ctftri (l)  Linux Manuals
ctftri: computes the inverse of a triangular matrix A stored in RFP format
NAME
CTFTRI  computes the inverse of a triangular matrix A stored in RFP formatSYNOPSIS
 SUBROUTINE CTFTRI(
 TRANSR, UPLO, DIAG, N, A, INFO )
 CHARACTER TRANSR, UPLO, DIAG
 INTEGER INFO, N
 COMPLEX A( 0: * )
PURPOSE
CTFTRI computes the inverse of a triangular matrix A stored in RFP format. This is a Level 3 BLAS version of the algorithm.ARGUMENTS
 TRANSR (input) CHARACTER

= aqNaq: The Normal TRANSR of RFP A is stored;
= aqCaq: The Conjugatetranspose TRANSR of RFP A is stored.  UPLO (input) CHARACTER

= aqUaq: A is upper triangular;
= aqLaq: A is lower triangular.  DIAG (input) CHARACTER

= aqNaq: A is nonunit triangular;
= aqUaq: A is unit triangular.  N (input) INTEGER
 The order of the matrix A. N >= 0.
 A (input/output) 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 =
aqNaq then RFP A is (0:N,0:k1) when N is even; k=N/2. RFP A is
(0:N1,0:k) when N is odd; k=N/2. IF TRANSR = aqCaq then RFP is the Conjugatetranspose of RFP A as defined when TRANSR = aqNaq. The contents of RFP A are defined by UPLO as follows: If UPLO = aqUaq the RFP A contains the nt elements of upper packed A; If UPLO = aqLaq the RFP A contains the nt elements of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = aqCaq. When TRANSR is aqNaq 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.  INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith 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.
FURTHER DETAILS
We first consider Standard Packed Format when N is even.We give an example where N = 6.
Let TRANSR = aqNaq. RFP holds AP as follows:
For UPLO = aqUaq 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 conjugatetranspose of the first three columns of AP upper. For UPLO = aqLaq 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 conjugatetranspose of the last three columns of AP lower. To denote conjugate we place  above the element. This covers the case N even and TRANSR = aqNaq.
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