slarzb.f(3) [debian man page]
slarzb.f(3) LAPACK slarzb.f(3) NAME
slarzb.f - SYNOPSIS
Functions/Subroutines subroutine slarzb (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, C, LDC, WORK, LDWORK) SLARZB Function/Subroutine Documentation subroutine slarzb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, integerL, real, dimension( ldv, * )V, integerLDV, real, dimension( ldt, * )T, integerLDT, real, dimension( ldc, * )C, integerLDC, real, dimension( ldwork, * )WORK, integerLDWORK) SLARZB Purpose: SLARZB applies a real block reflector H or its transpose H**T to a real distributed M-by-N C from the left or the right. Currently, only STOREV = 'R' and DIRECT = 'B' are supported. 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) = 'C': 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, not supported yet) = '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': Columnwise (not supported yet) = 'R': Rowwise M M is INTEGER The number of rows of the matrix C. N N is INTEGER The number of columns of the matrix C. K K is INTEGER The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector). L L is INTEGER The number of columns of the matrix V containing the meaningful part of the Householder reflectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. V V is REAL array, dimension (LDV,NV). If STOREV = 'C', NV = K; if STOREV = 'R', NV = L. LDV LDV is INTEGER The leading dimension of the array V. If STOREV = 'C', LDV >= L; 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. C C is REAL array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK WORK is REAL array, dimension (LDWORK,K) LDWORK LDWORK is INTEGER The leading dimension of the array WORK. If SIDE = 'L', LDWORK >= max(1,N); if SIDE = 'R', LDWORK >= max(1,M). Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 Contributors: A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA Further Details: Definition at line 183 of file slarzb.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 slarzb.f(3)
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slarfb.f(3) LAPACK slarfb.f(3) NAME
slarfb.f - SYNOPSIS
Functions/Subroutines subroutine slarfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK) SLARFB applies a block reflector or its transpose to a general rectangular matrix. Function/Subroutine Documentation subroutine slarfb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, real, dimension( ldv, * )V, integerLDV, real, dimension( ldt, * )T, integerLDT, real, dimension( ldc, * )C, integerLDC, real, dimension( ldwork, * )WORK, integerLDWORK) SLARFB applies a block reflector or its transpose to a general rectangular matrix. Purpose: SLARFB applies a real block reflector H or its transpose H**T to a real m by n matrix C, from either the left or the 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': Columnwise = 'R': Rowwise M M is INTEGER The number of rows of the matrix C. N N is INTEGER The number of columns of the matrix C. K K is INTEGER The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector). 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 matrix V. 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. C C is REAL array, dimension (LDC,N) On entry, the m by n matrix C. On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK WORK is REAL array, dimension (LDWORK,K) LDWORK LDWORK is INTEGER The leading dimension of the array WORK. If SIDE = 'L', LDWORK >= max(1,N); if SIDE = 'R', LDWORK >= max(1,M). Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 Further Details: The shape of the matrix V and the storage of the vectors which define the H(i) is best illustrated by the following example with n = 5 and k = 3. The elements equal to 1 are not stored; the corresponding array elements are modified but restored on exit. The rest of the array is not used. DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) ( v1 1 ) ( 1 v2 v2 v2 ) ( v1 v2 1 ) ( 1 v3 v3 ) ( v1 v2 v3 ) ( v1 v2 v3 ) DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': V = ( v1 v2 v3 ) V = ( v1 v1 1 ) ( v1 v2 v3 ) ( v2 v2 v2 1 ) ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) ( 1 v3 ) ( 1 ) Definition at line 195 of file slarfb.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 slarfb.f(3)