?tfsm

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?tfsm

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);

Include Files

mkl.h

Description

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

op( A )* X = alpha * B ,

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) = A^{T} for real flavors op(A) = A or op(A) = A^{H} 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

REAL for stfsm DOUBLE PRECISION for dtfsm COMPLEX for ctfsm DOUBLE COMPLEX for ztfsm Specifies the scalar alpha . When alpha is zero, then a is not referenced and b need not be set before entry.

a

REAL for stfsm DOUBLE PRECISION for dtfsm COMPLEX for ctfsm DOUBLE COMPLEX for ztfsm Array, size (n*(n+1)/2) . Contains the matrix A in RFP format .

b

REAL for stfsm DOUBLE PRECISION for dtfsm COMPLEX for ctfsm DOUBLE COMPLEX for ztfsm

Array, size (1, ldb*n)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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Developer Reference for Intel® oneAPI Math Kernel Library for C

?tfsm

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values