.TH "tftri" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME tftri \- tftri: triangular inverse, RFP .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBctftri\fP (transr, uplo, diag, n, a, info)" .br .RI "\fBCTFTRI\fP " .ti -1c .RI "subroutine \fBdtftri\fP (transr, uplo, diag, n, a, info)" .br .RI "\fBDTFTRI\fP " .ti -1c .RI "subroutine \fBstftri\fP (transr, uplo, diag, n, a, info)" .br .RI "\fBSTFTRI\fP " .ti -1c .RI "subroutine \fBztftri\fP (transr, uplo, diag, n, a, info)" .br .RI "\fBZTFTRI\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine ctftri (character transr, character uplo, character diag, integer n, complex, dimension( 0: * ) a, integer info)" .PP \fBCTFTRI\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> CTFTRI computes the inverse of a triangular matrix A stored in RFP !> format\&. !> !> This is a Level 3 BLAS version of the algorithm\&. !> .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': A is upper triangular; !> = 'L': A is lower triangular\&. !> .fi .PP .br \fIDIAG\fP .PP .nf !> DIAG is CHARACTER*1 !> = 'N': A is non-unit triangular; !> = 'U': A is unit triangular\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX array, dimension ( N*(N+1)/2 ); !> On entry, the triangular matrix A in RFP format\&. RFP format !> is described by TRANSR, UPLO, and N as follows: If TRANSR = !> 'N' then RFP A is (0:N,0:k-1) when N is even; k=N/2\&. RFP A is !> (0:N-1,0:k) when N is odd; k=N/2\&. IF TRANSR = 'C' then RFP is !> the Conjugate-transpose of RFP A as defined when !> TRANSR = 'N'\&. The contents of RFP A are defined by UPLO as !> follows: If UPLO = 'U' the RFP A contains the nt elements of !> upper packed A; If UPLO = 'L' the RFP A contains the nt !> elements of lower packed A\&. The LDA of RFP A is (N+1)/2 when !> TRANSR = 'C'\&. When TRANSR is 'N' the LDA is N+1 when N is !> even and N is odd\&. See the Note below for more details\&. !> !> On exit, the (triangular) inverse of the original matrix, in !> the same storage format\&. !> .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 !> > 0: if INFO = i, A(i,i) is exactly zero\&. The triangular !> matrix is singular and its inverse can not be computed\&. !> .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 \fB220\fP of file \fBctftri\&.f\fP\&. .SS "subroutine dtftri (character transr, character uplo, character diag, integer n, double precision, dimension( 0: * ) a, integer info)" .PP \fBDTFTRI\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> DTFTRI computes the inverse of a triangular matrix A stored in RFP !> format\&. !> !> This is a Level 3 BLAS version of the algorithm\&. !> .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; !> = 'T': The Transpose TRANSR of RFP A is stored\&. !> .fi .PP .br \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': A is upper triangular; !> = 'L': A is lower triangular\&. !> .fi .PP .br \fIDIAG\fP .PP .nf !> DIAG is CHARACTER*1 !> = 'N': A is non-unit triangular; !> = 'U': A is unit triangular\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is DOUBLE PRECISION array, dimension (0:nt-1); !> nt=N*(N+1)/2\&. On entry, the triangular factor of a Hermitian !> Positive Definite matrix A in RFP format\&. RFP format is !> described by TRANSR, UPLO, and N as follows: If TRANSR = 'N' !> then RFP A is (0:N,0:k-1) when N is even; k=N/2\&. RFP A is !> (0:N-1,0:k) when N is odd; k=N/2\&. IF TRANSR = 'T' then RFP is !> the transpose of RFP A as defined when !> TRANSR = 'N'\&. The contents of RFP A are defined by UPLO as !> follows: If UPLO = 'U' the RFP A contains the nt elements of !> upper packed A; If UPLO = 'L' the RFP A contains the nt !> elements of lower packed A\&. The LDA of RFP A is (N+1)/2 when !> TRANSR = 'T'\&. When TRANSR is 'N' the LDA is N+1 when N is !> even and N is odd\&. See the Note below for more details\&. !> !> On exit, the (triangular) inverse of the original matrix, in !> the same storage format\&. !> .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 !> > 0: if INFO = i, A(i,i) is exactly zero\&. The triangular !> matrix is singular and its inverse can not be computed\&. !> .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 Rectangular Full Packed (RFP) 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 !> the 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 !> the transpose of the last three columns of AP lower\&. !> 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 = 'T'\&. RFP A in both UPLO cases is just the !> 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 then consider Rectangular Full Packed (RFP) 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 !> the 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 !> the transpose of the last two columns of AP lower\&. !> 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 = 'T'\&. RFP A in both UPLO cases is just the !> 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 \fB200\fP of file \fBdtftri\&.f\fP\&. .SS "subroutine stftri (character transr, character uplo, character diag, integer n, real, dimension( 0: * ) a, integer info)" .PP \fBSTFTRI\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> STFTRI computes the inverse of a triangular matrix A stored in RFP !> format\&. !> !> This is a Level 3 BLAS version of the algorithm\&. !> .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; !> = 'T': The Transpose TRANSR of RFP A is stored\&. !> .fi .PP .br \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': A is upper triangular; !> = 'L': A is lower triangular\&. !> .fi .PP .br \fIDIAG\fP .PP .nf !> DIAG is CHARACTER*1 !> = 'N': A is non-unit triangular; !> = 'U': A is unit triangular\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is REAL array, dimension (NT); !> NT=N*(N+1)/2\&. On entry, the triangular factor of a Hermitian !> Positive Definite matrix A in RFP format\&. RFP format is !> described by TRANSR, UPLO, and N as follows: If TRANSR = 'N' !> then RFP A is (0:N,0:k-1) when N is even; k=N/2\&. RFP A is !> (0:N-1,0:k) when N is odd; k=N/2\&. IF TRANSR = 'T' then RFP is !> the transpose of RFP A as defined when !> TRANSR = 'N'\&. The contents of RFP A are defined by UPLO as !> follows: If UPLO = 'U' the RFP A contains the nt elements of !> upper packed A; If UPLO = 'L' the RFP A contains the nt !> elements of lower packed A\&. The LDA of RFP A is (N+1)/2 when !> TRANSR = 'T'\&. When TRANSR is 'N' the LDA is N+1 when N is !> even and N is odd\&. See the Note below for more details\&. !> !> On exit, the (triangular) inverse of the original matrix, in !> the same storage format\&. !> .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 !> > 0: if INFO = i, A(i,i) is exactly zero\&. The triangular !> matrix is singular and its inverse can not be computed\&. !> .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 Rectangular Full Packed (RFP) 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 !> the 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 !> the transpose of the last three columns of AP lower\&. !> 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 = 'T'\&. RFP A in both UPLO cases is just the !> 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 then consider Rectangular Full Packed (RFP) 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 !> the 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 !> the transpose of the last two columns of AP lower\&. !> 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 = 'T'\&. RFP A in both UPLO cases is just the !> 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 \fB200\fP of file \fBstftri\&.f\fP\&. .SS "subroutine ztftri (character transr, character uplo, character diag, integer n, complex*16, dimension( 0: * ) a, integer info)" .PP \fBZTFTRI\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> ZTFTRI computes the inverse of a triangular matrix A stored in RFP !> format\&. !> !> This is a Level 3 BLAS version of the algorithm\&. !> .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': A is upper triangular; !> = 'L': A is lower triangular\&. !> .fi .PP .br \fIDIAG\fP .PP .nf !> DIAG is CHARACTER*1 !> = 'N': A is non-unit triangular; !> = 'U': A is unit triangular\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX*16 array, dimension ( N*(N+1)/2 ); !> On entry, the triangular matrix A in RFP format\&. RFP format !> is described by TRANSR, UPLO, and N as follows: If TRANSR = !> 'N' then RFP A is (0:N,0:k-1) when N is even; k=N/2\&. RFP A is !> (0:N-1,0:k) when N is odd; k=N/2\&. IF TRANSR = 'C' then RFP is !> the Conjugate-transpose of RFP A as defined when !> TRANSR = 'N'\&. The contents of RFP A are defined by UPLO as !> follows: If UPLO = 'U' the RFP A contains the nt elements of !> upper packed A; If UPLO = 'L' the RFP A contains the nt !> elements of lower packed A\&. The LDA of RFP A is (N+1)/2 when !> TRANSR = 'C'\&. When TRANSR is 'N' the LDA is N+1 when N is !> even and N is odd\&. See the Note below for more details\&. !> !> On exit, the (triangular) inverse of the original matrix, in !> the same storage format\&. !> .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 !> > 0: if INFO = i, A(i,i) is exactly zero\&. The triangular !> matrix is singular and its inverse can not be computed\&. !> .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 \fB220\fP of file \fBztftri\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.