.TH "SRC/ztprfb.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/ztprfb.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBztprfb\fP (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb, work, ldwork)" .br .RI "\fBZTPRFB\fP applies a complex 'triangular-pentagonal' block reflector to a complex matrix, which is composed of two blocks\&. " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine ztprfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, complex*16, dimension( ldv, * ) v, integer ldv, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldwork, * ) work, integer ldwork)" .PP \fBZTPRFB\fP applies a complex 'triangular-pentagonal' block reflector to a complex matrix, which is composed of two blocks\&. .PP \fBPurpose:\fP .RS 4 .PP .nf ZTPRFB applies a complex 'triangular-pentagonal' block reflector H or its conjugate transpose H**H to a complex 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 Further Details\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. If SIDE = 'L', LDA >= max(1,K); If SIDE = 'R', LDA >= max(1,M)\&. .fi .PP .br \fIB\fP .PP .nf B is COMPLEX*16 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 COMPLEX*16 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 \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 \fB249\fP of file \fBztprfb\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.