NAME

upmtr - {up,op}mtr: multiply by Q from hptrd

SYNOPSIS

Functions

subroutine cupmtr (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)
CUPMTR subroutine dopmtr (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)
DOPMTR subroutine sopmtr (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)
SOPMTR subroutine zupmtr (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)
ZUPMTR

Detailed Description

Function Documentation

subroutine cupmtr (character side, character uplo, character trans, integer m, integer n, complex, dimension( * ) ap, complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer info)

CUPMTR

Purpose:



 CUPMTR overwrites the general complex M-by-N matrix C with


                 SIDE = 'L'     SIDE = 'R'


 TRANS = 'N':      Q * C          C * Q


 TRANS = 'C':      Q**H * C       C * Q**H


 where Q is a complex unitary matrix of order nq, with nq = m if


 SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of


 nq-1 elementary reflectors, as returned by CHPTRD using packed


 storage:


 if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);


 if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).

Parameters

SIDE



          SIDE is CHARACTER*1


          = 'L': apply Q or Q**H from the Left;


          = 'R': apply Q or Q**H from the Right.

UPLO



          UPLO is CHARACTER*1


          = 'U': Upper triangular packed storage used in previous


                 call to CHPTRD;


          = 'L': Lower triangular packed storage used in previous


                 call to CHPTRD.

TRANS



          TRANS is CHARACTER*1


          = 'N':  No transpose, apply Q;


          = 'C':  Conjugate transpose, apply Q**H.



          M is INTEGER


          The number of rows of the matrix C. M >= 0.



          N is INTEGER


          The number of columns of the matrix C. N >= 0.



          AP is COMPLEX array, dimension


                               (M*(M+1)/2) if SIDE = 'L'


                               (N*(N+1)/2) if SIDE = 'R'


          The vectors which define the elementary reflectors, as


          returned by CHPTRD.  AP is modified by the routine but


          restored on exit.

TAU



          TAU is COMPLEX array, dimension (M-1) if SIDE = 'L'


                                     or (N-1) if SIDE = 'R'


          TAU(i) must contain the scalar factor of the elementary


          reflector H(i), as returned by CHPTRD.



          C is COMPLEX array, dimension (LDC,N)


          On entry, the M-by-N matrix C.


          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.

LDC



          LDC is INTEGER


          The leading dimension of the array C. LDC >= max(1,M).

WORK



          WORK is COMPLEX array, dimension


                                   (N) if SIDE = 'L'


                                   (M) if SIDE = 'R'

INFO



          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 148 of file cupmtr.f.

subroutine dopmtr (character side, character uplo, character trans, integer m, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer info)

DOPMTR

Purpose:



 DOPMTR overwrites the general real M-by-N matrix C with


                 SIDE = 'L'     SIDE = 'R'


 TRANS = 'N':      Q * C          C * Q


 TRANS = 'T':      Q**T * C       C * Q**T


 where Q is a real orthogonal matrix of order nq, with nq = m if


 SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of


 nq-1 elementary reflectors, as returned by DSPTRD using packed


 storage:


 if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);


 if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).

Parameters

SIDE



          SIDE is CHARACTER*1


          = 'L': apply Q or Q**T from the Left;


          = 'R': apply Q or Q**T from the Right.

UPLO



          UPLO is CHARACTER*1


          = 'U': Upper triangular packed storage used in previous


                 call to DSPTRD;


          = 'L': Lower triangular packed storage used in previous


                 call to DSPTRD.

TRANS



          TRANS is CHARACTER*1


          = 'N':  No transpose, apply Q;


          = 'T':  Transpose, apply Q**T.



          M is INTEGER


          The number of rows of the matrix C. M >= 0.



          N is INTEGER


          The number of columns of the matrix C. N >= 0.



          AP is DOUBLE PRECISION array, dimension


                               (M*(M+1)/2) if SIDE = 'L'


                               (N*(N+1)/2) if SIDE = 'R'


          The vectors which define the elementary reflectors, as


          returned by DSPTRD.  AP is modified by the routine but


          restored on exit.

TAU



          TAU is DOUBLE PRECISION array, dimension (M-1) if SIDE = 'L'


                                     or (N-1) if SIDE = 'R'


          TAU(i) must contain the scalar factor of the elementary


          reflector H(i), as returned by DSPTRD.



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


          On entry, the M-by-N matrix C.


          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

LDC



          LDC is INTEGER


          The leading dimension of the array C. LDC >= max(1,M).

WORK



          WORK is DOUBLE PRECISION array, dimension


                                   (N) if SIDE = 'L'


                                   (M) if SIDE = 'R'

INFO



          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 148 of file dopmtr.f.

subroutine sopmtr (character side, character uplo, character trans, integer m, integer n, real, dimension( * ) ap, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer info)

SOPMTR

Purpose:



 SOPMTR overwrites the general real M-by-N matrix C with


                 SIDE = 'L'     SIDE = 'R'


 TRANS = 'N':      Q * C          C * Q


 TRANS = 'T':      Q**T * C       C * Q**T


 where Q is a real orthogonal matrix of order nq, with nq = m if


 SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of


 nq-1 elementary reflectors, as returned by SSPTRD using packed


 storage:


 if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);


 if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).

Parameters

SIDE



          SIDE is CHARACTER*1


          = 'L': apply Q or Q**T from the Left;


          = 'R': apply Q or Q**T from the Right.

UPLO



          UPLO is CHARACTER*1


          = 'U': Upper triangular packed storage used in previous


                 call to SSPTRD;


          = 'L': Lower triangular packed storage used in previous


                 call to SSPTRD.

TRANS



          TRANS is CHARACTER*1


          = 'N':  No transpose, apply Q;


          = 'T':  Transpose, apply Q**T.



          M is INTEGER


          The number of rows of the matrix C. M >= 0.



          N is INTEGER


          The number of columns of the matrix C. N >= 0.



          AP is REAL array, dimension


                               (M*(M+1)/2) if SIDE = 'L'


                               (N*(N+1)/2) if SIDE = 'R'


          The vectors which define the elementary reflectors, as


          returned by SSPTRD.  AP is modified by the routine but


          restored on exit.

TAU



          TAU is REAL array, dimension (M-1) if SIDE = 'L'


                                     or (N-1) if SIDE = 'R'


          TAU(i) must contain the scalar factor of the elementary


          reflector H(i), as returned by SSPTRD.



          C is REAL array, dimension (LDC,N)


          On entry, the M-by-N matrix C.


          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

LDC



          LDC is INTEGER


          The leading dimension of the array C. LDC >= max(1,M).

WORK



          WORK is REAL array, dimension


                                   (N) if SIDE = 'L'


                                   (M) if SIDE = 'R'

INFO



          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 148 of file sopmtr.f.

subroutine zupmtr (character side, character uplo, character trans, integer m, integer n, complex16, dimension( ) ap, complex16, dimension( ) tau, complex16, dimension( ldc, ) c, integer ldc, complex16, dimension( ) work, integer info)

ZUPMTR

Purpose:



 ZUPMTR overwrites the general complex M-by-N matrix C with


                 SIDE = 'L'     SIDE = 'R'


 TRANS = 'N':      Q * C          C * Q


 TRANS = 'C':      Q**H * C       C * Q**H


 where Q is a complex unitary matrix of order nq, with nq = m if


 SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of


 nq-1 elementary reflectors, as returned by ZHPTRD using packed


 storage:


 if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);


 if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).

Parameters

SIDE



          SIDE is CHARACTER*1


          = 'L': apply Q or Q**H from the Left;


          = 'R': apply Q or Q**H from the Right.

UPLO



          UPLO is CHARACTER*1


          = 'U': Upper triangular packed storage used in previous


                 call to ZHPTRD;


          = 'L': Lower triangular packed storage used in previous


                 call to ZHPTRD.

TRANS



          TRANS is CHARACTER*1


          = 'N':  No transpose, apply Q;


          = 'C':  Conjugate transpose, apply Q**H.



          M is INTEGER


          The number of rows of the matrix C. M >= 0.



          N is INTEGER


          The number of columns of the matrix C. N >= 0.



          AP is COMPLEX*16 array, dimension


                               (M*(M+1)/2) if SIDE = 'L'


                               (N*(N+1)/2) if SIDE = 'R'


          The vectors which define the elementary reflectors, as


          returned by ZHPTRD.  AP is modified by the routine but


          restored on exit.

TAU



          TAU is COMPLEX*16 array, dimension (M-1) if SIDE = 'L'


                                     or (N-1) if SIDE = 'R'


          TAU(i) must contain the scalar factor of the elementary


          reflector H(i), as returned by ZHPTRD.



          C is COMPLEX*16 array, dimension (LDC,N)


          On entry, the M-by-N matrix C.


          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.

LDC



          LDC is INTEGER


          The leading dimension of the array C. LDC >= max(1,M).

WORK



          WORK is COMPLEX*16 array, dimension


                                   (N) if SIDE = 'L'


                                   (M) if SIDE = 'R'

INFO



          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 148 of file zupmtr.f.

Author

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