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/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/dtfsm.f(3) Library Functions Manual /home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/dtfsm.f(3)

NAME

/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/dtfsm.f

SYNOPSIS

Functions/Subroutines


subroutine DTFSM (transr, side, uplo, trans, diag, m, n, alpha, a, b, ldb)
DTFSM solves a matrix equation (one operand is a triangular matrix in RFP format).

Function/Subroutine Documentation

subroutine DTFSM (character transr, character side, character uplo, character trans, character diag, integer m, integer n, double precision alpha, double precision, dimension( 0: * ) a, double precision, dimension( 0: ldb-1, 0: * ) b, integer ldb)

DTFSM solves a matrix equation (one operand is a triangular matrix in RFP format).

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.

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 275 of file dtfsm.f.

Author

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