Go to main content
Oracle Developer Studio 12.5 Man Pages

Exit Print View

Updated: June 2017
 
 

ctfsm (3p)

Name

ctfsm - solve a matrix equation (one operand is a triangular matrix in RFP format)

Synopsis

SUBROUTINE CTFSM(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N,  ALPHA,  A,  B,
LDB)


CHARACTER*1 TRANSR, DIAG, SIDE, TRANS, UPLO

INTEGER LDB, M, N

COMPLEX ALPHA

COMPLEX A(0:*), B(0:LDB-1,0:*)


SUBROUTINE CTFSM_64(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B,
LDB)


CHARACTER*1 TRANSR, DIAG, SIDE, TRANS, UPLO

INTEGER*8 LDB, M, N

COMPLEX ALPHA

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, DIMENSION(:,:) :: B

COMPLEX :: ALPHA

COMPLEX, 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, DIMENSION(:,:) :: B

COMPLEX :: ALPHA

COMPLEX, DIMENSION(:) :: A


C INTERFACE
#include <sunperf.h>

void ctfsm (char transr, char side, char uplo, char trans,  char  diag,
int m, int n, floatcomplex *alpha, floatcomplex *a, floatcom-
plex *b, int ldb);


void ctfsm_64 (char transr, char side,  char  uplo,  char  trans,  char
diag,  long  m, long n, floatcomplex *alpha, floatcomplex *a,
floatcomplex *b, long ldb);

Description

Oracle Solaris Studio Performance Library                            ctfsm(3P)



NAME
       ctfsm  - solve a matrix equation (one operand is a triangular matrix in
       RFP format)


SYNOPSIS
       SUBROUTINE CTFSM(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N,  ALPHA,  A,  B,
                 LDB)


       CHARACTER*1 TRANSR, DIAG, SIDE, TRANS, UPLO

       INTEGER LDB, M, N

       COMPLEX ALPHA

       COMPLEX A(0:*), B(0:LDB-1,0:*)


       SUBROUTINE CTFSM_64(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B,
                 LDB)


       CHARACTER*1 TRANSR, DIAG, SIDE, TRANS, UPLO

       INTEGER*8 LDB, M, N

       COMPLEX ALPHA

       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, DIMENSION(:,:) :: B

       COMPLEX :: ALPHA

       COMPLEX, 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, DIMENSION(:,:) :: B

       COMPLEX :: ALPHA

       COMPLEX, DIMENSION(:) :: A


   C INTERFACE
       #include <sunperf.h>

       void ctfsm (char transr, char side, char uplo, char trans,  char  diag,
                 int m, int n, floatcomplex *alpha, floatcomplex *a, floatcom-
                 plex *b, int ldb);


       void ctfsm_64 (char transr, char side,  char  uplo,  char  trans,  char
                 diag,  long  m, long n, floatcomplex *alpha, floatcomplex *a,
                 floatcomplex *b, long ldb);


PURPOSE
       ctfsm 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 over-
       written 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 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 COMPLEX
                 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 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 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                         ctfsm(3P)