# dtprfb.f - Man Page

SRC/dtprfb.f

## Synopsis

### Functions/Subroutines

subroutine **dtprfb** (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb, work, ldwork)**DTPRFB** applies a real 'triangular-pentagonal' block reflector to a real matrix, which is composed of two blocks.

## Function/Subroutine Documentation

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

**DTPRFB** applies a real 'triangular-pentagonal' block reflector to a real matrix, which is composed of two blocks.

**Purpose:**

DTPRFB applies a real 'triangular-pentagonal' 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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:**

The matrix 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 **dtprfb.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dtprfb(3) is an alias of dtprfb.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK