--- 
:name: stfsm
:md5sum: 1dcdb7177f893a4f654c7e71cf9bfb56
:category: :subroutine
:arguments: 
- transr: 
    :type: char
    :intent: input
- side: 
    :type: char
    :intent: input
- uplo: 
    :type: char
    :intent: input
- trans: 
    :type: char
    :intent: input
- diag: 
    :type: char
    :intent: input
- m: 
    :type: integer
    :intent: input
- n: 
    :type: integer
    :intent: input
- alpha: 
    :type: real
    :intent: input
- a: 
    :type: real
    :intent: input
    :dims: 
    - nt
- b: 
    :type: real
    :intent: input/output
    :dims: 
    - ldb
    - n
- ldb: 
    :type: integer
    :intent: input
:substitutions: 
  ldb: MAX(1,m)
:fortran_help: "      SUBROUTINE STFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B, LDB )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  Level 3 BLAS like routine for A in RFP Format.\n\
  *\n\
  *  STFSM  solves the matrix equation\n\
  *\n\
  *     op( A )*X = alpha*B  or  X*op( A ) = alpha*B\n\
  *\n\
  *  where alpha is a scalar, X and B are m by n matrices, A is a unit, or\n\
  *  non-unit,  upper or lower triangular matrix  and  op( A )  is one  of\n\
  *\n\
  *     op( A ) = A   or   op( A ) = A'.\n\
  *\n\
  *  A is in Rectangular Full Packed (RFP) Format.\n\
  *\n\
  *  The matrix X is overwritten on B.\n\
  *\n\n\
  *  Arguments\n\
  *  ==========\n\
  *\n\
  *  TRANSR  (input) CHARACTER*1\n\
  *          = 'N':  The Normal Form of RFP A is stored;\n\
  *          = 'T':  The Transpose Form of RFP A is stored.\n\
  *\n\
  *  SIDE    (input) CHARACTER*1\n\
  *           On entry, SIDE specifies whether op( A ) appears on the left\n\
  *           or right of X as follows:\n\
  *\n\
  *              SIDE = 'L' or 'l'   op( A )*X = alpha*B.\n\
  *\n\
  *              SIDE = 'R' or 'r'   X*op( A ) = alpha*B.\n\
  *\n\
  *           Unchanged on exit.\n\
  *\n\
  *  UPLO    (input) CHARACTER*1\n\
  *           On entry, UPLO specifies whether the RFP matrix A came from\n\
  *           an upper or lower triangular matrix as follows:\n\
  *           UPLO = 'U' or 'u' RFP A came from an upper triangular matrix\n\
  *           UPLO = 'L' or 'l' RFP A came from a  lower triangular matrix\n\
  *\n\
  *           Unchanged on exit.\n\
  *\n\
  *  TRANS   (input) CHARACTER*1\n\
  *           On entry, TRANS  specifies the form of op( A ) to be used\n\
  *           in the matrix multiplication as follows:\n\
  *\n\
  *              TRANS  = 'N' or 'n'   op( A ) = A.\n\
  *\n\
  *              TRANS  = 'T' or 't'   op( A ) = A'.\n\
  *\n\
  *           Unchanged on exit.\n\
  *\n\
  *  DIAG    (input) CHARACTER*1\n\
  *           On entry, DIAG specifies whether or not RFP A is unit\n\
  *           triangular as follows:\n\
  *\n\
  *              DIAG = 'U' or 'u'   A is assumed to be unit triangular.\n\
  *\n\
  *              DIAG = 'N' or 'n'   A is not assumed to be unit\n\
  *                                  triangular.\n\
  *\n\
  *           Unchanged on exit.\n\
  *\n\
  *  M       (input) INTEGER\n\
  *           On entry, M specifies the number of rows of B. M must be at\n\
  *           least zero.\n\
  *           Unchanged on exit.\n\
  *\n\
  *  N       (input) INTEGER\n\
  *           On entry, N specifies the number of columns of B.  N must be\n\
  *           at least zero.\n\
  *           Unchanged on exit.\n\
  *\n\
  *  ALPHA   (input) REAL\n\
  *           On entry,  ALPHA specifies the scalar  alpha. When  alpha is\n\
  *           zero then  A is not referenced and  B need not be set before\n\
  *           entry.\n\
  *           Unchanged on exit.\n\
  *\n\
  *  A       (input) REAL array, dimension (NT)\n\
  *           NT = N*(N+1)/2. On entry, the matrix A in RFP Format.\n\
  *           RFP Format is described by TRANSR, UPLO and N as follows:\n\
  *           If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even;\n\
  *           K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If\n\
  *           TRANSR = 'T' then RFP is the transpose of RFP A as\n\
  *           defined when TRANSR = 'N'. The contents of RFP A are defined\n\
  *           by UPLO as follows: If UPLO = 'U' the RFP A contains the NT\n\
  *           elements of upper packed A either in normal or\n\
  *           transpose Format. If UPLO = 'L' the RFP A contains\n\
  *           the NT elements of lower packed A either in normal or\n\
  *           transpose Format. The LDA of RFP A is (N+1)/2 when\n\
  *           TRANSR = 'T'. When TRANSR is 'N' the LDA is N+1 when N is\n\
  *           even and is N when is odd.\n\
  *           See the Note below for more details. Unchanged on exit.\n\
  *\n\
  *  B       (input/output) REAL array,  DIMENSION (LDB,N)\n\
  *           Before entry,  the leading  m by n part of the array  B must\n\
  *           contain  the  right-hand  side  matrix  B,  and  on exit  is\n\
  *           overwritten by the solution matrix  X.\n\
  *\n\
  *  LDB     (input) INTEGER\n\
  *           On entry, LDB specifies the first dimension of B as declared\n\
  *           in  the  calling  (sub)  program.   LDB  must  be  at  least\n\
  *           max( 1, m ).\n\
  *           Unchanged on exit.\n\
  *\n\n\
  *  Further Details\n\
  *  ===============\n\
  *\n\
  *  We first consider Rectangular Full Packed (RFP) Format when N is\n\
  *  even. We give an example where N = 6.\n\
  *\n\
  *      AP is Upper             AP is Lower\n\
  *\n\
  *   00 01 02 03 04 05       00\n\
  *      11 12 13 14 15       10 11\n\
  *         22 23 24 25       20 21 22\n\
  *            33 34 35       30 31 32 33\n\
  *               44 45       40 41 42 43 44\n\
  *                  55       50 51 52 53 54 55\n\
  *\n\
  *\n\
  *  Let TRANSR = 'N'. RFP holds AP as follows:\n\
  *  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last\n\
  *  three columns of AP upper. The lower triangle A(4:6,0:2) consists of\n\
  *  the transpose of the first three columns of AP upper.\n\
  *  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first\n\
  *  three columns of AP lower. The upper triangle A(0:2,0:2) consists of\n\
  *  the transpose of the last three columns of AP lower.\n\
  *  This covers the case N even and TRANSR = 'N'.\n\
  *\n\
  *         RFP A                   RFP A\n\
  *\n\
  *        03 04 05                33 43 53\n\
  *        13 14 15                00 44 54\n\
  *        23 24 25                10 11 55\n\
  *        33 34 35                20 21 22\n\
  *        00 44 45                30 31 32\n\
  *        01 11 55                40 41 42\n\
  *        02 12 22                50 51 52\n\
  *\n\
  *  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the\n\
  *  transpose of RFP A above. One therefore gets:\n\
  *\n\
  *\n\
  *           RFP A                   RFP A\n\
  *\n\
  *     03 13 23 33 00 01 02    33 00 10 20 30 40 50\n\
  *     04 14 24 34 44 11 12    43 44 11 21 31 41 51\n\
  *     05 15 25 35 45 55 22    53 54 55 22 32 42 52\n\
  *\n\
  *\n\
  *  We then consider Rectangular Full Packed (RFP) Format when N is\n\
  *  odd. We give an example where N = 5.\n\
  *\n\
  *     AP is Upper                 AP is Lower\n\
  *\n\
  *   00 01 02 03 04              00\n\
  *      11 12 13 14              10 11\n\
  *         22 23 24              20 21 22\n\
  *            33 34              30 31 32 33\n\
  *               44              40 41 42 43 44\n\
  *\n\
  *\n\
  *  Let TRANSR = 'N'. RFP holds AP as follows:\n\
  *  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last\n\
  *  three columns of AP upper. The lower triangle A(3:4,0:1) consists of\n\
  *  the transpose of the first two columns of AP upper.\n\
  *  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first\n\
  *  three columns of AP lower. The upper triangle A(0:1,1:2) consists of\n\
  *  the transpose of the last two columns of AP lower.\n\
  *  This covers the case N odd and TRANSR = 'N'.\n\
  *\n\
  *         RFP A                   RFP A\n\
  *\n\
  *        02 03 04                00 33 43\n\
  *        12 13 14                10 11 44\n\
  *        22 23 24                20 21 22\n\
  *        00 33 34                30 31 32\n\
  *        01 11 44                40 41 42\n\
  *\n\
  *  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the\n\
  *  transpose of RFP A above. One therefore gets:\n\
  *\n\
  *           RFP A                   RFP A\n\
  *\n\
  *     02 12 22 00 01             00 10 20 30 40 50\n\
  *     03 13 23 33 11             33 11 21 31 41 51\n\
  *     04 14 24 34 44             43 44 22 32 42 52\n\
  *\n\
  *  Reference\n\
  *  =========\n\
  *\n\
  *  =====================================================================\n\
  *\n\
  *     ..\n"
