spftri.f(3)							      LAPACK							       spftri.f(3)

NAME

       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
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Version 3.4.1							  Sun May 26 2013						       spftri.f(3)