.TH "SRC/spftri.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/spftri.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBspftri\fP (transr, uplo, n, a, info)"
.br
.RI "\fBSPFTRI\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine spftri (character transr, character uplo, integer n, real, dimension( 0: * ) a, integer info)"

.PP
\fBSPFTRI\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SPFTRI computes the inverse of a real (symmetric) positive definite
!> matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
!> computed by SPFTRF\&.
!> 
.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':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored\&.
!> 
.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 ( N*(N+1)/2 )
!>          On entry, the symmetric 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 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 symmetric 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, the (i,i) element of the factor U or L is
!>                zero, and the inverse could 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 \fB190\fP of file \fBspftri\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.