double_blas_level3(3) LAPACK double_blas_level3(3)

# NAME¶

double_blas_level3

# SYNOPSIS¶

## Functions¶

subroutine dgemm (TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM subroutine dsymm (SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DSYMM subroutine dsyr2k (UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DSYR2K subroutine dsyrk (UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
DSYRK subroutine dtrmm (SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRMM subroutine dtrsm (SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM

# Detailed Description¶

This is the group of double LEVEL 3 BLAS routines.

# Function Documentation¶

## subroutine dgemm (character TRANSA, character TRANSB, integer M, integer N, integer K, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(ldb,*) B, integer LDB, double precision BETA, double precision, dimension(ldc,*) C, integer LDC)¶

DGEMM

Purpose:

```
DGEMM  performs one of the matrix-matrix operations

C := alpha*op( A )*op( B ) + beta*C,

where  op( X ) is one of

op( X ) = X   or   op( X ) = X**T,

alpha and beta are scalars, and A, B and C are matrices, with op( A )

an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.```

Parameters

TRANSA

```
TRANSA is CHARACTER*1

On entry, TRANSA specifies the form of op( A ) to be used in

the matrix multiplication as follows:

TRANSA = 'N' or 'n',  op( A ) = A.

TRANSA = 'T' or 't',  op( A ) = A**T.

TRANSA = 'C' or 'c',  op( A ) = A**T.```

TRANSB

```
TRANSB is CHARACTER*1

On entry, TRANSB specifies the form of op( B ) to be used in

the matrix multiplication as follows:

TRANSB = 'N' or 'n',  op( B ) = B.

TRANSB = 'T' or 't',  op( B ) = B**T.

TRANSB = 'C' or 'c',  op( B ) = B**T.```

M

```
M is INTEGER

On entry,  M  specifies  the number  of rows  of the  matrix

op( A )  and of the  matrix  C.  M  must  be at least  zero.```

N

```
N is INTEGER

On entry,  N  specifies the number  of columns of the matrix

op( B ) and the number of columns of the matrix C. N must be

at least zero.```

K

```
K is INTEGER

On entry,  K  specifies  the number of columns of the matrix

op( A ) and the number of rows of the matrix op( B ). K must

be at least  zero.```

ALPHA

```
ALPHA is DOUBLE PRECISION.

On entry, ALPHA specifies the scalar alpha.```

A

```
A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is

k  when  TRANSA = 'N' or 'n',  and is  m  otherwise.

Before entry with  TRANSA = 'N' or 'n',  the leading  m by k

part of the array  A  must contain the matrix  A,  otherwise

the leading  k by m  part of the array  A  must contain  the

matrix A.```

LDA

```
LDA is INTEGER

On entry, LDA specifies the first dimension of A as declared

in the calling (sub) program. When  TRANSA = 'N' or 'n' then

LDA must be at least  max( 1, m ), otherwise  LDA must be at

least  max( 1, k ).```

B

```
B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is

n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.

Before entry with  TRANSB = 'N' or 'n',  the leading  k by n

part of the array  B  must contain the matrix  B,  otherwise

the leading  n by k  part of the array  B  must contain  the

matrix B.```

LDB

```
LDB is INTEGER

On entry, LDB specifies the first dimension of B as declared

in the calling (sub) program. When  TRANSB = 'N' or 'n' then

LDB must be at least  max( 1, k ), otherwise  LDB must be at

least  max( 1, n ).```

BETA

```
BETA is DOUBLE PRECISION.

On entry,  BETA  specifies the scalar  beta.  When  BETA  is

supplied as zero then C need not be set on input.```

C

```
C is DOUBLE PRECISION array, dimension ( LDC, N )

Before entry, the leading  m by n  part of the array  C must

contain the matrix  C,  except when  beta  is zero, in which

case C need not be set on entry.

On exit, the array  C  is overwritten by the  m by n  matrix

( alpha*op( A )*op( B ) + beta*C ).```

LDC

```
LDC is INTEGER

On entry, LDC specifies the first dimension of C as declared

in  the  calling  (sub)  program.   LDC  must  be  at  least

max( 1, m ).```

Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date

December 2016

Further Details:

```
Level 3 Blas routine.

-- Written on 8-February-1989.

Jack Dongarra, Argonne National Laboratory.

Iain Duff, AERE Harwell.

Jeremy Du Croz, Numerical Algorithms Group Ltd.

Sven Hammarling, Numerical Algorithms Group Ltd.```

## subroutine dsymm (character SIDE, character UPLO, integer M, integer N, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(ldb,*) B, integer LDB, double precision BETA, double precision, dimension(ldc,*) C, integer LDC)¶

DSYMM

Purpose:

```
DSYMM  performs one of the matrix-matrix operations

C := alpha*A*B + beta*C,

or

C := alpha*B*A + beta*C,

where alpha and beta are scalars,  A is a symmetric matrix and  B and

C are  m by n matrices.```

Parameters

SIDE

```
SIDE is CHARACTER*1

On entry,  SIDE  specifies whether  the  symmetric matrix  A

appears on the  left or right  in the  operation as follows:

SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,

SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,```

UPLO

```
UPLO is CHARACTER*1

On  entry,   UPLO  specifies  whether  the  upper  or  lower

triangular  part  of  the  symmetric  matrix   A  is  to  be

referenced as follows:

UPLO = 'U' or 'u'   Only the upper triangular part of the

symmetric matrix is to be referenced.

UPLO = 'L' or 'l'   Only the lower triangular part of the

symmetric matrix is to be referenced.```

M

```
M is INTEGER

On entry,  M  specifies the number of rows of the matrix  C.

M  must be at least zero.```

N

```
N is INTEGER

On entry, N specifies the number of columns of the matrix C.

N  must be at least zero.```

ALPHA

```
ALPHA is DOUBLE PRECISION.

On entry, ALPHA specifies the scalar alpha.```

A

```
A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is

m  when  SIDE = 'L' or 'l'  and is  n otherwise.

Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of

the array  A  must contain the  symmetric matrix,  such that

when  UPLO = 'U' or 'u', the leading m by m upper triangular

part of the array  A  must contain the upper triangular part

of the  symmetric matrix and the  strictly  lower triangular

part of  A  is not referenced,  and when  UPLO = 'L' or 'l',

the leading  m by m  lower triangular part  of the  array  A

must  contain  the  lower triangular part  of the  symmetric

matrix and the  strictly upper triangular part of  A  is not

referenced.

Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of

the array  A  must contain the  symmetric matrix,  such that

when  UPLO = 'U' or 'u', the leading n by n upper triangular

part of the array  A  must contain the upper triangular part

of the  symmetric matrix and the  strictly  lower triangular

part of  A  is not referenced,  and when  UPLO = 'L' or 'l',

the leading  n by n  lower triangular part  of the  array  A

must  contain  the  lower triangular part  of the  symmetric

matrix and the  strictly upper triangular part of  A  is not

referenced.```

LDA

```
LDA is INTEGER

On entry, LDA specifies the first dimension of A as declared

in the calling (sub) program.  When  SIDE = 'L' or 'l'  then

LDA must be at least  max( 1, m ), otherwise  LDA must be at

least  max( 1, n ).```

B

```
B is DOUBLE PRECISION array, dimension ( LDB, N )

Before entry, the leading  m by n part of the array  B  must

contain the matrix B.```

LDB

```
LDB is INTEGER

On entry, LDB specifies the first dimension of B as declared

in  the  calling  (sub)  program.   LDB  must  be  at  least

max( 1, m ).```

BETA

```
BETA is DOUBLE PRECISION.

On entry,  BETA  specifies the scalar  beta.  When  BETA  is

supplied as zero then C need not be set on input.```

C

```
C is DOUBLE PRECISION array, dimension ( LDC, N )

Before entry, the leading  m by n  part of the array  C must

contain the matrix  C,  except when  beta  is zero, in which

case C need not be set on entry.

On exit, the array  C  is overwritten by the  m by n updated

matrix.```

LDC

```
LDC is INTEGER

On entry, LDC specifies the first dimension of C as declared

in  the  calling  (sub)  program.   LDC  must  be  at  least

max( 1, m ).```

Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date

December 2016

Further Details:

```
Level 3 Blas routine.

-- Written on 8-February-1989.

Jack Dongarra, Argonne National Laboratory.

Iain Duff, AERE Harwell.

Jeremy Du Croz, Numerical Algorithms Group Ltd.

Sven Hammarling, Numerical Algorithms Group Ltd.```

## subroutine dsyr2k (character UPLO, character TRANS, integer N, integer K, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(ldb,*) B, integer LDB, double precision BETA, double precision, dimension(ldc,*) C, integer LDC)¶

DSYR2K

Purpose:

```
DSYR2K  performs one of the symmetric rank 2k operations

C := alpha*A*B**T + alpha*B*A**T + beta*C,

or

C := alpha*A**T*B + alpha*B**T*A + beta*C,

where  alpha and beta  are scalars, C is an  n by n  symmetric matrix

and  A and B  are  n by k  matrices  in the  first  case  and  k by n

matrices in the second case.```

Parameters

UPLO

```
UPLO is CHARACTER*1

On  entry,   UPLO  specifies  whether  the  upper  or  lower

triangular  part  of the  array  C  is to be  referenced  as

follows:

UPLO = 'U' or 'u'   Only the  upper triangular part of  C

is to be referenced.

UPLO = 'L' or 'l'   Only the  lower triangular part of  C

is to be referenced.```

TRANS

```
TRANS is CHARACTER*1

On entry,  TRANS  specifies the operation to be performed as

follows:

TRANS = 'N' or 'n'   C := alpha*A*B**T + alpha*B*A**T +

beta*C.

TRANS = 'T' or 't'   C := alpha*A**T*B + alpha*B**T*A +

beta*C.

TRANS = 'C' or 'c'   C := alpha*A**T*B + alpha*B**T*A +

beta*C.```

N

```
N is INTEGER

On entry,  N specifies the order of the matrix C.  N must be

at least zero.```

K

```
K is INTEGER

On entry with  TRANS = 'N' or 'n',  K  specifies  the number

of  columns  of the  matrices  A and B,  and on  entry  with

TRANS = 'T' or 't' or 'C' or 'c',  K  specifies  the  number

of rows of the matrices  A and B.  K must be at least  zero.```

ALPHA

```
ALPHA is DOUBLE PRECISION.

On entry, ALPHA specifies the scalar alpha.```

A

```
A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is

k  when  TRANS = 'N' or 'n',  and is  n  otherwise.

Before entry with  TRANS = 'N' or 'n',  the  leading  n by k

part of the array  A  must contain the matrix  A,  otherwise

the leading  k by n  part of the array  A  must contain  the

matrix A.```

LDA

```
LDA is INTEGER

On entry, LDA specifies the first dimension of A as declared

in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'

then  LDA must be at least  max( 1, n ), otherwise  LDA must

be at least  max( 1, k ).```

B

```
B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is

k  when  TRANS = 'N' or 'n',  and is  n  otherwise.

Before entry with  TRANS = 'N' or 'n',  the  leading  n by k

part of the array  B  must contain the matrix  B,  otherwise

the leading  k by n  part of the array  B  must contain  the

matrix B.```

LDB

```
LDB is INTEGER

On entry, LDB specifies the first dimension of B as declared

in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'

then  LDB must be at least  max( 1, n ), otherwise  LDB must

be at least  max( 1, k ).```

BETA

```
BETA is DOUBLE PRECISION.

On entry, BETA specifies the scalar beta.```

C

```
C is DOUBLE PRECISION array, dimension ( LDC, N )

Before entry  with  UPLO = 'U' or 'u',  the leading  n by n

upper triangular part of the array C must contain the upper

triangular part  of the  symmetric matrix  and the strictly

lower triangular part of C is not referenced.  On exit, the

upper triangular part of the array  C is overwritten by the

upper triangular part of the updated matrix.

Before entry  with  UPLO = 'L' or 'l',  the leading  n by n

lower triangular part of the array C must contain the lower

triangular part  of the  symmetric matrix  and the strictly

upper triangular part of C is not referenced.  On exit, the

lower triangular part of the array  C is overwritten by the

lower triangular part of the updated matrix.```

LDC

```
LDC is INTEGER

On entry, LDC specifies the first dimension of C as declared

in  the  calling  (sub)  program.   LDC  must  be  at  least

max( 1, n ).```

Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date

December 2016

Further Details:

```
Level 3 Blas routine.

-- Written on 8-February-1989.

Jack Dongarra, Argonne National Laboratory.

Iain Duff, AERE Harwell.

Jeremy Du Croz, Numerical Algorithms Group Ltd.

Sven Hammarling, Numerical Algorithms Group Ltd.```

## subroutine dsyrk (character UPLO, character TRANS, integer N, integer K, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA, double precision BETA, double precision, dimension(ldc,*) C, integer LDC)¶

DSYRK

Purpose:

```
DSYRK  performs one of the symmetric rank k operations

C := alpha*A*A**T + beta*C,

or

C := alpha*A**T*A + beta*C,

where  alpha and beta  are scalars, C is an  n by n  symmetric matrix

and  A  is an  n by k  matrix in the first case and a  k by n  matrix

in the second case.```

Parameters

UPLO

```
UPLO is CHARACTER*1

On  entry,   UPLO  specifies  whether  the  upper  or  lower

triangular  part  of the  array  C  is to be  referenced  as

follows:

UPLO = 'U' or 'u'   Only the  upper triangular part of  C

is to be referenced.

UPLO = 'L' or 'l'   Only the  lower triangular part of  C

is to be referenced.```

TRANS

```
TRANS is CHARACTER*1

On entry,  TRANS  specifies the operation to be performed as

follows:

TRANS = 'N' or 'n'   C := alpha*A*A**T + beta*C.

TRANS = 'T' or 't'   C := alpha*A**T*A + beta*C.

TRANS = 'C' or 'c'   C := alpha*A**T*A + beta*C.```

N

```
N is INTEGER

On entry,  N specifies the order of the matrix C.  N must be

at least zero.```

K

```
K is INTEGER

On entry with  TRANS = 'N' or 'n',  K  specifies  the number

of  columns   of  the   matrix   A,   and  on   entry   with

TRANS = 'T' or 't' or 'C' or 'c',  K  specifies  the  number

of rows of the matrix  A.  K must be at least zero.```

ALPHA

```
ALPHA is DOUBLE PRECISION.

On entry, ALPHA specifies the scalar alpha.```

A

```
A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is

k  when  TRANS = 'N' or 'n',  and is  n  otherwise.

Before entry with  TRANS = 'N' or 'n',  the  leading  n by k

part of the array  A  must contain the matrix  A,  otherwise

the leading  k by n  part of the array  A  must contain  the

matrix A.```

LDA

```
LDA is INTEGER

On entry, LDA specifies the first dimension of A as declared

in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'

then  LDA must be at least  max( 1, n ), otherwise  LDA must

be at least  max( 1, k ).```

BETA

```
BETA is DOUBLE PRECISION.

On entry, BETA specifies the scalar beta.```

C

```
C is DOUBLE PRECISION array, dimension ( LDC, N )

Before entry  with  UPLO = 'U' or 'u',  the leading  n by n

upper triangular part of the array C must contain the upper

triangular part  of the  symmetric matrix  and the strictly

lower triangular part of C is not referenced.  On exit, the

upper triangular part of the array  C is overwritten by the

upper triangular part of the updated matrix.

Before entry  with  UPLO = 'L' or 'l',  the leading  n by n

lower triangular part of the array C must contain the lower

triangular part  of the  symmetric matrix  and the strictly

upper triangular part of C is not referenced.  On exit, the

lower triangular part of the array  C is overwritten by the

lower triangular part of the updated matrix.```

LDC

```
LDC is INTEGER

On entry, LDC specifies the first dimension of C as declared

in  the  calling  (sub)  program.   LDC  must  be  at  least

max( 1, n ).```

Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date

December 2016

Further Details:

```
Level 3 Blas routine.

-- Written on 8-February-1989.

Jack Dongarra, Argonne National Laboratory.

Iain Duff, AERE Harwell.

Jeremy Du Croz, Numerical Algorithms Group Ltd.

Sven Hammarling, Numerical Algorithms Group Ltd.```

## subroutine dtrmm (character SIDE, character UPLO, character TRANSA, character DIAG, integer M, integer N, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(ldb,*) B, integer LDB)¶

DTRMM

Purpose:

```
DTRMM  performs one of the matrix-matrix operations

B := alpha*op( A )*B,   or   B := alpha*B*op( A ),

where  alpha  is a scalar,  B  is an m by n matrix,  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.```

Parameters

SIDE

```
SIDE is CHARACTER*1

On entry,  SIDE specifies whether  op( A ) multiplies B from

the left or right as follows:

SIDE = 'L' or 'l'   B := alpha*op( A )*B.

SIDE = 'R' or 'r'   B := alpha*B*op( A ).```

UPLO

```
UPLO is CHARACTER*1

On entry, UPLO specifies whether the matrix A is an upper or

lower triangular matrix as follows:

UPLO = 'U' or 'u'   A is an upper triangular matrix.

UPLO = 'L' or 'l'   A is a lower triangular matrix.```

TRANSA

```
TRANSA is CHARACTER*1

On entry, TRANSA specifies the form of op( A ) to be used in

the matrix multiplication as follows:

TRANSA = 'N' or 'n'   op( A ) = A.

TRANSA = 'T' or 't'   op( A ) = A**T.

TRANSA = 'C' or 'c'   op( A ) = A**T.```

DIAG

```
DIAG is CHARACTER*1

On entry, DIAG specifies whether or not 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.```

M

```
M is INTEGER

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

least zero.```

N

```
N is INTEGER

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

at least zero.```

ALPHA

```
ALPHA is DOUBLE PRECISION.

On entry,  ALPHA specifies the scalar  alpha. When  alpha is

zero then  A is not referenced and  B need not be set before

entry.```

A

```
A is DOUBLE PRECISION array, dimension ( LDA, k ), where k is m

when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.

Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k

upper triangular part of the array  A must contain the upper

triangular matrix  and the strictly lower triangular part of

A is not referenced.

Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k

lower triangular part of the array  A must contain the lower

triangular matrix  and the strictly upper triangular part of

A is not referenced.

Note that when  DIAG = 'U' or 'u',  the diagonal elements of

A  are not referenced either,  but are assumed to be  unity.```

LDA

```
LDA is INTEGER

On entry, LDA specifies the first dimension of A as declared

in the calling (sub) program.  When  SIDE = 'L' or 'l'  then

LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'

then LDA must be at least max( 1, n ).```

B

```
B is DOUBLE PRECISION array, dimension ( LDB, N )

Before entry,  the leading  m by n part of the array  B must

contain the matrix  B,  and  on exit  is overwritten  by the

transformed matrix.```

LDB

```
LDB is INTEGER

On entry, LDB specifies the first dimension of B as declared

in  the  calling  (sub)  program.   LDB  must  be  at  least

max( 1, m ).```

Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date

December 2016

Further Details:

```
Level 3 Blas routine.

-- Written on 8-February-1989.

Jack Dongarra, Argonne National Laboratory.

Iain Duff, AERE Harwell.

Jeremy Du Croz, Numerical Algorithms Group Ltd.

Sven Hammarling, Numerical Algorithms Group Ltd.```

## subroutine dtrsm (character SIDE, character UPLO, character TRANSA, character DIAG, integer M, integer N, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(ldb,*) B, integer LDB)¶

DTRSM

Purpose:

```
DTRSM  solves one of the 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  and  op( A )  is one  of

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

The matrix X is overwritten on B.```

Parameters

SIDE

```
SIDE is CHARACTER*1

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.```

UPLO

```
UPLO is CHARACTER*1

On entry, UPLO specifies whether the matrix A is an upper or

lower triangular matrix as follows:

UPLO = 'U' or 'u'   A is an upper triangular matrix.

UPLO = 'L' or 'l'   A is a lower triangular matrix.```

TRANSA

```
TRANSA is CHARACTER*1

On entry, TRANSA specifies the form of op( A ) to be used in

the matrix multiplication as follows:

TRANSA = 'N' or 'n'   op( A ) = A.

TRANSA = 'T' or 't'   op( A ) = A**T.

TRANSA = 'C' or 'c'   op( A ) = A**T.```

DIAG

```
DIAG is CHARACTER*1

On entry, DIAG specifies whether or not 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.```

M

```
M is INTEGER

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

least zero.```

N

```
N is INTEGER

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

at least zero.```

ALPHA

```
ALPHA is DOUBLE PRECISION.

On entry,  ALPHA specifies the scalar  alpha. When  alpha is

zero then  A is not referenced and  B need not be set before

entry.```

A

```
A is DOUBLE PRECISION array, dimension ( LDA, k ),

where k is m when SIDE = 'L' or 'l'

and k is n when SIDE = 'R' or 'r'.

Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k

upper triangular part of the array  A must contain the upper

triangular matrix  and the strictly lower triangular part of

A is not referenced.

Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k

lower triangular part of the array  A must contain the lower

triangular matrix  and the strictly upper triangular part of

A is not referenced.

Note that when  DIAG = 'U' or 'u',  the diagonal elements of

A  are not referenced either,  but are assumed to be  unity.```

LDA

```
LDA is INTEGER

On entry, LDA specifies the first dimension of A as declared

in the calling (sub) program.  When  SIDE = 'L' or 'l'  then

LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'

then LDA must be at least max( 1, n ).```

B

```
B is 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.```

LDB

```
LDB is INTEGER

On entry, LDB specifies the first dimension of B as declared

in  the  calling  (sub)  program.   LDB  must  be  at  least

max( 1, m ).```

Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date

December 2016

Further Details:

```
Level 3 Blas routine.

-- Written on 8-February-1989.

Jack Dongarra, Argonne National Laboratory.

Iain Duff, AERE Harwell.

Jeremy Du Croz, Numerical Algorithms Group Ltd.

Sven Hammarling, Numerical Algorithms Group Ltd.```

# Author¶

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