dtfsm.f(3)							      LAPACK								dtfsm.f(3)

NAME

       dtfsm.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dtfsm (TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B, LDB)
	   DTFSM

Function/Subroutine Documentation
   subroutine dtfsm (characterTRANSR, characterSIDE, characterUPLO, characterTRANS, characterDIAG, integerM, integerN, double precisionALPHA,
       double precision, dimension( 0: * )A, double precision, dimension( 0: ldb-1, 0: * )B, integerLDB)
       DTFSM

       Purpose:

	    Level 3 BLAS like routine for A in RFP Format.

	    DTFSM  solves the matrix equation

	       op( A )*X = alpha*B  or	X*op( A ) = alpha*B

	    where alpha is a scalar, X and B are m by n matrices, A is a unit, or
	    non-unit,  upper or lower triangular matrix  and  op( A )  is one  of

	       op( A ) = A   or   op( A ) = A**T.

	    A is in Rectangular Full Packed (RFP) Format.

	    The matrix X is overwritten on B.

       Parameters:
	   TRANSR

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

	   SIDE

		     SIDE is CHARACTER*1
		      On entry, SIDE specifies whether op( A ) appears on the left
		      or right of X as follows:

			 SIDE = 'L' or 'l'   op( A )*X = alpha*B.

			 SIDE = 'R' or 'r'   X*op( A ) = alpha*B.

		      Unchanged on exit.

	   UPLO

		     UPLO is CHARACTER*1
		      On entry, UPLO specifies whether the RFP matrix A came from
		      an upper or lower triangular matrix as follows:
		      UPLO = 'U' or 'u' RFP A came from an upper triangular matrix
		      UPLO = 'L' or 'l' RFP A came from a  lower triangular matrix

		      Unchanged on exit.

	   TRANS

		     TRANS is CHARACTER*1
		      On entry, TRANS  specifies the form of op( A ) to be used
		      in the matrix multiplication as follows:

			 TRANS	= 'N' or 'n'   op( A ) = A.

			 TRANS	= 'T' or 't'   op( A ) = A'.

		      Unchanged on exit.

	   DIAG

		     DIAG is CHARACTER*1
		      On entry, DIAG specifies whether or not RFP A is unit
		      triangular as follows:

			 DIAG = 'U' or 'u'   A is assumed to be unit triangular.

			 DIAG = 'N' or 'n'   A is not assumed to be unit
					     triangular.

		      Unchanged on exit.

	   M

		     M is INTEGER
		      On entry, M specifies the number of rows of B. M must be at
		      least zero.
		      Unchanged on exit.

	   N

		     N is INTEGER
		      On entry, N specifies the number of columns of B.  N must be
		      at least zero.
		      Unchanged on exit.

	   ALPHA

		     ALPHA is DOUBLE PRECISION
		      On entry,  ALPHA specifies the scalar  alpha. When  alpha is
		      zero then  A is not referenced and  B need not be set before
		      entry.
		      Unchanged on exit.

	   A

		     A is DOUBLE PRECISION array, dimension (NT)
		      NT = N*(N+1)/2. On entry, the 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 either in normal or
		      transpose Format. If UPLO = 'L' the RFP A contains
		      the NT elements of lower packed A either in normal or
		      transpose Format. 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 is N when is odd.
		      See the Note below for more details. Unchanged on exit.

	   B

		     B is DOUBLE PRECISION array, dimension (LDB,N)
		      Before entry,  the leading  m by n part of the array  B must
		      contain  the  right-hand	side  matrix  B,  and  on exit	is
		      overwritten by the solution matrix  X.

	   LDB

		     LDB is INTEGER
		      On entry, LDB specifies the first dimension of B as declared
		      in  the  calling	(sub)  program.   LDB  must  be  at  least
		      max( 1, m ).
		      Unchanged on exit.

       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 277 of file dtfsm.f.

Author
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Version 3.4.1							  Sun May 26 2013							dtfsm.f(3)