.TH "stprfb.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME stprfb.f \- .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBstprfb\fP (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)" .br .RI "\fI\fBSTPRFB\fP applies a real or complex 'triangular-pentagonal' blocked reflector to a real or complex matrix, which is composed of two blocks\&. \fP" .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine stprfb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, integerL, real, dimension( ldv, * )V, integerLDV, real, dimension( ldt, * )T, integerLDT, real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, real, dimension( ldwork, * )WORK, integerLDWORK)" .PP \fBSTPRFB\fP applies a real or complex 'triangular-pentagonal' blocked reflector to a real or complex matrix, which is composed of two blocks\&. .PP \fBPurpose: \fP .RS 4 .PP .nf STPRFB applies a real "triangular-pentagonal" block reflector H or its conjugate transpose H^H to a real matrix C, which is composed of two blocks A and B, either from the left or right. .fi .PP .RE .PP \fBParameters:\fP .RS 4 \fISIDE\fP .PP .nf SIDE is CHARACTER*1 = 'L': apply H or H^H from the Left = 'R': apply H or H^H from the Right .fi .PP .br \fITRANS\fP .PP .nf TRANS is CHARACTER*1 = 'N': apply H (No transpose) = 'C': apply H^H (Conjugate transpose) .fi .PP .br \fIDIRECT\fP .PP .nf 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) .fi .PP .br \fISTOREV\fP .PP .nf STOREV is CHARACTER*1 Indicates how the vectors which define the elementary reflectors are stored: = 'C': Columns = 'R': Rows .fi .PP .br \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix B. M >= 0. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix B. N >= 0. .fi .PP .br \fIK\fP .PP .nf K is INTEGER The order of the matrix T, i.e. the number of elementary reflectors whose product defines the block reflector. K >= 0. .fi .PP .br \fIL\fP .PP .nf L is INTEGER The order of the trapezoidal part of V. K >= L >= 0. See Further Details. .fi .PP .br \fIV\fP .PP .nf 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. .fi .PP .br \fILDV\fP .PP .nf 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. .fi .PP .br \fIT\fP .PP .nf T is REAL array, dimension (LDT,K) The triangular K-by-K matrix T in the representation of the block reflector. .fi .PP .br \fILDT\fP .PP .nf LDT is INTEGER The leading dimension of the array T. LDT >= K. .fi .PP .br \fIA\fP .PP .nf 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^H*C or C*H or C*H^H. See Futher Details. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A. If SIDE = 'L', LDC >= max(1,K); If SIDE = 'R', LDC >= max(1,M). .fi .PP .br \fIB\fP .PP .nf 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^H*C or C*H or C*H^H. See Further Details. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M). .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (LDWORK,N) if SIDE = 'L', (LDWORK,K) if SIDE = 'R'. .fi .PP .br \fILDWORK\fP .PP .nf LDWORK is INTEGER The leading dimension of the array WORK. If SIDE = 'L', LDWORK >= K; if SIDE = 'R', LDWORK >= M. .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 September 2012 .RE .PP \fBFurther Details: \fP .RS 4 .PP .nf 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. .fi .PP .RE .PP .PP Definition at line 251 of file stprfb\&.f\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.