stfsm - solve a matrix equation (one operand is a triangular matrix in RFP format)
SUBROUTINE STFSM(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B, LDB) CHARACTER*1 TRANSR, DIAG, SIDE, TRANS, UPLO INTEGER LDB, M, N REAL ALPHA REAL A(0:*), B(0:LDB-1,0:*) SUBROUTINE STFSM_64(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B, LDB) CHARACTER*1 TRANSR, DIAG, SIDE, TRANS, UPLO INTEGER*8 LDB, M, N REAL ALPHA REAL A(0:*), B(0:LDB-1,0:*) F95 INTERFACE SUBROUTINE TFSM(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B, LDB) REAL, DIMENSION(:,:) :: B INTEGER :: M, N, LDB CHARACTER(LEN=1) :: TRANSR, SIDE, UPLO, TRANS, DIAG REAL, DIMENSION(:) :: A REAL :: ALPHA SUBROUTINE TFSM_64(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B, LDB) REAL, DIMENSION(:,:) :: B INTEGER(8) :: M, N, LDB CHARACTER(LEN=1) :: TRANSR, SIDE, UPLO, TRANS, DIAG REAL, DIMENSION(:) :: A REAL :: ALPHA C INTERFACE #include <sunperf.h> void stfsm (char transr, char side, char uplo, char trans, char diag, int m, int n, float alpha, float *a, float *b, int ldb); void stfsm_64 (char transr, char side, char uplo, char trans, char diag, long m, long n, float alpha, float *a, float *b, long ldb);
Oracle Solaris Studio Performance Library stfsm(3P)
NAME
stfsm - solve a matrix equation (one operand is a triangular matrix in
RFP format)
SYNOPSIS
SUBROUTINE STFSM(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B,
LDB)
CHARACTER*1 TRANSR, DIAG, SIDE, TRANS, UPLO
INTEGER LDB, M, N
REAL ALPHA
REAL A(0:*), B(0:LDB-1,0:*)
SUBROUTINE STFSM_64(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B,
LDB)
CHARACTER*1 TRANSR, DIAG, SIDE, TRANS, UPLO
INTEGER*8 LDB, M, N
REAL ALPHA
REAL A(0:*), B(0:LDB-1,0:*)
F95 INTERFACE
SUBROUTINE TFSM(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B,
LDB)
REAL, DIMENSION(:,:) :: B
INTEGER :: M, N, LDB
CHARACTER(LEN=1) :: TRANSR, SIDE, UPLO, TRANS, DIAG
REAL, DIMENSION(:) :: A
REAL :: ALPHA
SUBROUTINE TFSM_64(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B,
LDB)
REAL, DIMENSION(:,:) :: B
INTEGER(8) :: M, N, LDB
CHARACTER(LEN=1) :: TRANSR, SIDE, UPLO, TRANS, DIAG
REAL, DIMENSION(:) :: A
REAL :: ALPHA
C INTERFACE
#include <sunperf.h>
void stfsm (char transr, char side, char uplo, char trans, char diag,
int m, int n, float alpha, float *a, float *b, int ldb);
void stfsm_64 (char transr, char side, char uplo, char trans, char
diag, long m, long n, float alpha, float *a, float *b, long
ldb);
PURPOSE
stfsm 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
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 (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 REAL
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 REAL 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 (input/output)
B is REAL 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 (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 stfsm(3P)