A is of size K-by-N.

If SIDE = 'R' and DIRECT = 'F', C = [A B].

If SIDE = 'L' and DIRECT = 'F':

C = [A]
    [B].

If SIDE = 'R' and DIRECT = 'B', C = [B A].

If SIDE = 'L' and DIRECT = 'B':

C = [B]
    [A].

The pentagonal matrix V is composed of a rectangular block V1 and a trapezoidal block V2. The size of the trapezoidal block is determined by the parameter L, where 0<=L<=K. If L=K, the V2 block of V is triangular; if L=0, there is no trapezoidal block, thus V = V1 is rectangular.

If DIRECT = 'F' and STOREV = 'C':

V = [V1]
    [V2]

• V2 is upper trapezoidal (first L rows of K-by-K upper triangular)

If DIRECT = 'F' and STOREV = 'R':

V = [V1 V2]

• V2 is lower trapezoidal (first L columns of K-by-K lower triangular)

If DIRECT = 'B' and STOREV = 'C':

V = [V2]
    [V1]

• V2 is lower trapezoidal (last L rows of K-by-K lower triangular)

If DIRECT = 'B' and STOREV = 'R':

V = [V2 V1]

• V2 is upper trapezoidal (last L columns of K-by-K upper triangular)

If STOREV = 'C' and SIDE = 'L', V is M-by-K with V2 L-by-K.

If STOREV = 'C' and SIDE = 'R', V is N-by-K with V2 L-by-K.

If STOREV = 'R' and SIDE = 'L', V is K-by-M with V2 K-by-L.

If STOREV = 'R' and SIDE = 'R', V is K-by-N with V2 K-by-L.

Definition at line 249 of file stprfb.f.

🫶 Author

Generated automatically by Doxygen for LAPACK from the source code.

💖 okay bestie, that's the whole page. The footer vibes: LAPACK Version 3.12.0, source file SRC/stprfb.f(3), and the original footer doesn't show a date, so I'm not making one up. Periodt. 🫶✨