.TH "SRC/zpftrs.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/zpftrs.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBzpftrs\fP (transr, uplo, n, nrhs, a, b, ldb, info)" .br .RI "\fBZPFTRS\fP " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine zpftrs (character transr, character uplo, integer n, integer nrhs, complex*16, dimension( 0: * ) a, complex*16, dimension( ldb, * ) b, integer ldb, integer info)" .PP \fBZPFTRS\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> ZPFTRS solves a system of linear equations A*X = B with a Hermitian !> positive definite matrix A using the Cholesky factorization !> A = U**H*U or A = L*L**H computed by ZPFTRF\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fITRANSR\fP .PP .nf !> TRANSR is CHARACTER*1 !> = 'N': The Normal TRANSR of RFP A is stored; !> = 'C': The Conjugate-transpose TRANSR of RFP A is stored\&. !> .fi .PP .br \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of RFP A is stored; !> = 'L': Lower triangle of RFP A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fINRHS\fP .PP .nf !> NRHS is INTEGER !> The number of right hand sides, i\&.e\&., the number of columns !> of the matrix B\&. NRHS >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX*16 array, dimension ( N*(N+1)/2 ); !> The triangular factor U or L from the Cholesky factorization !> of RFP A = U**H*U or RFP A = L*L**H, as computed by ZPFTRF\&. !> See note below for more details about RFP A\&. !> .fi .PP .br \fIB\fP .PP .nf !> B is COMPLEX*16 array, dimension (LDB,NRHS) !> On entry, the right hand side matrix B\&. !> On exit, the solution matrix X\&. !> .fi .PP .br \fILDB\fP .PP .nf !> LDB is INTEGER !> The leading dimension of the array B\&. LDB >= max(1,N)\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> .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 !> !> We first consider Standard Packed Format when N is even\&. !> We give an example where N = 6\&. !> !> AP is Upper AP is Lower !> !> 00 01 02 03 04 05 00 !> 11 12 13 14 15 10 11 !> 22 23 24 25 20 21 22 !> 33 34 35 30 31 32 33 !> 44 45 40 41 42 43 44 !> 55 50 51 52 53 54 55 !> !> !> Let TRANSR = 'N'\&. RFP holds AP as follows: !> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last !> three columns of AP upper\&. The lower triangle A(4:6,0:2) consists of !> conjugate-transpose of the first three columns of AP upper\&. !> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first !> three columns of AP lower\&. The upper triangle A(0:2,0:2) consists of !> conjugate-transpose of the last three columns of AP lower\&. !> To denote conjugate we place -- above the element\&. This covers the !> case N even and TRANSR = 'N'\&. !> !> RFP A RFP A !> !> -- -- -- !> 03 04 05 33 43 53 !> -- -- !> 13 14 15 00 44 54 !> -- !> 23 24 25 10 11 55 !> !> 33 34 35 20 21 22 !> -- !> 00 44 45 30 31 32 !> -- -- !> 01 11 55 40 41 42 !> -- -- -- !> 02 12 22 50 51 52 !> !> Now let TRANSR = 'C'\&. RFP A in both UPLO cases is just the conjugate- !> transpose of RFP A above\&. One therefore gets: !> !> !> RFP A RFP A !> !> -- -- -- -- -- -- -- -- -- -- !> 03 13 23 33 00 01 02 33 00 10 20 30 40 50 !> -- -- -- -- -- -- -- -- -- -- !> 04 14 24 34 44 11 12 43 44 11 21 31 41 51 !> -- -- -- -- -- -- -- -- -- -- !> 05 15 25 35 45 55 22 53 54 55 22 32 42 52 !> !> !> We next consider Standard Packed Format when N is odd\&. !> We give an example where N = 5\&. !> !> AP is Upper AP is Lower !> !> 00 01 02 03 04 00 !> 11 12 13 14 10 11 !> 22 23 24 20 21 22 !> 33 34 30 31 32 33 !> 44 40 41 42 43 44 !> !> !> Let TRANSR = 'N'\&. RFP holds AP as follows: !> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last !> three columns of AP upper\&. The lower triangle A(3:4,0:1) consists of !> conjugate-transpose of the first two columns of AP upper\&. !> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first !> three columns of AP lower\&. The upper triangle A(0:1,1:2) consists of !> conjugate-transpose of the last two columns of AP lower\&. !> To denote conjugate we place -- above the element\&. This covers the !> case N odd and TRANSR = 'N'\&. !> !> RFP A RFP A !> !> -- -- !> 02 03 04 00 33 43 !> -- !> 12 13 14 10 11 44 !> !> 22 23 24 20 21 22 !> -- !> 00 33 34 30 31 32 !> -- -- !> 01 11 44 40 41 42 !> !> Now let TRANSR = 'C'\&. RFP A in both UPLO cases is just the conjugate- !> transpose of RFP A above\&. One therefore gets: !> !> !> RFP A RFP A !> !> -- -- -- -- -- -- -- -- -- !> 02 12 22 00 01 00 10 20 30 40 50 !> -- -- -- -- -- -- -- -- -- !> 03 13 23 33 11 33 11 21 31 41 51 !> -- -- -- -- -- -- -- -- -- !> 04 14 24 34 44 43 44 22 32 42 52 !> .fi .PP .RE .PP .PP Definition at line \fB219\fP of file \fBzpftrs\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.