spftri.f man page

spftri.f —

Synopsis

Functions/Subroutines

subroutine spftri (TRANSR, UPLO, N, A, INFO)
SPFTRI

Function/Subroutine Documentation

subroutine spftri (characterTRANSR, characterUPLO, integerN, real, dimension( 0: * )A, integerINFO)

SPFTRI

Purpose:

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.

Parameters:

TRANSR

TRANSR is CHARACTER*1
= 'N':  The Normal TRANSR of RFP A is stored;
= 'T':  The Transpose TRANSR of RFP A is stored.

UPLO

UPLO is CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A.  N >= 0.

A

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.

INFO

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.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details:

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

Definition at line 192 of file spftri.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

spftri(3) is an alias of spftri.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK