?tfsm

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?tfsm

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

Syntax

call stfsm ( transr , side , uplo , trans , diag , m , n , alpha , a , b , ldb )

call dtfsm ( transr , side , uplo , trans , diag , m , n , alpha , a , b , ldb )

call ctfsm ( transr , side , uplo , trans , diag , m , n , alpha , a , b , ldb )

call ztfsm ( transr , side , uplo , trans , diag , m , n , alpha , a , b , ldb )

Include Files

mkl.fi

Description

stfsm dtfsm ctfsm ztfsm tfsm

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

transr

CHARACTER*1 .

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

CHARACTER*1 . 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

CHARACTER*1 . 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

CHARACTER*1 . 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

CHARACTER*1 . 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

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

n

INTEGER . 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)

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

ldb

INTEGER . Specifies the leading dimension of b as declared in the calling (sub)program. The value of ldb must be at least max(1, m ) .

Output Parameters

b: Overwritten by the solution matrix X .

Return Values

No return value.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?tfsm

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values