dtfsm (l)  Linux Manuals
dtfsm: 3 BLAS like routine for A in RFP Format
NAME
DTFSM  3 BLAS like routine for A in RFP FormatSYNOPSIS
 SUBROUTINE DTFSM(
 TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A,
 + B, LDB )
 CHARACTER TRANSR, DIAG, SIDE, TRANS, UPLO
 INTEGER LDB, M, N
 DOUBLE PRECISION ALPHA
 DOUBLE PRECISION A( 0: * ), B( 0: LDB1, 0: * )
PURPOSE
Level 3 BLAS like routine for A in RFP Format. DTFSM solves the matrix equationop(
where alpha is a scalar, X and B are m by n matrices, A is a unit, or nonunit, upper or lower triangular matrix and op( A ) is one of
op(
A is in Rectangular Full Packed (RFP) Format.
The matrix X is overwritten on B.
ARGUMENTS
TRANSR  (input) CHARACTER = aqNaq: The Normal Form of RFP A is stored;= aqTaq: The Transpose Form of RFP A is stored.
 SIDE  (input) CHARACTER
 On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows: SIDE = aqLaq or aqlaq op( A )*X = alpha*B. SIDE = aqRaq or aqraq X*op( A ) = alpha*B. Unchanged on exit.
 UPLO  (input) CHARACTER
 On entry, UPLO specifies whether the RFP matrix A came from an upper or lower triangular matrix as follows: UPLO = aqUaq or aquaq RFP A came from an upper triangular matrix UPLO = aqLaq or aqlaq RFP A came from a lower triangular matrix Unchanged on exit.
 TRANS  (input) CHARACTER
 On entry, TRANS specifies the form of op( A ) to be used in the matrix multiplication as follows:
 TRANS = aqNaq or aqnaq op( A ) = A.
 TRANS = aqTaq or aqtaq op( A ) = Aaq.
 Unchanged on exit.
 DIAG  (input) CHARACTER
 On entry, DIAG specifies whether or not RFP A is unit triangular as follows: DIAG = aqUaq or aquaq A is assumed to be unit triangular. DIAG = aqNaq or aqnaq A is not assumed to be unit triangular. Unchanged on exit.
 M  (input) INTEGER.
 On entry, M specifies the number of rows of B. M must be at least zero. Unchanged on exit.
 N  (input) INTEGER.
 On entry, N specifies the number of columns of B. N must be at least zero. Unchanged on exit.
 ALPHA  (input) 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  (input) 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=aqNaq then RFP A is (0:N,0:K1) when N is even;
K=N/2. RFP A is (0:N1,0:K) when N is odd; K=N/2. If TRANSR = aqTaq then RFP is the transpose of RFP A as defined when TRANSR = aqNaq. The contents of RFP A are defined by UPLO as follows: If UPLO = aqUaq the RFP A contains the NT elements of upper packed A either in normal or transpose Format. If UPLO = aqLaq 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 = aqTaq. When TRANSR is aqNaq 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  (input/ouptut) DOUBLE PRECISION array, DIMENSION (LDB,N)
 Before entry, the leading m by n part of the array B must contain the righthand side matrix B, and on exit is overwritten by the solution matrix X.
 LDB  (input) 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.
FURTHER DETAILS
We first consider Rectangular Full Packed (RFP) Format when N is even. We give an example where N = 6.Let TRANSR = aqNaq. RFP holds AP as follows:
For UPLO = aqUaq 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 = aqLaq 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 = aqNaq.
03 04 05
13 14 15
23 24 25
33 34 35
00 44 45
01 11 55
02 12 22
Now let TRANSR = aqTaq. RFP A in both UPLO cases is just the transpose of RFP A above. One therefore gets: