LinearAlgebraOperations<T>.MultiplyAndAddInPlace Method

public void MultiplyAndAddInPlace(
	int n,
	T a,
	ArraySlice<T> x,
	ArraySlice<T> y
)

Public Sub MultiplyAndAddInPlace ( 
	n As Integer,
	a As T,
	x As ArraySlice(Of T),
	y As ArraySlice(Of T)
)

public:
void MultiplyAndAddInPlace(
	int n, 
	T a, 
	ArraySlice<T> x, 
	ArraySlice<T> y
)

member MultiplyAndAddInPlace : 
        n : int * 
        a : 'T * 
        x : ArraySlice<'T> * 
        y : ArraySlice<'T> -> unit 

Parameters

n  Int32

 

a  T

 

x  ArraySlice<T>

 

y  ArraySlice<T>

 

            uses unrolled loops for increments equal to one.
            

Further Details:

            jack dongarra, linpack, 3/11/78.
            modified 12/3/93, array(1) declarations changed to array(*)
            

Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Date: November 2011

public void MultiplyAndAddInPlace(
	int n,
	Complex<T> za,
	ArraySlice<Complex<T>> x,
	ArraySlice<Complex<T>> y
)

Public Sub MultiplyAndAddInPlace ( 
	n As Integer,
	za As Complex(Of T),
	x As ArraySlice(Of Complex(Of T)),
	y As ArraySlice(Of Complex(Of T))
)

public:
void MultiplyAndAddInPlace(
	int n, 
	Complex<T> za, 
	ArraySlice<Complex<T>> x, 
	ArraySlice<Complex<T>> y
)

member MultiplyAndAddInPlace : 
        n : int * 
        za : Complex<'T> * 
        x : ArraySlice<Complex<'T>> * 
        y : ArraySlice<Complex<'T>> -> unit 

Parameters

n  Int32

 

za  Complex<T>

 

x  ArraySlice<Complex<T>>

 

y  ArraySlice<Complex<T>>

 

 Further Details:
            jack dongarra, 3/11/78.
            modified 12/3/93, array(1) declarations changed to array(*)
            
Authors: 
             Univ. of Tennessee,
             Univ. of California Berkeley,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

public void MultiplyAndAddInPlace(
	int n,
	Complex<T> za,
	ReadOnlySpanSlice<Complex<T>> x,
	SpanSlice<Complex<T>> y
)

Public Sub MultiplyAndAddInPlace ( 
	n As Integer,
	za As Complex(Of T),
	x As ReadOnlySpanSlice(Of Complex(Of T)),
	y As SpanSlice(Of Complex(Of T))
)

public:
void MultiplyAndAddInPlace(
	int n, 
	Complex<T> za, 
	ReadOnlySpanSlice<Complex<T>> x, 
	SpanSlice<Complex<T>> y
)

member MultiplyAndAddInPlace : 
        n : int * 
        za : Complex<'T> * 
        x : ReadOnlySpanSlice<Complex<'T>> * 
        y : SpanSlice<Complex<'T>> -> unit 

Parameters

n  Int32

 

za  Complex<T>

 

x  ReadOnlySpanSlice<Complex<T>>

 

y  SpanSlice<Complex<T>>

 

 Further Details:
            jack dongarra, 3/11/78.
            modified 12/3/93, array(1) declarations changed to array(*)
            
Authors: 
             Univ. of Tennessee,
             Univ. of California Berkeley,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

public abstract void MultiplyAndAddInPlace(
	int n,
	T a,
	ReadOnlySpan<T> x,
	int incx,
	Span<T> y,
	int incy
)

Public MustOverride Sub MultiplyAndAddInPlace ( 
	n As Integer,
	a As T,
	x As ReadOnlySpan(Of T),
	incx As Integer,
	y As Span(Of T),
	incy As Integer
)

public:
virtual void MultiplyAndAddInPlace(
	int n, 
	T a, 
	ReadOnlySpan<T> x, 
	int incx, 
	Span<T> y, 
	int incy
) abstract

abstract MultiplyAndAddInPlace : 
        n : int * 
        a : 'T * 
        x : ReadOnlySpan<'T> * 
        incx : int * 
        y : Span<'T> * 
        incy : int -> unit 

Parameters

n  Int32

 

a  T

 

x  ReadOnlySpan<T>

 

incx  Int32

 

y  Span<T>

 

incy  Int32

 

Implements

            uses unrolled loops for increments equal to one.
            

Further Details:

            jack dongarra, linpack, 3/11/78.
            modified 12/3/93, array(1) declarations changed to array(*)
            

Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Date: November 2011

public abstract void MultiplyAndAddInPlace(
	int n,
	Complex<T> za,
	ReadOnlySpan<Complex<T>> zx,
	int incx,
	Span<Complex<T>> zy,
	int incy
)

Public MustOverride Sub MultiplyAndAddInPlace ( 
	n As Integer,
	za As Complex(Of T),
	zx As ReadOnlySpan(Of Complex(Of T)),
	incx As Integer,
	zy As Span(Of Complex(Of T)),
	incy As Integer
)

public:
virtual void MultiplyAndAddInPlace(
	int n, 
	Complex<T> za, 
	ReadOnlySpan<Complex<T>> zx, 
	int incx, 
	Span<Complex<T>> zy, 
	int incy
) abstract

abstract MultiplyAndAddInPlace : 
        n : int * 
        za : Complex<'T> * 
        zx : ReadOnlySpan<Complex<'T>> * 
        incx : int * 
        zy : Span<Complex<'T>> * 
        incy : int -> unit 

Parameters

n  Int32

 

za  Complex<T>

 

zx  ReadOnlySpan<Complex<T>>

 

incx  Int32

 

zy  Span<Complex<T>>

 

incy  Int32

 

Implements

 Further Details:
            jack dongarra, 3/11/78.
            modified 12/3/93, array(1) declarations changed to array(*)
            
Authors: 
             Univ. of Tennessee,
             Univ. of California Berkeley,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

public void MultiplyAndAddInPlace(
	TransposeOperation trans,
	int m,
	int n,
	T alpha,
	Array2D<T> a,
	ArraySlice<T> x,
	T beta,
	ArraySlice<T> y
)

Public Sub MultiplyAndAddInPlace ( 
	trans As TransposeOperation,
	m As Integer,
	n As Integer,
	alpha As T,
	a As Array2D(Of T),
	x As ArraySlice(Of T),
	beta As T,
	y As ArraySlice(Of T)
)

public:
void MultiplyAndAddInPlace(
	TransposeOperation trans, 
	int m, 
	int n, 
	T alpha, 
	Array2D<T> a, 
	ArraySlice<T> x, 
	T beta, 
	ArraySlice<T> y
)

member MultiplyAndAddInPlace : 
        trans : TransposeOperation * 
        m : int * 
        n : int * 
        alpha : 'T * 
        a : Array2D<'T> * 
        x : ArraySlice<'T> * 
        beta : 'T * 
        y : ArraySlice<'T> -> unit 

Parameters

trans  TransposeOperation

             On entry, TRANS specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
                TRANS = 'T' or 't'   y := alpha*AT*x + beta*y.
                TRANS = 'C' or 'c'   y := alpha*AT*x + beta*y.
            

m  Int32

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

n  Int32

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

alpha  T

            ALPHA is DOUBLE PRECISION.
             On entry, ALPHA specifies the scalar alpha.
            

a  Array2D<T>

            A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
             Before entry, the leading m by n part of the array A must
             contain the matrix of coefficients.
            

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

x  ArraySlice<T>

            X is DOUBLE PRECISION array of DIMENSION at least
             ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
             Before entry, the incremented array X must contain the
             vector x.
            

             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.
            

beta  T

            BETA is DOUBLE PRECISION.
             On entry, BETA specifies the scalar beta. When BETA is
             supplied as zero then Y need not be set on input.
            

y  ArraySlice<T>

            Y is DOUBLE PRECISION array of DIMENSION at least
             ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
             Before entry with BETA non-zero, the incremented array Y
             must contain the vector y. On exit, Y is overwritten by the
             updated vector y.
            

             On entry, INCY specifies the increment for the elements of
             Y. INCY must not be zero.
            

 Further Details:
            Level 2 LinearAlgebra routine.
            The vector and matrix arguments are not referenced when N = 0, or M = 0
            -- Written on 22-October-1986.
               Jack Dongarra, Argonne National Lab.
               Jeremy Du Croz, Nag Central Office.
               Sven Hammarling, Nag Central Office.
               Richard Hanson, Sandia National Labs.
            
Authors: 
             Univ. of Tennessee,
             Univ. of California Berkeley,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

public void MultiplyAndAddInPlace(
	TransposeOperation trans,
	int m,
	int n,
	Complex<T> alpha,
	Array2D<Complex<T>> a,
	ArraySlice<Complex<T>> x,
	Complex<T> beta,
	ArraySlice<Complex<T>> y
)

Public Sub MultiplyAndAddInPlace ( 
	trans As TransposeOperation,
	m As Integer,
	n As Integer,
	alpha As Complex(Of T),
	a As Array2D(Of Complex(Of T)),
	x As ArraySlice(Of Complex(Of T)),
	beta As Complex(Of T),
	y As ArraySlice(Of Complex(Of T))
)

public:
void MultiplyAndAddInPlace(
	TransposeOperation trans, 
	int m, 
	int n, 
	Complex<T> alpha, 
	Array2D<Complex<T>> a, 
	ArraySlice<Complex<T>> x, 
	Complex<T> beta, 
	ArraySlice<Complex<T>> y
)

member MultiplyAndAddInPlace : 
        trans : TransposeOperation * 
        m : int * 
        n : int * 
        alpha : Complex<'T> * 
        a : Array2D<Complex<'T>> * 
        x : ArraySlice<Complex<'T>> * 
        beta : Complex<'T> * 
        y : ArraySlice<Complex<'T>> -> unit 

Parameters

trans  TransposeOperation

             On entry, TRANS specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
                TRANS = 'T' or 't'   y := alpha*AT*x + beta*y.
                TRANS = 'C' or 'c'   y := alpha*AH*x + beta*y.
            

m  Int32

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

n  Int32

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

alpha  Complex<T>

             On entry, ALPHA specifies the scalar alpha.
            

a  Array2D<Complex<T>>

            A is complex array of DIMENSION ( LDA, n ).
             Before entry, the leading m by n part of the array A must
             contain the matrix of coefficients.
            

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

x  ArraySlice<Complex<T>>

            X is complex array of DIMENSION at least
             ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
             Before entry, the incremented array X must contain the
             vector x.
            

             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.
            

beta  Complex<T>

             On entry, BETA specifies the scalar beta. When BETA is
             supplied as zero then Y need not be set on input.
            

y  ArraySlice<Complex<T>>

            Y is complex array of DIMENSION at least
             ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
             Before entry with BETA non-zero, the incremented array Y
             must contain the vector y. On exit, Y is overwritten by the
             updated vector y.
            

             On entry, INCY specifies the increment for the elements of
             Y. INCY must not be zero.
            

 Further Details:
            Level 2 LinearAlgebra routine.
            The vector and matrix arguments are not referenced when N = 0, or M = 0
            -- Written on 22-October-1986.
               Jack Dongarra, Argonne National Lab.
               Jeremy Du Croz, Nag Central Office.
               Sven Hammarling, Nag Central Office.
               Richard Hanson, Sandia National Labs.
            
Authors: 
             Univ. of Tennessee,
             Univ. of California Berkeley,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

public void MultiplyAndAddInPlace(
	TransposeOperation trans,
	int m,
	int n,
	Complex<T> alpha,
	ReadOnlySpan2D<Complex<T>> a,
	ReadOnlySpanSlice<Complex<T>> x,
	Complex<T> beta,
	SpanSlice<Complex<T>> y
)

Public Sub MultiplyAndAddInPlace ( 
	trans As TransposeOperation,
	m As Integer,
	n As Integer,
	alpha As Complex(Of T),
	a As ReadOnlySpan2D(Of Complex(Of T)),
	x As ReadOnlySpanSlice(Of Complex(Of T)),
	beta As Complex(Of T),
	y As SpanSlice(Of Complex(Of T))
)

public:
void MultiplyAndAddInPlace(
	TransposeOperation trans, 
	int m, 
	int n, 
	Complex<T> alpha, 
	ReadOnlySpan2D<Complex<T>> a, 
	ReadOnlySpanSlice<Complex<T>> x, 
	Complex<T> beta, 
	SpanSlice<Complex<T>> y
)

member MultiplyAndAddInPlace : 
        trans : TransposeOperation * 
        m : int * 
        n : int * 
        alpha : Complex<'T> * 
        a : ReadOnlySpan2D<Complex<'T>> * 
        x : ReadOnlySpanSlice<Complex<'T>> * 
        beta : Complex<'T> * 
        y : SpanSlice<Complex<'T>> -> unit 

Parameters

trans  TransposeOperation

             On entry, TRANS specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
                TRANS = 'T' or 't'   y := alpha*AT*x + beta*y.
                TRANS = 'C' or 'c'   y := alpha*AH*x + beta*y.
            

m  Int32

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

n  Int32

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

alpha  Complex<T>

             On entry, ALPHA specifies the scalar alpha.
            

a  ReadOnlySpan2D<Complex<T>>

            A is complex array of DIMENSION ( LDA, n ).
             Before entry, the leading m by n part of the array A must
             contain the matrix of coefficients.
            

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

x  ReadOnlySpanSlice<Complex<T>>

            X is complex array of DIMENSION at least
             ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
             Before entry, the incremented array X must contain the
             vector x.
            

             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.
            

beta  Complex<T>

             On entry, BETA specifies the scalar beta. When BETA is
             supplied as zero then Y need not be set on input.
            

y  SpanSlice<Complex<T>>

            Y is complex array of DIMENSION at least
             ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
             Before entry with BETA non-zero, the incremented array Y
             must contain the vector y. On exit, Y is overwritten by the
             updated vector y.
            

             On entry, INCY specifies the increment for the elements of
             Y. INCY must not be zero.
            

 Further Details:
            Level 2 LinearAlgebra routine.
            The vector and matrix arguments are not referenced when N = 0, or M = 0
            -- Written on 22-October-1986.
               Jack Dongarra, Argonne National Lab.
               Jeremy Du Croz, Nag Central Office.
               Sven Hammarling, Nag Central Office.
               Richard Hanson, Sandia National Labs.
            
Authors: 
             Univ. of Tennessee,
             Univ. of California Berkeley,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

public void MultiplyAndAddInPlace(
	TransposeOperation transa,
	TransposeOperation transb,
	int m,
	int n,
	int k,
	T alpha,
	Array2D<T> a,
	Array2D<T> b,
	T beta,
	Array2D<T> c
)

Public Sub MultiplyAndAddInPlace ( 
	transa As TransposeOperation,
	transb As TransposeOperation,
	m As Integer,
	n As Integer,
	k As Integer,
	alpha As T,
	a As Array2D(Of T),
	b As Array2D(Of T),
	beta As T,
	c As Array2D(Of T)
)

public:
void MultiplyAndAddInPlace(
	TransposeOperation transa, 
	TransposeOperation transb, 
	int m, 
	int n, 
	int k, 
	T alpha, 
	Array2D<T> a, 
	Array2D<T> b, 
	T beta, 
	Array2D<T> c
)

member MultiplyAndAddInPlace : 
        transa : TransposeOperation * 
        transb : TransposeOperation * 
        m : int * 
        n : int * 
        k : int * 
        alpha : 'T * 
        a : Array2D<'T> * 
        b : Array2D<'T> * 
        beta : 'T * 
        c : Array2D<'T> -> unit 

Parameters

transa  TransposeOperation

             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 ) = AT.
                TRANSA = 'C' or 'c',  op( A ) = AT.
            

transb  TransposeOperation

             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 ) = BT.
                TRANSB = 'C' or 'c',  op( B ) = BT.
            

m  Int32

             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  Int32

             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  Int32

             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  T

            ALPHA is DOUBLE PRECISION.
             On entry, ALPHA specifies the scalar alpha.
            

a  Array2D<T>

            A is DOUBLE PRECISION array of 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.
            

             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  Array2D<T>

            B is DOUBLE PRECISION array of 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.
            

             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  T

            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  Array2D<T>

            C is DOUBLE PRECISION array of 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 ).
            

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

 Further Details:
            Level 3 LinearAlgebra 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.
            
Authors: 
             Univ. of Tennessee,
             Univ. of California Berkeley,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

public void MultiplyAndAddInPlace(
	TransposeOperation transa,
	TransposeOperation transb,
	int m,
	int n,
	int k,
	Complex<T> alpha,
	Array2D<Complex<T>> a,
	Array2D<Complex<T>> b,
	Complex<T> beta,
	Array2D<Complex<T>> c
)

Public Sub MultiplyAndAddInPlace ( 
	transa As TransposeOperation,
	transb As TransposeOperation,
	m As Integer,
	n As Integer,
	k As Integer,
	alpha As Complex(Of T),
	a As Array2D(Of Complex(Of T)),
	b As Array2D(Of Complex(Of T)),
	beta As Complex(Of T),
	c As Array2D(Of Complex(Of T))
)

public:
void MultiplyAndAddInPlace(
	TransposeOperation transa, 
	TransposeOperation transb, 
	int m, 
	int n, 
	int k, 
	Complex<T> alpha, 
	Array2D<Complex<T>> a, 
	Array2D<Complex<T>> b, 
	Complex<T> beta, 
	Array2D<Complex<T>> c
)

member MultiplyAndAddInPlace : 
        transa : TransposeOperation * 
        transb : TransposeOperation * 
        m : int * 
        n : int * 
        k : int * 
        alpha : Complex<'T> * 
        a : Array2D<Complex<'T>> * 
        b : Array2D<Complex<'T>> * 
        beta : Complex<'T> * 
        c : Array2D<Complex<'T>> -> unit 

Parameters

transa  TransposeOperation

             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 ) = AT.
                TRANSA = 'C' or 'c',  op( A ) = AH.
            

transb  TransposeOperation

             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 ) = BT.
                TRANSB = 'C' or 'c',  op( B ) = BH.
            

m  Int32

             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  Int32

             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  Int32

             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  Complex<T>

             On entry, ALPHA specifies the scalar alpha.
            

a  Array2D<Complex<T>>

            A is complex array of 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.
            

             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  Array2D<Complex<T>>

            B is complex array of 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.
            

             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  Complex<T>

             On entry,  BETA  specifies the scalar  beta.  When  BETA  is
             supplied as zero then C need not be set on input.
            

c  Array2D<Complex<T>>

            C is complex array of 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 ).
            

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

 Further Details:
            Level 3 LinearAlgebra 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.
            
Authors: 
             Univ. of Tennessee,
             Univ. of California Berkeley,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

public void MultiplyAndAddInPlace(
	TransposeOperation transa,
	TransposeOperation transb,
	int m,
	int n,
	int k,
	Complex<T> alpha,
	ReadOnlySpan2D<Complex<T>> a,
	ReadOnlySpan2D<Complex<T>> b,
	Complex<T> beta,
	Span2D<Complex<T>> c
)

Public Sub MultiplyAndAddInPlace ( 
	transa As TransposeOperation,
	transb As TransposeOperation,
	m As Integer,
	n As Integer,
	k As Integer,
	alpha As Complex(Of T),
	a As ReadOnlySpan2D(Of Complex(Of T)),
	b As ReadOnlySpan2D(Of Complex(Of T)),
	beta As Complex(Of T),
	c As Span2D(Of Complex(Of T))
)

public:
void MultiplyAndAddInPlace(
	TransposeOperation transa, 
	TransposeOperation transb, 
	int m, 
	int n, 
	int k, 
	Complex<T> alpha, 
	ReadOnlySpan2D<Complex<T>> a, 
	ReadOnlySpan2D<Complex<T>> b, 
	Complex<T> beta, 
	Span2D<Complex<T>> c
)

member MultiplyAndAddInPlace : 
        transa : TransposeOperation * 
        transb : TransposeOperation * 
        m : int * 
        n : int * 
        k : int * 
        alpha : Complex<'T> * 
        a : ReadOnlySpan2D<Complex<'T>> * 
        b : ReadOnlySpan2D<Complex<'T>> * 
        beta : Complex<'T> * 
        c : Span2D<Complex<'T>> -> unit 

Parameters

transa  TransposeOperation

             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 ) = AT.
                TRANSA = 'C' or 'c',  op( A ) = AH.
            

transb  TransposeOperation

             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 ) = BT.
                TRANSB = 'C' or 'c',  op( B ) = BH.
            

m  Int32

             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  Int32

             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  Int32

             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  Complex<T>

             On entry, ALPHA specifies the scalar alpha.
            

a  ReadOnlySpan2D<Complex<T>>

            A is complex array of 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.
            

             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  ReadOnlySpan2D<Complex<T>>

            B is complex array of 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.
            

             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  Complex<T>

             On entry,  BETA  specifies the scalar  beta.  When  BETA  is
             supplied as zero then C need not be set on input.
            

c  Span2D<Complex<T>>

            C is complex array of 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 ).
            

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

 Further Details:
            Level 3 LinearAlgebra 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.
            
Authors: 
             Univ. of Tennessee,
             Univ. of California Berkeley,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

public abstract void MultiplyAndAddInPlace(
	TransposeOperation trans,
	int m,
	int n,
	T alpha,
	ReadOnlySpan<T> a,
	int lda,
	ReadOnlySpan<T> x,
	int incx,
	T beta,
	Span<T> y,
	int incy
)

Public MustOverride Sub MultiplyAndAddInPlace ( 
	trans As TransposeOperation,
	m As Integer,
	n As Integer,
	alpha As T,
	a As ReadOnlySpan(Of T),
	lda As Integer,
	x As ReadOnlySpan(Of T),
	incx As Integer,
	beta As T,
	y As Span(Of T),
	incy As Integer
)

public:
virtual void MultiplyAndAddInPlace(
	TransposeOperation trans, 
	int m, 
	int n, 
	T alpha, 
	ReadOnlySpan<T> a, 
	int lda, 
	ReadOnlySpan<T> x, 
	int incx, 
	T beta, 
	Span<T> y, 
	int incy
) abstract

abstract MultiplyAndAddInPlace : 
        trans : TransposeOperation * 
        m : int * 
        n : int * 
        alpha : 'T * 
        a : ReadOnlySpan<'T> * 
        lda : int * 
        x : ReadOnlySpan<'T> * 
        incx : int * 
        beta : 'T * 
        y : Span<'T> * 
        incy : int -> unit 

Parameters

trans  TransposeOperation

             On entry, TRANS specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
                TRANS = 'T' or 't'   y := alpha*AT*x + beta*y.
                TRANS = 'C' or 'c'   y := alpha*AT*x + beta*y.
            

m  Int32

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

n  Int32

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

alpha  T

            ALPHA is DOUBLE PRECISION.
             On entry, ALPHA specifies the scalar alpha.
            

a  ReadOnlySpan<T>

            A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
             Before entry, the leading m by n part of the array A must
             contain the matrix of coefficients.
            

lda  Int32

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

x  ReadOnlySpan<T>

            X is DOUBLE PRECISION array of DIMENSION at least
             ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
             Before entry, the incremented array X must contain the
             vector x.
            

incx  Int32

             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.
            

beta  T

            BETA is DOUBLE PRECISION.
             On entry, BETA specifies the scalar beta. When BETA is
             supplied as zero then Y need not be set on input.
            

y  Span<T>

            Y is DOUBLE PRECISION array of DIMENSION at least
             ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
             Before entry with BETA non-zero, the incremented array Y
             must contain the vector y. On exit, Y is overwritten by the
             updated vector y.
            

incy  Int32

             On entry, INCY specifies the increment for the elements of
             Y. INCY must not be zero.
            

Implements

 Further Details:
            Level 2 LinearAlgebra routine.
            The vector and matrix arguments are not referenced when N = 0, or M = 0
            -- Written on 22-October-1986.
               Jack Dongarra, Argonne National Lab.
               Jeremy Du Croz, Nag Central Office.
               Sven Hammarling, Nag Central Office.
               Richard Hanson, Sandia National Labs.
            
Authors: 
             Univ. of Tennessee,
             Univ. of California Berkeley,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

public abstract void MultiplyAndAddInPlace(
	TransposeOperation trans,
	int m,
	int n,
	Complex<T> alpha,
	ReadOnlySpan<Complex<T>> a,
	int lda,
	ReadOnlySpan<Complex<T>> x,
	int incx,
	Complex<T> beta,
	Span<Complex<T>> y,
	int incy
)

Public MustOverride Sub MultiplyAndAddInPlace ( 
	trans As TransposeOperation,
	m As Integer,
	n As Integer,
	alpha As Complex(Of T),
	a As ReadOnlySpan(Of Complex(Of T)),
	lda As Integer,
	x As ReadOnlySpan(Of Complex(Of T)),
	incx As Integer,
	beta As Complex(Of T),
	y As Span(Of Complex(Of T)),
	incy As Integer
)

public:
virtual void MultiplyAndAddInPlace(
	TransposeOperation trans, 
	int m, 
	int n, 
	Complex<T> alpha, 
	ReadOnlySpan<Complex<T>> a, 
	int lda, 
	ReadOnlySpan<Complex<T>> x, 
	int incx, 
	Complex<T> beta, 
	Span<Complex<T>> y, 
	int incy
) abstract

abstract MultiplyAndAddInPlace : 
        trans : TransposeOperation * 
        m : int * 
        n : int * 
        alpha : Complex<'T> * 
        a : ReadOnlySpan<Complex<'T>> * 
        lda : int * 
        x : ReadOnlySpan<Complex<'T>> * 
        incx : int * 
        beta : Complex<'T> * 
        y : Span<Complex<'T>> * 
        incy : int -> unit 

Parameters

trans  TransposeOperation

             On entry, TRANS specifies the operation to be performed as
             follows:
                TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
                TRANS = 'T' or 't'   y := alpha*AT*x + beta*y.
                TRANS = 'C' or 'c'   y := alpha*AH*x + beta*y.
            

m  Int32

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

n  Int32

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

alpha  Complex<T>

             On entry, ALPHA specifies the scalar alpha.
            

a  ReadOnlySpan<Complex<T>>

            A is complex array of DIMENSION ( LDA, n ).
             Before entry, the leading m by n part of the array A must
             contain the matrix of coefficients.
            

lda  Int32

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

x  ReadOnlySpan<Complex<T>>

            X is complex array of DIMENSION at least
             ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
             Before entry, the incremented array X must contain the
             vector x.
            

incx  Int32

             On entry, INCX specifies the increment for the elements of
             X. INCX must not be zero.
            

beta  Complex<T>

             On entry, BETA specifies the scalar beta. When BETA is
             supplied as zero then Y need not be set on input.
            

y  Span<Complex<T>>

            Y is complex array of DIMENSION at least
             ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
             and at least
             ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
             Before entry with BETA non-zero, the incremented array Y
             must contain the vector y. On exit, Y is overwritten by the
             updated vector y.
            

incy  Int32

             On entry, INCY specifies the increment for the elements of
             Y. INCY must not be zero.
            

Implements

 Further Details:
            Level 2 LinearAlgebra routine.
            The vector and matrix arguments are not referenced when N = 0, or M = 0
            -- Written on 22-October-1986.
               Jack Dongarra, Argonne National Lab.
               Jeremy Du Croz, Nag Central Office.
               Sven Hammarling, Nag Central Office.
               Richard Hanson, Sandia National Labs.
            
Authors: 
             Univ. of Tennessee,
             Univ. of California Berkeley,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

public abstract void MultiplyAndAddInPlace(
	TransposeOperation transa,
	TransposeOperation transb,
	int m,
	int n,
	int k,
	T alpha,
	ReadOnlySpan<T> a,
	int lda,
	ReadOnlySpan<T> b,
	int ldb,
	T beta,
	Span<T> c,
	int ldc
)

Public MustOverride Sub MultiplyAndAddInPlace ( 
	transa As TransposeOperation,
	transb As TransposeOperation,
	m As Integer,
	n As Integer,
	k As Integer,
	alpha As T,
	a As ReadOnlySpan(Of T),
	lda As Integer,
	b As ReadOnlySpan(Of T),
	ldb As Integer,
	beta As T,
	c As Span(Of T),
	ldc As Integer
)

public:
virtual void MultiplyAndAddInPlace(
	TransposeOperation transa, 
	TransposeOperation transb, 
	int m, 
	int n, 
	int k, 
	T alpha, 
	ReadOnlySpan<T> a, 
	int lda, 
	ReadOnlySpan<T> b, 
	int ldb, 
	T beta, 
	Span<T> c, 
	int ldc
) abstract

abstract MultiplyAndAddInPlace : 
        transa : TransposeOperation * 
        transb : TransposeOperation * 
        m : int * 
        n : int * 
        k : int * 
        alpha : 'T * 
        a : ReadOnlySpan<'T> * 
        lda : int * 
        b : ReadOnlySpan<'T> * 
        ldb : int * 
        beta : 'T * 
        c : Span<'T> * 
        ldc : int -> unit 

Parameters

transa  TransposeOperation

             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 ) = AT.
                TRANSA = 'C' or 'c',  op( A ) = AT.
            

transb  TransposeOperation

             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 ) = BT.
                TRANSB = 'C' or 'c',  op( B ) = BT.
            

m  Int32

             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  Int32

             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  Int32

             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  T

            ALPHA is DOUBLE PRECISION.
             On entry, ALPHA specifies the scalar alpha.
            

a  ReadOnlySpan<T>

            A is DOUBLE PRECISION array of 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  Int32

             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  ReadOnlySpan<T>

            B is DOUBLE PRECISION array of 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  Int32

             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  T

            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  Span<T>

            C is DOUBLE PRECISION array of 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  Int32

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

Implements

 Further Details:
            Level 3 LinearAlgebra 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.
            
Authors: 
             Univ. of Tennessee,
             Univ. of California Berkeley,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

public abstract void MultiplyAndAddInPlace(
	TransposeOperation transa,
	TransposeOperation transb,
	int m,
	int n,
	int k,
	Complex<T> alpha,
	ReadOnlySpan<Complex<T>> a,
	int lda,
	ReadOnlySpan<Complex<T>> b,
	int ldb,
	Complex<T> beta,
	Span<Complex<T>> c,
	int ldc
)

Public MustOverride Sub MultiplyAndAddInPlace ( 
	transa As TransposeOperation,
	transb As TransposeOperation,
	m As Integer,
	n As Integer,
	k As Integer,
	alpha As Complex(Of T),
	a As ReadOnlySpan(Of Complex(Of T)),
	lda As Integer,
	b As ReadOnlySpan(Of Complex(Of T)),
	ldb As Integer,
	beta As Complex(Of T),
	c As Span(Of Complex(Of T)),
	ldc As Integer
)

public:
virtual void MultiplyAndAddInPlace(
	TransposeOperation transa, 
	TransposeOperation transb, 
	int m, 
	int n, 
	int k, 
	Complex<T> alpha, 
	ReadOnlySpan<Complex<T>> a, 
	int lda, 
	ReadOnlySpan<Complex<T>> b, 
	int ldb, 
	Complex<T> beta, 
	Span<Complex<T>> c, 
	int ldc
) abstract

abstract MultiplyAndAddInPlace : 
        transa : TransposeOperation * 
        transb : TransposeOperation * 
        m : int * 
        n : int * 
        k : int * 
        alpha : Complex<'T> * 
        a : ReadOnlySpan<Complex<'T>> * 
        lda : int * 
        b : ReadOnlySpan<Complex<'T>> * 
        ldb : int * 
        beta : Complex<'T> * 
        c : Span<Complex<'T>> * 
        ldc : int -> unit 

Parameters

transa  TransposeOperation

             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 ) = AT.
                TRANSA = 'C' or 'c',  op( A ) = AH.
            

transb  TransposeOperation

             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 ) = BT.
                TRANSB = 'C' or 'c',  op( B ) = BH.
            

m  Int32

             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  Int32

             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  Int32

             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  Complex<T>

             On entry, ALPHA specifies the scalar alpha.
            

a  ReadOnlySpan<Complex<T>>

            A is complex array of 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  Int32

             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  ReadOnlySpan<Complex<T>>

            B is complex array of 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  Int32

             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  Complex<T>

             On entry,  BETA  specifies the scalar  beta.  When  BETA  is
             supplied as zero then C need not be set on input.
            

c  Span<Complex<T>>

            C is complex array of 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  Int32

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

Implements

 Further Details:
            Level 3 LinearAlgebra 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.
            
Authors: 
             Univ. of Tennessee,
             Univ. of California Berkeley,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

Reference