tfsm

stfsm

Functions

void stfsm(
    const char*          transr,
    const char*          side,
    const char*          uplo,
    const char*          trans,
    const char*          diag,
    const INT            m,
    const INT            n,
    const f32            alpha,
    const f32*  restrict A,
          f32*  restrict B,
    const INT            ldb
);

void stfsm(const char *transr, const char *side, const char *uplo, const char *trans, const char *diag, const INT m, const INT n, const f32 alpha, const f32 *restrict A, f32 *restrict B, const INT ldb)

Level 3 BLAS like routine for A in RFP Format.

STFSM solves the matrix equation

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 and op( A ) is one of

op( A ) = A or op( A ) = A**T.

A is in Rectangular Full Packed (RFP) Format.

The matrix X is overwritten on B.

Parameters

in

transr

= ‘N’: The Normal Form of RFP A is stored; = ‘T’: The Transpose Form of RFP A is stored.

in

side

On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows: SIDE = ‘L’ or ‘l’ op( A )*X = alpha*B. SIDE = ‘R’ or ‘r’ X*op( A ) = alpha*B.

in

uplo

On entry, UPLO specifies whether the RFP matrix A came from an upper or lower triangular matrix as follows: UPLO = ‘U’ or ‘u’ RFP A came from an upper triangular matrix UPLO = ‘L’ or ‘l’ RFP A came from a lower triangular matrix

in

trans

On entry, TRANS specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANS = ‘N’ or ‘n’ op( A ) = A. TRANS = ‘T’ or ‘t’ op( A ) = A’.

in

diag

On entry, DIAG specifies whether or not RFP A is unit triangular as follows: DIAG = ‘U’ or ‘u’ A is assumed to be unit triangular. DIAG = ‘N’ or ‘n’ A is not assumed to be unit triangular.

in

m

On entry, M specifies the number of rows of B. M must be at least zero.

in

n

On entry, N specifies the number of columns of B. N must be at least zero.

in

alpha

On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry.

in

A

Double precision array, dimension (NT) NT = N*(N+1)/2 if SIDE=’R’ and NT = M*(M+1)/2 otherwise. On entry, the matrix A in RFP Format.

inout

B

Double precision array, dimension (LDB,N) Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X.

in

ldb

On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).

dtfsm

Functions

void dtfsm(
    const char*          transr,
    const char*          side,
    const char*          uplo,
    const char*          trans,
    const char*          diag,
    const INT            m,
    const INT            n,
    const f64            alpha,
    const f64*  restrict A,
          f64*  restrict B,
    const INT            ldb
);

void dtfsm(const char *transr, const char *side, const char *uplo, const char *trans, const char *diag, const INT m, const INT n, const f64 alpha, const f64 *restrict A, f64 *restrict B, const INT ldb)

Level 3 BLAS like routine for A in RFP Format.

DTFSM solves the matrix equation

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 and op( A ) is one of

op( A ) = A or op( A ) = A**T.

A is in Rectangular Full Packed (RFP) Format.

The matrix X is overwritten on B.

Parameters

in

transr

= ‘N’: The Normal Form of RFP A is stored; = ‘T’: The Transpose Form of RFP A is stored.

in

side

On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows: SIDE = ‘L’ or ‘l’ op( A )*X = alpha*B. SIDE = ‘R’ or ‘r’ X*op( A ) = alpha*B.

in

uplo

On entry, UPLO specifies whether the RFP matrix A came from an upper or lower triangular matrix as follows: UPLO = ‘U’ or ‘u’ RFP A came from an upper triangular matrix UPLO = ‘L’ or ‘l’ RFP A came from a lower triangular matrix

in

trans

On entry, TRANS specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANS = ‘N’ or ‘n’ op( A ) = A. TRANS = ‘T’ or ‘t’ op( A ) = A’.

in

diag

On entry, DIAG specifies whether or not RFP A is unit triangular as follows: DIAG = ‘U’ or ‘u’ A is assumed to be unit triangular. DIAG = ‘N’ or ‘n’ A is not assumed to be unit triangular.

in

m

On entry, M specifies the number of rows of B. M must be at least zero.

in

n

On entry, N specifies the number of columns of B. N must be at least zero.

in

alpha

On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry.

in

A

Double precision array, dimension (NT) NT = N*(N+1)/2 if SIDE=’R’ and NT = M*(M+1)/2 otherwise. On entry, the matrix A in RFP Format.

inout

B

Double precision array, dimension (LDB,N) Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X.

in

ldb

On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).

ctfsm

Functions

void ctfsm(
    const char*          transr,
    const char*          side,
    const char*          uplo,
    const char*          trans,
    const char*          diag,
    const INT            m,
    const INT            n,
    const c64            alpha,
    const c64*  restrict A,
          c64*  restrict B,
    const INT            ldb
);

void ctfsm(const char *transr, const char *side, const char *uplo, const char *trans, const char *diag, const INT m, const INT n, const c64 alpha, const c64 *restrict A, c64 *restrict B, const INT ldb)

Level 3 BLAS like routine for A in RFP Format.

CTFSM solves the matrix equation

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 and op( A ) is one of

op( A ) = A or op( A ) = A**H.

A is in Rectangular Full Packed (RFP) Format.

The matrix X is overwritten on B.

Parameters

in

transr

= ‘N’: The Normal Form of RFP A is stored; = ‘C’: The Conjugate-transpose Form of RFP A is stored.

in

side

On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows: SIDE = ‘L’ or ‘l’ op( A )*X = alpha*B. SIDE = ‘R’ or ‘r’ X*op( A ) = alpha*B.

in

uplo

On entry, UPLO specifies whether the RFP matrix A came from an upper or lower triangular matrix as follows: UPLO = ‘U’ or ‘u’ RFP A came from an upper triangular matrix UPLO = ‘L’ or ‘l’ RFP A came from a lower triangular matrix

in

trans

On entry, TRANS specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANS = ‘N’ or ‘n’ op( A ) = A. TRANS = ‘C’ or ‘c’ op( A ) = conjg( A’ ).

in

diag

On entry, DIAG specifies whether or not RFP A is unit triangular as follows: DIAG = ‘U’ or ‘u’ A is assumed to be unit triangular. DIAG = ‘N’ or ‘n’ A is not assumed to be unit triangular.

in

m

On entry, M specifies the number of rows of B. M must be at least zero.

in

n

On entry, N specifies the number of columns of B. N must be at least zero.

in

alpha

On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry.

in

A

Complex*16 array, dimension (NT) NT = N*(N+1)/2 if SIDE=’R’ and NT = M*(M+1)/2 otherwise. On entry, the matrix A in RFP Format.

inout

B

Complex*16 array, dimension (LDB,N) Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X.

in

ldb

On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).

ztfsm

Functions

void ztfsm(
    const char*          transr,
    const char*          side,
    const char*          uplo,
    const char*          trans,
    const char*          diag,
    const INT            m,
    const INT            n,
    const c128           alpha,
    const c128* restrict A,
          c128* restrict B,
    const INT            ldb
);

void ztfsm(const char *transr, const char *side, const char *uplo, const char *trans, const char *diag, const INT m, const INT n, const c128 alpha, const c128 *restrict A, c128 *restrict B, const INT ldb)

Level 3 BLAS like routine for A in RFP Format.

ZTFSM solves the matrix equation

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 and op( A ) is one of

op( A ) = A or op( A ) = A**H.

A is in Rectangular Full Packed (RFP) Format.

The matrix X is overwritten on B.

Parameters

in

transr

= ‘N’: The Normal Form of RFP A is stored; = ‘C’: The Conjugate-transpose Form of RFP A is stored.

in

side

On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows: SIDE = ‘L’ or ‘l’ op( A )*X = alpha*B. SIDE = ‘R’ or ‘r’ X*op( A ) = alpha*B.

in

uplo

On entry, UPLO specifies whether the RFP matrix A came from an upper or lower triangular matrix as follows: UPLO = ‘U’ or ‘u’ RFP A came from an upper triangular matrix UPLO = ‘L’ or ‘l’ RFP A came from a lower triangular matrix

in

trans

On entry, TRANS specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANS = ‘N’ or ‘n’ op( A ) = A. TRANS = ‘C’ or ‘c’ op( A ) = conjg( A’ ).

in

diag

On entry, DIAG specifies whether or not RFP A is unit triangular as follows: DIAG = ‘U’ or ‘u’ A is assumed to be unit triangular. DIAG = ‘N’ or ‘n’ A is not assumed to be unit triangular.

in

m

On entry, M specifies the number of rows of B. M must be at least zero.

in

n

On entry, N specifies the number of columns of B. N must be at least zero.

in

alpha

On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry.

in

A

Complex*16 array, dimension (NT) NT = N*(N+1)/2 if SIDE=’R’ and NT = M*(M+1)/2 otherwise. On entry, the matrix A in RFP Format.

inout

B

Complex*16 array, dimension (LDB,N) Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X.

in

ldb

On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).