dtfsm - solve a matrix equation (one operand is a triangular matrix in RFP format)
SUBROUTINE DTFSM(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B, LDB) CHARACTER*1 TRANSR, DIAG, SIDE, TRANS, UPLO INTEGER LDB, M, N DOUBLE PRECISION ALPHA DOUBLE PRECISION A(0:*), B(0:LDB-1,0:*) SUBROUTINE DTFSM_64(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B, LDB) CHARACTER*1 TRANSR, DIAG, SIDE, TRANS, UPLO INTEGER*8 LDB, M, N DOUBLE PRECISION ALPHA DOUBLE PRECISION A(0:*), B(0:LDB-1,0:*) F95 INTERFACE SUBROUTINE TFSM(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B, LDB) INTEGER :: M, N, LDB CHARACTER(LEN=1) :: TRANSR, SIDE, UPLO, TRANS, DIAG REAL(8), DIMENSION(:,:) :: B REAL(8), DIMENSION(:) :: A REAL(8) :: ALPHA SUBROUTINE TFSM_64(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B, LDB) INTEGER(8) :: M, N, LDB CHARACTER(LEN=1) :: TRANSR, SIDE, UPLO, TRANS, DIAG REAL(8), DIMENSION(:,:) :: B REAL(8), DIMENSION(:) :: A REAL(8) :: ALPHA C INTERFACE #include <sunperf.h> void dtfsm (char transr, char side, char uplo, char trans, char diag, int m, int n, double alpha, double *a, double *b, int ldb); void dtfsm_64 (char transr, char side, char uplo, char trans, char diag, long m, long n, double alpha, double *a, double *b, long ldb);
Oracle Solaris Studio Performance Library dtfsm(3P)
NAME
dtfsm - solve a matrix equation (one operand is a triangular matrix in
RFP format)
SYNOPSIS
SUBROUTINE DTFSM(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B,
LDB)
CHARACTER*1 TRANSR, DIAG, SIDE, TRANS, UPLO
INTEGER LDB, M, N
DOUBLE PRECISION ALPHA
DOUBLE PRECISION A(0:*), B(0:LDB-1,0:*)
SUBROUTINE DTFSM_64(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B,
LDB)
CHARACTER*1 TRANSR, DIAG, SIDE, TRANS, UPLO
INTEGER*8 LDB, M, N
DOUBLE PRECISION ALPHA
DOUBLE PRECISION A(0:*), B(0:LDB-1,0:*)
F95 INTERFACE
SUBROUTINE TFSM(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B,
LDB)
INTEGER :: M, N, LDB
CHARACTER(LEN=1) :: TRANSR, SIDE, UPLO, TRANS, DIAG
REAL(8), DIMENSION(:,:) :: B
REAL(8), DIMENSION(:) :: A
REAL(8) :: ALPHA
SUBROUTINE TFSM_64(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B,
LDB)
INTEGER(8) :: M, N, LDB
CHARACTER(LEN=1) :: TRANSR, SIDE, UPLO, TRANS, DIAG
REAL(8), DIMENSION(:,:) :: B
REAL(8), DIMENSION(:) :: A
REAL(8) :: ALPHA
C INTERFACE
#include <sunperf.h>
void dtfsm (char transr, char side, char uplo, char trans, char diag,
int m, int n, double alpha, double *a, double *b, int ldb);
void dtfsm_64 (char transr, char side, char uplo, char trans, char
diag, long m, long n, double alpha, double *a, double *b,
long ldb);
PURPOSE
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.
ARGUMENTS
TRANSR (input)
TRANSR is CHARACTER*1
= 'N': The Normal Form of RFP A is stored;
= 'T': The Transpose Form of RFP A is stored.
SIDE (input)
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 (input)
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 (input)
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 (input)
DIAG is CHARACTER*1
On entry, DIAG specifies whether or not RFP A is unit trian-
gular 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 (input)
M is INTEGER
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.
N (input)
N is INTEGER
On entry, N specifies the number of columns of B. N must be
at least zero.
Unchanged on exit.
ALPHA (input)
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 (input)
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 con-
tents 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 con-
tains 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 (input/output)
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 over-
written by the solution matrix X.
LDB (input)
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.
FURTHER NOTES ON RFP FORMAT
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
7 Nov 2015 dtfsm(3P)