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

## Syntax

lapack_int LAPACKE_stfsm (int matrix_layout , char transr , char side , char uplo , char trans , char diag , lapack_int m , lapack_int n , float alpha , const float * a , float * b , lapack_int ldb );

lapack_int LAPACKE_dtfsm (int matrix_layout , char transr , char side , char uplo , char trans , char diag , lapack_int m , lapack_int n , double alpha , const double * a , double * b , lapack_int ldb );

lapack_int LAPACKE_ctfsm (int matrix_layout , char transr , char side , char uplo , char trans , char diag , lapack_int m , lapack_int n , lapack_complex_float alpha , const lapack_complex_float * a , lapack_complex_float * b , lapack_int ldb );

lapack_int LAPACKE_ztfsm (int matrix_layout , char transr , char side , char uplo , char trans , char diag , lapack_int m , lapack_int n , lapack_complex_double alpha , const lapack_complex_double * a , lapack_complex_double * b , lapack_int ldb );

• mkl.h

## Description

The ?tfsm routines solve one of the following matrix equations:

`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 in rectangular full packed (RFP) format.

op(A) can be one of the following:

• op(A) = A or op(A) = AT for real flavors

• op(A) = A or op(A) = AH for complex flavors

The matrix B is overwritten by the solution matrix X.

## Input Parameters

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major ( LAPACK_COL_MAJOR ).

transr

if transr = 'N' or 'n', the normal form of RFP A is stored;

if transr = 'T' or 't', the transpose form of RFP A is stored;

if transr = 'C' or 'c', the conjugate-transpose form of RFP A is stored.

side

Specifies whether op(A) appears on the left or right of X in the equation:

if side = 'L' or 'l', then op(A)*X = alpha*B;

if side = 'R' or 'r', then X*op(A) = alpha*B.

uplo

Specifies whether the RFP matrix A is upper or lower triangular:

if uplo = 'U' or 'u', then the matrix is upper triangular;

if uplo = 'L' or 'l', then the matrix is low triangular.

trans

Specifies the form of op(A) used in the matrix multiplication:

if trans = 'N' or 'n', then op(A) = A;

if trans = 'T' or 't', then op(A) = A';

if trans = 'C' or 'c', then op(A) = conjg(A').

diag

Specifies whether the RFP matrix A is unit triangular:

if diag = 'U' or 'u' then the matrix is unit triangular;

if diag = 'N' or 'n', then the matrix is not unit triangular.

m

Specifies the number of rows of B. The value of m must be at least zero.

n

Specifies the number of columns of B. The value of n must be at least zero.

alpha

Specifies the scalar alpha.

When alpha is zero, then a is not referenced and b need not be set before entry.

a

Array, size (n*(n+1)/2). Contains the matrix A in RFP format.

b

Array, size max(1, ldb*n) for column major and max(1, ldb*m) for row major.

Before entry, the leading m-by-n part of the array b must contain the right-hand side matrix B.

ldb

Specifies the leading dimension of b as declared in the calling (sub)program. The value of ldb must be at least max(1, m) for column major and max(1,n) for row major.

## Output Parameters

b

Overwritten by the solution matrix X.

## Return Values

This function returns a value info.

If info = 0, the execution is successful.

If info < 0, the i-th parameter had an illegal value.

If info = -1011, memory allocation error occurred.

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