stfsm.f man page

stfsm.f —

Synopsis

Functions/Subroutines

subroutine stfsm (TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B, LDB)
STFSM solves a matrix equation (one operand is a triangular matrix in RFP format).

Function/Subroutine Documentation

subroutine stfsm (characterTRANSR, characterSIDE, characterUPLO, characterTRANS, characterDIAG, integerM, integerN, realALPHA, real, dimension( 0: * )A, real, dimension( 0: ldb-1, 0: * )B, integerLDB)

STFSM solves a matrix equation (one operand is a triangular matrix in RFP format).

Purpose:

Level 3 BLAS like routine for A in RFP Format.

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.

Parameters:

TRANSR

TRANSR is CHARACTER*1
= 'N':  The Normal Form of RFP A is stored;
= 'T':  The Transpose Form of RFP A is stored.

SIDE

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

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

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

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

M is INTEGER
 On entry, M specifies the number of rows of B. M must be at
 least zero.
 Unchanged on exit.

N

N is INTEGER
 On entry, N specifies the number of columns of B.  N must be
 at least zero.
 Unchanged on exit.

ALPHA

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

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

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

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.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Further Details:

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

Definition at line 277 of file stfsm.f.

Author

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Referenced By

stfsm(3) is an alias of stfsm.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK