ztfsm - solve a matrix equation (one operand is a triangular matrix in RFP format)
SUBROUTINE ZTFSM(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B, LDB) CHARACTER*1 TRANSR, DIAG, SIDE, TRANS, UPLO INTEGER LDB, M, N DOUBLE COMPLEX ALPHA DOUBLE COMPLEX A(0:*), B(0:LDB-1,0:*) SUBROUTINE ZTFSM_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 COMPLEX ALPHA DOUBLE COMPLEX 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 COMPLEX(8) :: ALPHA COMPLEX(8), DIMENSION(:,:) :: B COMPLEX(8), DIMENSION(:) :: A 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 COMPLEX(8) :: ALPHA COMPLEX(8), DIMENSION(:,:) :: B COMPLEX(8), DIMENSION(:) :: A C INTERFACE #include <sunperf.h> void ztfsm (char transr, char side, char uplo, char trans, char diag, int m, int n, doublecomplex *alpha, doublecomplex *a, double- complex *b, int ldb); void ztfsm_64 (char transr, char side, char uplo, char trans, char diag, long m, long n, doublecomplex *alpha, doublecomplex *a, doublecomplex *b, long ldb);
Oracle Solaris Studio Performance Library ztfsm(3P)
NAME
ztfsm - solve a matrix equation (one operand is a triangular matrix in
RFP format)
SYNOPSIS
SUBROUTINE ZTFSM(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B,
LDB)
CHARACTER*1 TRANSR, DIAG, SIDE, TRANS, UPLO
INTEGER LDB, M, N
DOUBLE COMPLEX ALPHA
DOUBLE COMPLEX A(0:*), B(0:LDB-1,0:*)
SUBROUTINE ZTFSM_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 COMPLEX ALPHA
DOUBLE COMPLEX 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
COMPLEX(8) :: ALPHA
COMPLEX(8), DIMENSION(:,:) :: B
COMPLEX(8), DIMENSION(:) :: A
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
COMPLEX(8) :: ALPHA
COMPLEX(8), DIMENSION(:,:) :: B
COMPLEX(8), DIMENSION(:) :: A
C INTERFACE
#include <sunperf.h>
void ztfsm (char transr, char side, char uplo, char trans, char diag,
int m, int n, doublecomplex *alpha, doublecomplex *a, double-
complex *b, int ldb);
void ztfsm_64 (char transr, char side, char uplo, char trans, char
diag, long m, long n, doublecomplex *alpha, doublecomplex *a,
doublecomplex *b, long ldb);
PURPOSE
ztfsm 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**H.
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;
= 'C': The Conjugate-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 = 'C' or 'c' op( A ) = conjg( 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 COMPLEX*16
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 COMPLEX*16 array, dimension (N*(N+1)/2)
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 = 'C'
then RFP is the Conjugate-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 conjugate-transpose For-
mat. If UPLO = 'L' the RFP A contains the NT elements of
lower packed A either in normal or conjugate-transpose For-
mat. The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. 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 COMPLEX*16 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 DETAILS
We first consider Standard Packed 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
conjugate-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
conjugate-transpose of the last three columns of AP lower.
To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate-
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 next consider Standard Packed 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
conjugate-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
conjugate-transpose of the last two columns of AP lower.
To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate-
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 ztfsm(3P)