DPFTRS man page on Oracle

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dpftrs.f(3)			    LAPACK			   dpftrs.f(3)

NAME
       dpftrs.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dpftrs (TRANSR, UPLO, N, NRHS, A, B, LDB, INFO)
	   DPFTRS

Function/Subroutine Documentation
   subroutine dpftrs (characterTRANSR, characterUPLO, integerN, integerNRHS,
       double precision, dimension( 0: * )A, double precision, dimension( ldb,
       * )B, integerLDB, integerINFO)
       DPFTRS

       Purpose:

	    DPFTRS solves a system of linear equations A*X = B with a symmetric
	    positive definite matrix A using the Cholesky factorization
	    A = U**T*U or A = L*L**T computed by DPFTRF.

       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 RFP A is stored;
		     = 'L':  Lower triangle of RFP A is stored.

	   N

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

	   NRHS

		     NRHS is INTEGER
		     The number of right hand sides, i.e., the number of columns
		     of the matrix B.  NRHS >= 0.

	   A

		     A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ).
		     The triangular factor U or L from the Cholesky factorization
		     of RFP A = U**T*U or RFP A = L*L**T, as computed by DPFTRF.
		     See note below for more details about RFP A.

	   B

		     B is DOUBLE PRECISION array, dimension (LDB,NRHS)
		     On entry, the right hand side matrix B.
		     On exit, the solution matrix X.

	   LDB

		     LDB is INTEGER
		     The leading dimension of the array B.  LDB >= max(1,N).

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  if INFO = -i, the i-th argument had an illegal value

       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 200 of file dpftrs.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2			Tue Sep 25 2012			   dpftrs.f(3)
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