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---
: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"
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