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---
:name: dormhr
:md5sum: 1aa88be0d6f9f382347ae47d367d3cfc
:category: :subroutine
:arguments:
- side:
:type: char
:intent: input
- trans:
:type: char
:intent: input
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- ilo:
:type: integer
:intent: input
- ihi:
:type: integer
:intent: input
- a:
:type: doublereal
:intent: input
:dims:
- lda
- m
- lda:
:type: integer
:intent: input
- tau:
:type: doublereal
:intent: input
:dims:
- m-1
- c:
:type: doublereal
:intent: input/output
:dims:
- ldc
- n
- ldc:
:type: integer
:intent: input
- work:
:type: doublereal
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: "lsame_(&side,\"L\") ? n : lsame_(&side,\"R\") ? m : 0"
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DORMHR overwrites the general real M-by-N matrix C with\n\
*\n\
* SIDE = 'L' SIDE = 'R'\n\
* TRANS = 'N': Q * C C * Q\n\
* TRANS = 'T': Q**T * C C * Q**T\n\
*\n\
* where Q is a real orthogonal matrix of order nq, with nq = m if\n\
* SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of\n\
* IHI-ILO elementary reflectors, as returned by DGEHRD:\n\
*\n\
* Q = H(ilo) H(ilo+1) . . . H(ihi-1).\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* SIDE (input) CHARACTER*1\n\
* = 'L': apply Q or Q**T from the Left;\n\
* = 'R': apply Q or Q**T from the Right.\n\
*\n\
* TRANS (input) CHARACTER*1\n\
* = 'N': No transpose, apply Q;\n\
* = 'T': Transpose, apply Q**T.\n\
*\n\
* M (input) INTEGER\n\
* The number of rows of the matrix C. M >= 0.\n\
*\n\
* N (input) INTEGER\n\
* The number of columns of the matrix C. N >= 0.\n\
*\n\
* ILO (input) INTEGER\n\
* IHI (input) INTEGER\n\
* ILO and IHI must have the same values as in the previous call\n\
* of DGEHRD. Q is equal to the unit matrix except in the\n\
* submatrix Q(ilo+1:ihi,ilo+1:ihi).\n\
* If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and\n\
* ILO = 1 and IHI = 0, if M = 0;\n\
* if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and\n\
* ILO = 1 and IHI = 0, if N = 0.\n\
*\n\
* A (input) DOUBLE PRECISION array, dimension\n\
* (LDA,M) if SIDE = 'L'\n\
* (LDA,N) if SIDE = 'R'\n\
* The vectors which define the elementary reflectors, as\n\
* returned by DGEHRD.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A.\n\
* LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.\n\
*\n\
* TAU (input) DOUBLE PRECISION array, dimension\n\
* (M-1) if SIDE = 'L'\n\
* (N-1) if SIDE = 'R'\n\
* TAU(i) must contain the scalar factor of the elementary\n\
* reflector H(i), as returned by DGEHRD.\n\
*\n\
* C (input/output) DOUBLE PRECISION array, dimension (LDC,N)\n\
* On entry, the M-by-N matrix C.\n\
* On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.\n\
*\n\
* LDC (input) INTEGER\n\
* The leading dimension of the array C. LDC >= max(1,M).\n\
*\n\
* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))\n\
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n\
*\n\
* LWORK (input) INTEGER\n\
* The dimension of the array WORK.\n\
* If SIDE = 'L', LWORK >= max(1,N);\n\
* if SIDE = 'R', LWORK >= max(1,M).\n\
* For optimum performance LWORK >= N*NB if SIDE = 'L', and\n\
* LWORK >= M*NB if SIDE = 'R', where NB is the optimal\n\
* blocksize.\n\
*\n\
* If LWORK = -1, then a workspace query is assumed; the routine\n\
* only calculates the optimal size of the WORK array, returns\n\
* this value as the first entry of the WORK array, and no error\n\
* message related to LWORK is issued by XERBLA.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
*\n\n\
* =====================================================================\n\
*\n\
* .. Local Scalars ..\n LOGICAL LEFT, LQUERY\n INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NH, NI, NQ, NW\n\
* ..\n\
* .. External Functions ..\n LOGICAL LSAME\n INTEGER ILAENV\n EXTERNAL LSAME, ILAENV\n\
* ..\n\
* .. External Subroutines ..\n EXTERNAL DORMQR, XERBLA\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC MAX, MIN\n\
* ..\n"
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